diff --git a/doc/Programs/SVD/Fortran/fit.x b/doc/Programs/SVD/Fortran/fit.x new file mode 100755 index 000000000..294c40df3 Binary files /dev/null and b/doc/Programs/SVD/Fortran/fit.x differ diff --git a/doc/Programs/SVD/Fortran/out b/doc/Programs/SVD/Fortran/out new file mode 100644 index 000000000..238eb3844 --- /dev/null +++ b/doc/Programs/SVD/Fortran/out @@ -0,0 +1,5 @@ + Quality of fit: + Number of terms in polynomial expansion: 7 +CHISQ = 2.99542 + Extrapolated energy with error + -2.8898506204392826 Infinity diff --git a/doc/Programs/SVD/Fortran/simplefit.dat b/doc/Programs/SVD/Fortran/simplefit.dat index 2ed9a6136..1d1d96d8e 100755 --- a/doc/Programs/SVD/Fortran/simplefit.dat +++ b/doc/Programs/SVD/Fortran/simplefit.dat @@ -1,4 +1,4 @@ -8 3 +8 7 0.001 -2.89017 0.00073621 0.002 -2.88946 0.00052732 0.005 -2.89067 0.00055038 diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs000.html b/doc/pub/NeuralNet/html/._NeuralNet-bs000.html index 9644c2e5a..d01faf980 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs000.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs000.html @@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source Data Analysis and Machine Learning: Elements of machine learning - + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Types of Machine Learning

+ +

+The approaches to machine learning are many, but are often split into two main categories. +In supervised learning we know the answer to a problem, +and let the computer deduce the logic behind it. On the other hand, unsupervised learning +is a method for finding patterns and relationship in data sets without any prior knowledge of the system. +Some authours also operate with a third category, namely reinforcement learning. This is a paradigm +of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, +solely from rewards and punishment. + +

+Another way to categorize machine learning tasks is to consider the desired output of a system. +Some of the most common tasks are: + +

+ +

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs003.html b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html new file mode 100644 index 000000000..7126463dc --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html @@ -0,0 +1,188 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Artificial neurons

+The field of artificial neural networks has a long history of development, and is closely connected with +the advancement of computer science and computers in general. A model of artificial neurons +was first developed by McCulloch and Pitts in 1943 to study signal processing in the brain and +has later been refined by others. The general idea is to mimic neural networks in the human brain, which +is composed of billions of neurons that communicate with each other by sending electrical signals. +Each neuron accumulates its incoming signals, +which must exceed an activation threshold to yield an output. If the threshold is not overcome, the neuron +remains inactive, i.e. has zero output. + +

+This behaviour has inspired a simple mathematical model for an artificial neuron. + +$$ +\begin{equation} + y = f\left(\sum_{i=1}^n w_ix_i\right) = f(u) +\tag{1} +\end{equation} +$$ + +Here, the output \( y \) of the neuron is the value of its activation function, which have as input +a weighted sum of signals \( x_i, \dots ,x_n \) received by \( n \) other neurons. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs004.html b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html new file mode 100644 index 000000000..2d4cbb22b --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html @@ -0,0 +1,175 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Neural network types

+ +

+An artificial neural network (NN), is a computational model that consists of layers of connected neurons, or nodes. +It is supposed to mimic a biological nervous system by letting each neuron interact with other neurons +by sending signals in the form of mathematical functions between layers. +A wide variety of different NNs have +been developed, but most of them consist of an input layer, an output layer and eventual layers in-between, called +hidden layers. All layers can contain an arbitrary number of nodes, and each connection between two nodes +is associated with a weight variable. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs005.html b/doc/pub/NeuralNet/html/._NeuralNet-bs005.html new file mode 100644 index 000000000..2377ef139 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs005.html @@ -0,0 +1,190 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Feed-forward neural networks

+The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, +the information moves in only one direction: forward through the layers. + +

+Nodes are represented by circles, while the arrows display the connections between the nodes, including the +direction of information flow. Additionally, each arrow corresponds to a weight variable, not displayed here. +We observe that each node in a layer is connected to all nodes in the subsequent layer, +making this a so-called fully-connected FFNN. + +

+A different variant of FFNNs are convolutional neural networks (CNNs), which have a connectivity pattern +inspired by the animal visual cortex. Individual neurons in the visual cortex only respond to stimuli from +small sub-regions of the visual field, called a receptive field. This makes the neurons well-suited to exploit the strong +spatially local correlation present in natural images. The response of each neuron can be approximated mathematically +as a convolution operation. + +

+CNNs emulate the behaviour of neurons in the visual cortex by enforcing a local connectivity pattern +between nodes of adjacent layers: Each node +in a convolutional layer is connected only to a subset of the nodes in the previous layer, +in contrast to the fully-connected FFNN. +Often, CNNs +consist of several convolutional layers that learn local features of the input, with a fully-connected layer at the end, +which gathers all the local data and produces the outputs. They have wide applications in image and video recognition + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs006.html b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html new file mode 100644 index 000000000..bbd2ff0fd --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html @@ -0,0 +1,174 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Recurrent neural networks

+ +

+So far we have only mentioned NNs where information flows in one direction: forward. Recurrent neural networks on +the other hand, have connections between nodes that form directed cycles. This creates a form of +internal memory which are able to capture information on what has been calculated before; the output is dependent +on the previous computations. Recurrent NNs make use of sequential information by performing the same task for +every element in a sequence, where each element depends on previous elements. An example of such information is +sentences, making recurrent NNs especially well-suited for handwriting and speech recognition. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs007.html b/doc/pub/NeuralNet/html/._NeuralNet-bs007.html new file mode 100644 index 000000000..6fc8d5f9a --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs007.html @@ -0,0 +1,178 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Other types of networks

+ +

+There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation +in multidimensional space is the radial basis function (RBF) network. RBFs are typically made up of three layers: +an input layer, a hidden layer with non-linear radial symmetric activation functions and a linear output layer (''linear'' here +means that each node in the output layer has a linear activation function). The layers are normally fully-connected and +there are no cycles, thus RBFs can be viewed as a type of fully-connected FFNN. They are however usually treated as +a separate type of NN due the unusual activation functions. + +

+Other types of NNs could also be mentioned, but are outside the scope of this work. We will now move on to a detailed description +of how a fully-connected FFNN works, and how it can be used to interpolate data sets. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs008.html b/doc/pub/NeuralNet/html/._NeuralNet-bs008.html new file mode 100644 index 000000000..0145387c7 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs008.html @@ -0,0 +1,177 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Mathematical model

+ +$$ +\begin{equation} + y = f\left(\sum_{i=1}^n w_ix_i + b_i\right) = f(u) +\tag{2} +\end{equation} +$$ + +In an FFNN of such neurons, the inputs \( x_i \) +are the outputs of the neurons in the preceding layer. Furthermore, a MLP is fully-connected, +which means that each neuron receives a weighted sum of the outputs of all neurons in the previous layer. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs009.html b/doc/pub/NeuralNet/html/._NeuralNet-bs009.html new file mode 100644 index 000000000..34a1eebc1 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs009.html @@ -0,0 +1,198 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Mathematical model

+ +

+First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \), + +$$ +\begin{equation} + u_i^1 = \sum_{j=1}^2 w_{ij}^1 x_j + b_i^1 +\tag{3} +\end{equation} +$$ + +This value is the argument to the activation function \( f_1 \) of each neuron \( i \), +producing the output \( y_i^1 \) of all neurons in layer 1, + +$$ +\begin{equation} + y_i^1 = f_1(u_i^1) = f_1\left(\sum_{j=1}^2 w_{ij}^1 x_j + b_i^1\right) +\tag{4} +\end{equation} +$$ + +where we assume that all nodes in the same layer have identical activation functions, hence the notation \( f_l \) + +$$ +\begin{equation} + y_i^l = f_l(u_i^l) = f_l\left(\sum_{j=1}^{N_{l-1}} w_{ij}^l y_j^{l-1} + b_i^l\right) +\tag{5} +\end{equation} +$$ + +where \( N_l \) is the number of nodes in layer \( l \). When the output of all the nodes in the first hidden layer are computed, +the values of the subsequent layer can be calculated and so forth until the output is obtained. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs010.html b/doc/pub/NeuralNet/html/._NeuralNet-bs010.html new file mode 100644 index 000000000..adb0065c3 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs010.html @@ -0,0 +1,190 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Mathematical model

+ +

+The output of neuron \( i \) in layer 2 is thus, + +$$ +\begin{align} + y_i^2 &= f_2\left(\sum_{j=1}^3 w_{ij}^2 y_j^1 + b_i^2\right) +\tag{6}\\ + &= f_2\left[\sum_{j=1}^3 w_{ij}^2f_1\left(\sum_{k=1}^2 w_{jk}^1 x_k + b_j^1\right) + b_i^2\right] +\tag{7} +\end{align} +$$ + +where we have substituted \( y_m^1 \) with. Finally, the NN output yields, + +$$ +\begin{align} + y_1^3 &= f_3\left(\sum_{j=1}^3 w_{1m}^3 y_j^2 + b_1^3\right) +\tag{8}\\ + &= f_3\left[\sum_{j=1}^3 w_{1j}^3 f_2\left(\sum_{k=1}^3 w_{jk}^2 f_1\left(\sum_{m=1}^2 w_{km}^1 x_m + b_k^1\right) + b_j^2\right) + + b_1^3\right] +\tag{9} +\end{align} +$$ + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs011.html b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html new file mode 100644 index 000000000..3523b4833 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html @@ -0,0 +1,180 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Mathematical model

+ +

+We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form +is, +$$ +\begin{align} +&y^{l+1}_1\! = \!f_{l+1}\!\left[\!\sum_{j=1}^{N_l}\! w_{1j}^3 f_l\!\left(\!\sum_{k=1}^{N_{l-1}}\! w_{jk}^2 f_{l-1}\!\left(\! + \dots \!f_1\!\left(\!\sum_{n=1}^{N_0} \!w_{mn}^1 x_n\! + \!b_m^1\!\right) + \!\dots \!\right) \!+ \!b_k^2\!\right) + \!+ \!b_1^3\!\right] && +\tag{10} +\end{align} +$$ + +which illustrates a basic property of MLPs: The only independent variables are the input values \( x_n \). + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs012.html b/doc/pub/NeuralNet/html/._NeuralNet-bs012.html new file mode 100644 index 000000000..8a028540a --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs012.html @@ -0,0 +1,193 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Mathematical model

+ +

+This confirms that an MLP, +despite its quite convoluted mathematical form, is nothing more than an analytic function, specifically a +mapping of real-valued vectors \( \vec{x} \in \mathbb{R}^n \rightarrow \vec{y} \in \mathbb{R}^m \). +In our example, \( n=2 \) and \( m=1 \). Consequentially, +the number of input and output values of the function we want to fit must be equal to the number of inputs and outputs of our MLP. + +

+Furthermore, the flexibility and universality of a MLP can be illustrated by realizing that +the expression is essentially a nested sum of scaled activation functions of the form + +$$ +\begin{equation} + h(x) = c_1 f(c_2 x + c_3) + c_4 +\tag{11} +\end{equation} +$$ + +where the parameters \( c_i \) are weights and biases. By adjusting these parameters, the activation functions +can be shifted up and down or left and right, change slope or be rescaled +which is the key to the flexibility of a NN. + +$$ +\begin{equation} + f_o = f(u_o) = u_o +\tag{12} +\end{equation} +$$ + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs013.html b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html new file mode 100644 index 000000000..a1e542a34 --- /dev/null +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html @@ -0,0 +1,213 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of machine learning + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Data Analysis and Machine Learning: Elements of machine learning +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Matrix-vector notation

+ +We can introduce a more convenient notation for the activations in a NN. + +

+Additionally, we can represent the biases and activations +as layer-wise column vectors \( \vec{b}_l \) and \( \vec{y}_l \), so that the \( i \)-th element of each vector +is the bias \( b_i^l \) and activation \( y_i^l \) of node \( i \) in layer \( l \) respectively. + +

+We have that \( \mathrm{W}_l \) is a \( N_{l-1} \times N_l \) matrix, while \( \vec{b}_l \) and \( \vec{y}_l \) are \( N_l \times 1 \) column vectors. +With this notation, the sum in becomes a matrix-vector multiplication, and we can write +the equation for the activations of hidden layer 2 in + +$$ +\begin{equation} + \vec{y}_2 = f_2(\mathrm{W}_2 \vec{y}_{1} + \vec{b}_{2}) = + f_2\left(\left[\begin{array}{ccc} + w^2_{11} &w^2_{12} &w^2_{13} \\ + w^2_{21} &w^2_{22} &w^2_{23} \\ + w^2_{31} &w^2_{32} &w^2_{33} \\ + \end{array} \right] \cdot + \left[\begin{array}{c} + y^1_1 \\ + y^1_2 \\ + y^1_3 \\ + \end{array}\right] + + \left[\begin{array}{c} + b^2_1 \\ + b^2_2 \\ + b^2_3 \\ + \end{array}\right]\right) +\tag{13} +\end{equation} +$$ + +and we see that the activation of node \( i \) in layer 2 is + +$$ +\begin{equation} + y^2_i = f_2\Bigr(w^2_{i1}y^1_1 + w^2_{i2}y^1_2 + w^2_{i3}y^1_3 + b^2_i\Bigr) = + f_2\left(\sum_{j=1}^3 w^2_{ij} y_j^1 + b^2_i\right) +\tag{14} +\end{equation} +$$ + +which is in accordance with. Note that +This is not just a convenient and compact notation, but also +a useful and intuitive way to think about MLPs: The output is calculated by a series of matrix-vector multiplications +and vector additions that are used as input to the activation functions. For each operation +\( \mathrm{W}_l \vec{y}_{l-1} \) we move forward one layer. + +

+ +

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/NeuralNet/html/NeuralNet-bs.html b/doc/pub/NeuralNet/html/NeuralNet-bs.html index 9644c2e5a..d01faf980 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-bs.html +++ b/doc/pub/NeuralNet/html/NeuralNet-bs.html @@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source Data Analysis and Machine Learning: Elements of machine learning - + @@ -59,11 +33,40 @@ div { text-align: justify; text-justify: inter-word; } + + + + + + + @@ -85,19 +88,339 @@ end of tocinfo -->
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Sep 20, 2017

+

Nov 2, 2017












-

Introduction

-
- +

What is Machine Learning?

+

+Machine learning is the science of giving computers the ability to learn without being explicitly programmed. +The idea is that there exist generic algorithms which can be used to find patterns in a broad class of data sets without +having to write code specifically for each problem. The algorithm will build its own logic based on the data. +

+Machine learning is a subfield of computer science, and is closely related to computational statistics. +It evolved from the study of pattern recognition in artificial intelligence (AI) research, and has made contributions to +AI tasks like computer vision, natural language processing +and speech recognition. It has also, especially in later years, +found applications in a wide variety of other areas, including bioinformatics, economy, physics, finance and marketing. -

+

+









+

Types of Machine Learning

+ +

+The approaches to machine learning are many, but are often split into two main categories. +In supervised learning we know the answer to a problem, +and let the computer deduce the logic behind it. On the other hand, unsupervised learning +is a method for finding patterns and relationship in data sets without any prior knowledge of the system. +Some authours also operate with a third category, namely reinforcement learning. This is a paradigm +of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, +solely from rewards and punishment. + +

+Another way to categorize machine learning tasks is to consider the desired output of a system. +Some of the most common tasks are: + +

+ +









+ +

Artificial neurons

+The field of artificial neural networks has a long history of development, and is closely connected with +the advancement of computer science and computers in general. A model of artificial neurons +was first developed by McCulloch and Pitts in 1943 to study signal processing in the brain and +has later been refined by others. The general idea is to mimic neural networks in the human brain, which +is composed of billions of neurons that communicate with each other by sending electrical signals. +Each neuron accumulates its incoming signals, +which must exceed an activation threshold to yield an output. If the threshold is not overcome, the neuron +remains inactive, i.e. has zero output. + +

+This behaviour has inspired a simple mathematical model for an artificial neuron. + +$$ +\begin{equation} + y = f\left(\sum_{i=1}^n w_ix_i\right) = f(u) +\label{artificialNeuron} +\end{equation} +$$ + +Here, the output \( y \) of the neuron is the value of its activation function, which have as input +a weighted sum of signals \( x_i, \dots ,x_n \) received by \( n \) other neurons. + +

+









+ +

Neural network types

+ +

+An artificial neural network (NN), is a computational model that consists of layers of connected neurons, or nodes. +It is supposed to mimic a biological nervous system by letting each neuron interact with other neurons +by sending signals in the form of mathematical functions between layers. +A wide variety of different NNs have +been developed, but most of them consist of an input layer, an output layer and eventual layers in-between, called +hidden layers. All layers can contain an arbitrary number of nodes, and each connection between two nodes +is associated with a weight variable. + +

+









+ +

Feed-forward neural networks

+The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, +the information moves in only one direction: forward through the layers. + +

+Nodes are represented by circles, while the arrows display the connections between the nodes, including the +direction of information flow. Additionally, each arrow corresponds to a weight variable, not displayed here. +We observe that each node in a layer is connected to all nodes in the subsequent layer, +making this a so-called fully-connected FFNN. + +

+A different variant of FFNNs are convolutional neural networks (CNNs), which have a connectivity pattern +inspired by the animal visual cortex. Individual neurons in the visual cortex only respond to stimuli from +small sub-regions of the visual field, called a receptive field. This makes the neurons well-suited to exploit the strong +spatially local correlation present in natural images. The response of each neuron can be approximated mathematically +as a convolution operation. + +

+CNNs emulate the behaviour of neurons in the visual cortex by enforcing a local connectivity pattern +between nodes of adjacent layers: Each node +in a convolutional layer is connected only to a subset of the nodes in the previous layer, +in contrast to the fully-connected FFNN. +Often, CNNs +consist of several convolutional layers that learn local features of the input, with a fully-connected layer at the end, +which gathers all the local data and produces the outputs. They have wide applications in image and video recognition + +

+









+ +

Recurrent neural networks

+ +

+So far we have only mentioned NNs where information flows in one direction: forward. Recurrent neural networks on +the other hand, have connections between nodes that form directed cycles. This creates a form of +internal memory which are able to capture information on what has been calculated before; the output is dependent +on the previous computations. Recurrent NNs make use of sequential information by performing the same task for +every element in a sequence, where each element depends on previous elements. An example of such information is +sentences, making recurrent NNs especially well-suited for handwriting and speech recognition. + +

+









+ +

Other types of networks

+ +

+There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation +in multidimensional space is the radial basis function (RBF) network. RBFs are typically made up of three layers: +an input layer, a hidden layer with non-linear radial symmetric activation functions and a linear output layer (''linear'' here +means that each node in the output layer has a linear activation function). The layers are normally fully-connected and +there are no cycles, thus RBFs can be viewed as a type of fully-connected FFNN. They are however usually treated as +a separate type of NN due the unusual activation functions. + +

+Other types of NNs could also be mentioned, but are outside the scope of this work. We will now move on to a detailed description +of how a fully-connected FFNN works, and how it can be used to interpolate data sets. + +

+









+ +

Mathematical model

+ +$$ +\begin{equation} + y = f\left(\sum_{i=1}^n w_ix_i + b_i\right) = f(u) +\label{artificialNeuron2} +\end{equation} +$$ + +In an FFNN of such neurons, the inputs \( x_i \) +are the outputs of the neurons in the preceding layer. Furthermore, a MLP is fully-connected, +which means that each neuron receives a weighted sum of the outputs of all neurons in the previous layer. + +

+









+ +

Mathematical model

+ +

+First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \), + +$$ +\begin{equation} + u_i^1 = \sum_{j=1}^2 w_{ij}^1 x_j + b_i^1 +\label{_auto1} +\end{equation} +$$ + +This value is the argument to the activation function \( f_1 \) of each neuron \( i \), +producing the output \( y_i^1 \) of all neurons in layer 1, + +$$ +\begin{equation} + y_i^1 = f_1(u_i^1) = f_1\left(\sum_{j=1}^2 w_{ij}^1 x_j + b_i^1\right) +\label{outputLayer1} +\end{equation} +$$ + +where we assume that all nodes in the same layer have identical activation functions, hence the notation \( f_l \) + +$$ +\begin{equation} + y_i^l = f_l(u_i^l) = f_l\left(\sum_{j=1}^{N_{l-1}} w_{ij}^l y_j^{l-1} + b_i^l\right) +\label{generalLayer} +\end{equation} +$$ + +where \( N_l \) is the number of nodes in layer \( l \). When the output of all the nodes in the first hidden layer are computed, +the values of the subsequent layer can be calculated and so forth until the output is obtained. + +

+









+ +

Mathematical model

+ +

+The output of neuron \( i \) in layer 2 is thus, + +$$ +\begin{align} + y_i^2 &= f_2\left(\sum_{j=1}^3 w_{ij}^2 y_j^1 + b_i^2\right) +\label{_auto2}\\ + &= f_2\left[\sum_{j=1}^3 w_{ij}^2f_1\left(\sum_{k=1}^2 w_{jk}^1 x_k + b_j^1\right) + b_i^2\right] +\label{outputLayer2} +\end{align} +$$ + +where we have substituted \( y_m^1 \) with. Finally, the NN output yields, + +$$ +\begin{align} + y_1^3 &= f_3\left(\sum_{j=1}^3 w_{1m}^3 y_j^2 + b_1^3\right) +\label{_auto3}\\ + &= f_3\left[\sum_{j=1}^3 w_{1j}^3 f_2\left(\sum_{k=1}^3 w_{jk}^2 f_1\left(\sum_{m=1}^2 w_{km}^1 x_m + b_k^1\right) + b_j^2\right) + + b_1^3\right] +\label{_auto4} +\end{align} +$$ + +

+









+ +

Mathematical model

+ +

+We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form +is, +$$ +\begin{align} +&y^{l+1}_1\! = \!f_{l+1}\!\left[\!\sum_{j=1}^{N_l}\! w_{1j}^3 f_l\!\left(\!\sum_{k=1}^{N_{l-1}}\! w_{jk}^2 f_{l-1}\!\left(\! + \dots \!f_1\!\left(\!\sum_{n=1}^{N_0} \!w_{mn}^1 x_n\! + \!b_m^1\!\right) + \!\dots \!\right) \!+ \!b_k^2\!\right) + \!+ \!b_1^3\!\right] && +\label{completeNN} +\end{align} +$$ + +which illustrates a basic property of MLPs: The only independent variables are the input values \( x_n \). + +

+









+ +

Mathematical model

+ +

+This confirms that an MLP, +despite its quite convoluted mathematical form, is nothing more than an analytic function, specifically a +mapping of real-valued vectors \( \vec{x} \in \mathbb{R}^n \rightarrow \vec{y} \in \mathbb{R}^m \). +In our example, \( n=2 \) and \( m=1 \). Consequentially, +the number of input and output values of the function we want to fit must be equal to the number of inputs and outputs of our MLP. + +

+Furthermore, the flexibility and universality of a MLP can be illustrated by realizing that +the expression is essentially a nested sum of scaled activation functions of the form + +$$ +\begin{equation} + h(x) = c_1 f(c_2 x + c_3) + c_4 +\label{_auto5} +\end{equation} +$$ + +where the parameters \( c_i \) are weights and biases. By adjusting these parameters, the activation functions +can be shifted up and down or left and right, change slope or be rescaled +which is the key to the flexibility of a NN. + +$$ +\begin{equation} + f_o = f(u_o) = u_o +\label{outputActivation} +\end{equation} +$$ + +

+









+ +

Matrix-vector notation

+ +We can introduce a more convenient notation for the activations in a NN. + +

+Additionally, we can represent the biases and activations +as layer-wise column vectors \( \vec{b}_l \) and \( \vec{y}_l \), so that the \( i \)-th element of each vector +is the bias \( b_i^l \) and activation \( y_i^l \) of node \( i \) in layer \( l \) respectively. + +

+We have that \( \mathrm{W}_l \) is a \( N_{l-1} \times N_l \) matrix, while \( \vec{b}_l \) and \( \vec{y}_l \) are \( N_l \times 1 \) column vectors. +With this notation, the sum in becomes a matrix-vector multiplication, and we can write +the equation for the activations of hidden layer 2 in + +$$ +\begin{equation} + \vec{y}_2 = f_2(\mathrm{W}_2 \vec{y}_{1} + \vec{b}_{2}) = + f_2\left(\left[\begin{array}{ccc} + w^2_{11} &w^2_{12} &w^2_{13} \\ + w^2_{21} &w^2_{22} &w^2_{23} \\ + w^2_{31} &w^2_{32} &w^2_{33} \\ + \end{array} \right] \cdot + \left[\begin{array}{c} + y^1_1 \\ + y^1_2 \\ + y^1_3 \\ + \end{array}\right] + + \left[\begin{array}{c} + b^2_1 \\ + b^2_2 \\ + b^2_3 \\ + \end{array}\right]\right) +\label{_auto6} +\end{equation} +$$ + +and we see that the activation of node \( i \) in layer 2 is + +$$ +\begin{equation} + y^2_i = f_2\Bigr(w^2_{i1}y^1_1 + w^2_{i2}y^1_2 + w^2_{i3}y^1_3 + b^2_i\Bigr) = + f_2\left(\sum_{j=1}^3 w^2_{ij} y_j^1 + b^2_i\right) +\label{_auto7} +\end{equation} +$$ + +which is in accordance with. Note that +This is not just a convenient and compact notation, but also +a useful and intuitive way to think about MLPs: The output is calculated by a series of matrix-vector multiplications +and vector additions that are used as input to the activation functions. For each operation +\( \mathrm{W}_l \vec{y}_{l-1} \) we move forward one layer. + +

diff --git a/doc/pub/NeuralNet/html/NeuralNet.html b/doc/pub/NeuralNet/html/NeuralNet.html index 6e5932a34..7996c51ce 100644 --- a/doc/pub/NeuralNet/html/NeuralNet.html +++ b/doc/pub/NeuralNet/html/NeuralNet.html @@ -30,32 +30,6 @@ p { text-indent: 0px; } hr { border: 0; width: 80%; border-bottom: 1px solid #aaa} p.caption { width: 80%; font-style: normal; text-align: left; } hr.figure { border: 0; width: 80%; border-bottom: 1px solid #aaa} -.alert-text-small { font-size: 80%; } -.alert-text-large { font-size: 130%; } -.alert-text-normal { font-size: 90%; } -.alert { - padding:8px 35px 8px 14px; margin-bottom:18px; - text-shadow:0 1px 0 rgba(255,255,255,0.5); - border:1px solid #bababa; - border-radius: 4px; - -webkit-border-radius: 4px; - -moz-border-radius: 4px; - color: #555; - background-color: #f8f8f8; - background-position: 10px 5px; - background-repeat: no-repeat; - background-size: 38px; - padding-left: 55px; - width: 75%; - } -.alert-block {padding-top:14px; padding-bottom:14px} -.alert-block > p, .alert-block > ul {margin-bottom:1em} -.alert li {margin-top: 1em} -.alert-block p+p {margin-top:5px} -.alert-notice { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_notice.png); } -.alert-summary { background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_summary.png); } -.alert-warning { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_warning.png); } -.alert-question {background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_question.png); } div { text-align: justify; text-justify: inter-word; } @@ -64,11 +38,40 @@ div { text-align: justify; text-justify: inter-word; } + + + + + + + @@ -90,19 +93,339 @@ end of tocinfo -->

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Sep 20, 2017

+

Nov 2, 2017












-

Introduction

-
- +

What is Machine Learning?

+

+Machine learning is the science of giving computers the ability to learn without being explicitly programmed. +The idea is that there exist generic algorithms which can be used to find patterns in a broad class of data sets without +having to write code specifically for each problem. The algorithm will build its own logic based on the data. +

+Machine learning is a subfield of computer science, and is closely related to computational statistics. +It evolved from the study of pattern recognition in artificial intelligence (AI) research, and has made contributions to +AI tasks like computer vision, natural language processing +and speech recognition. It has also, especially in later years, +found applications in a wide variety of other areas, including bioinformatics, economy, physics, finance and marketing. -

+

+









+

Types of Machine Learning

+ +

+The approaches to machine learning are many, but are often split into two main categories. +In supervised learning we know the answer to a problem, +and let the computer deduce the logic behind it. On the other hand, unsupervised learning +is a method for finding patterns and relationship in data sets without any prior knowledge of the system. +Some authours also operate with a third category, namely reinforcement learning. This is a paradigm +of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, +solely from rewards and punishment. + +

+Another way to categorize machine learning tasks is to consider the desired output of a system. +Some of the most common tasks are: + +

+ +









+ +

Artificial neurons

+The field of artificial neural networks has a long history of development, and is closely connected with +the advancement of computer science and computers in general. A model of artificial neurons +was first developed by McCulloch and Pitts in 1943 to study signal processing in the brain and +has later been refined by others. The general idea is to mimic neural networks in the human brain, which +is composed of billions of neurons that communicate with each other by sending electrical signals. +Each neuron accumulates its incoming signals, +which must exceed an activation threshold to yield an output. If the threshold is not overcome, the neuron +remains inactive, i.e. has zero output. + +

+This behaviour has inspired a simple mathematical model for an artificial neuron. + +$$ +\begin{equation} + y = f\left(\sum_{i=1}^n w_ix_i\right) = f(u) +\label{artificialNeuron} +\end{equation} +$$ + +Here, the output \( y \) of the neuron is the value of its activation function, which have as input +a weighted sum of signals \( x_i, \dots ,x_n \) received by \( n \) other neurons. + +

+









+ +

Neural network types

+ +

+An artificial neural network (NN), is a computational model that consists of layers of connected neurons, or nodes. +It is supposed to mimic a biological nervous system by letting each neuron interact with other neurons +by sending signals in the form of mathematical functions between layers. +A wide variety of different NNs have +been developed, but most of them consist of an input layer, an output layer and eventual layers in-between, called +hidden layers. All layers can contain an arbitrary number of nodes, and each connection between two nodes +is associated with a weight variable. + +

+









+ +

Feed-forward neural networks

+The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, +the information moves in only one direction: forward through the layers. + +

+Nodes are represented by circles, while the arrows display the connections between the nodes, including the +direction of information flow. Additionally, each arrow corresponds to a weight variable, not displayed here. +We observe that each node in a layer is connected to all nodes in the subsequent layer, +making this a so-called fully-connected FFNN. + +

+A different variant of FFNNs are convolutional neural networks (CNNs), which have a connectivity pattern +inspired by the animal visual cortex. Individual neurons in the visual cortex only respond to stimuli from +small sub-regions of the visual field, called a receptive field. This makes the neurons well-suited to exploit the strong +spatially local correlation present in natural images. The response of each neuron can be approximated mathematically +as a convolution operation. + +

+CNNs emulate the behaviour of neurons in the visual cortex by enforcing a local connectivity pattern +between nodes of adjacent layers: Each node +in a convolutional layer is connected only to a subset of the nodes in the previous layer, +in contrast to the fully-connected FFNN. +Often, CNNs +consist of several convolutional layers that learn local features of the input, with a fully-connected layer at the end, +which gathers all the local data and produces the outputs. They have wide applications in image and video recognition + +

+









+ +

Recurrent neural networks

+ +

+So far we have only mentioned NNs where information flows in one direction: forward. Recurrent neural networks on +the other hand, have connections between nodes that form directed cycles. This creates a form of +internal memory which are able to capture information on what has been calculated before; the output is dependent +on the previous computations. Recurrent NNs make use of sequential information by performing the same task for +every element in a sequence, where each element depends on previous elements. An example of such information is +sentences, making recurrent NNs especially well-suited for handwriting and speech recognition. + +

+









+ +

Other types of networks

+ +

+There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation +in multidimensional space is the radial basis function (RBF) network. RBFs are typically made up of three layers: +an input layer, a hidden layer with non-linear radial symmetric activation functions and a linear output layer (''linear'' here +means that each node in the output layer has a linear activation function). The layers are normally fully-connected and +there are no cycles, thus RBFs can be viewed as a type of fully-connected FFNN. They are however usually treated as +a separate type of NN due the unusual activation functions. + +

+Other types of NNs could also be mentioned, but are outside the scope of this work. We will now move on to a detailed description +of how a fully-connected FFNN works, and how it can be used to interpolate data sets. + +

+









+ +

Mathematical model

+ +$$ +\begin{equation} + y = f\left(\sum_{i=1}^n w_ix_i + b_i\right) = f(u) +\label{artificialNeuron2} +\end{equation} +$$ + +In an FFNN of such neurons, the inputs \( x_i \) +are the outputs of the neurons in the preceding layer. Furthermore, a MLP is fully-connected, +which means that each neuron receives a weighted sum of the outputs of all neurons in the previous layer. + +

+









+ +

Mathematical model

+ +

+First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \), + +$$ +\begin{equation} + u_i^1 = \sum_{j=1}^2 w_{ij}^1 x_j + b_i^1 +\label{_auto1} +\end{equation} +$$ + +This value is the argument to the activation function \( f_1 \) of each neuron \( i \), +producing the output \( y_i^1 \) of all neurons in layer 1, + +$$ +\begin{equation} + y_i^1 = f_1(u_i^1) = f_1\left(\sum_{j=1}^2 w_{ij}^1 x_j + b_i^1\right) +\label{outputLayer1} +\end{equation} +$$ + +where we assume that all nodes in the same layer have identical activation functions, hence the notation \( f_l \) + +$$ +\begin{equation} + y_i^l = f_l(u_i^l) = f_l\left(\sum_{j=1}^{N_{l-1}} w_{ij}^l y_j^{l-1} + b_i^l\right) +\label{generalLayer} +\end{equation} +$$ + +where \( N_l \) is the number of nodes in layer \( l \). When the output of all the nodes in the first hidden layer are computed, +the values of the subsequent layer can be calculated and so forth until the output is obtained. + +

+









+ +

Mathematical model

+ +

+The output of neuron \( i \) in layer 2 is thus, + +$$ +\begin{align} + y_i^2 &= f_2\left(\sum_{j=1}^3 w_{ij}^2 y_j^1 + b_i^2\right) +\label{_auto2}\\ + &= f_2\left[\sum_{j=1}^3 w_{ij}^2f_1\left(\sum_{k=1}^2 w_{jk}^1 x_k + b_j^1\right) + b_i^2\right] +\label{outputLayer2} +\end{align} +$$ + +where we have substituted \( y_m^1 \) with. Finally, the NN output yields, + +$$ +\begin{align} + y_1^3 &= f_3\left(\sum_{j=1}^3 w_{1m}^3 y_j^2 + b_1^3\right) +\label{_auto3}\\ + &= f_3\left[\sum_{j=1}^3 w_{1j}^3 f_2\left(\sum_{k=1}^3 w_{jk}^2 f_1\left(\sum_{m=1}^2 w_{km}^1 x_m + b_k^1\right) + b_j^2\right) + + b_1^3\right] +\label{_auto4} +\end{align} +$$ + +

+









+ +

Mathematical model

+ +

+We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form +is, +$$ +\begin{align} +&y^{l+1}_1\! = \!f_{l+1}\!\left[\!\sum_{j=1}^{N_l}\! w_{1j}^3 f_l\!\left(\!\sum_{k=1}^{N_{l-1}}\! w_{jk}^2 f_{l-1}\!\left(\! + \dots \!f_1\!\left(\!\sum_{n=1}^{N_0} \!w_{mn}^1 x_n\! + \!b_m^1\!\right) + \!\dots \!\right) \!+ \!b_k^2\!\right) + \!+ \!b_1^3\!\right] && +\label{completeNN} +\end{align} +$$ + +which illustrates a basic property of MLPs: The only independent variables are the input values \( x_n \). + +

+









+ +

Mathematical model

+ +

+This confirms that an MLP, +despite its quite convoluted mathematical form, is nothing more than an analytic function, specifically a +mapping of real-valued vectors \( \vec{x} \in \mathbb{R}^n \rightarrow \vec{y} \in \mathbb{R}^m \). +In our example, \( n=2 \) and \( m=1 \). Consequentially, +the number of input and output values of the function we want to fit must be equal to the number of inputs and outputs of our MLP. + +

+Furthermore, the flexibility and universality of a MLP can be illustrated by realizing that +the expression is essentially a nested sum of scaled activation functions of the form + +$$ +\begin{equation} + h(x) = c_1 f(c_2 x + c_3) + c_4 +\label{_auto5} +\end{equation} +$$ + +where the parameters \( c_i \) are weights and biases. By adjusting these parameters, the activation functions +can be shifted up and down or left and right, change slope or be rescaled +which is the key to the flexibility of a NN. + +$$ +\begin{equation} + f_o = f(u_o) = u_o +\label{outputActivation} +\end{equation} +$$ + +

+









+ +

Matrix-vector notation

+ +We can introduce a more convenient notation for the activations in a NN. + +

+Additionally, we can represent the biases and activations +as layer-wise column vectors \( \vec{b}_l \) and \( \vec{y}_l \), so that the \( i \)-th element of each vector +is the bias \( b_i^l \) and activation \( y_i^l \) of node \( i \) in layer \( l \) respectively. + +

+We have that \( \mathrm{W}_l \) is a \( N_{l-1} \times N_l \) matrix, while \( \vec{b}_l \) and \( \vec{y}_l \) are \( N_l \times 1 \) column vectors. +With this notation, the sum in becomes a matrix-vector multiplication, and we can write +the equation for the activations of hidden layer 2 in + +$$ +\begin{equation} + \vec{y}_2 = f_2(\mathrm{W}_2 \vec{y}_{1} + \vec{b}_{2}) = + f_2\left(\left[\begin{array}{ccc} + w^2_{11} &w^2_{12} &w^2_{13} \\ + w^2_{21} &w^2_{22} &w^2_{23} \\ + w^2_{31} &w^2_{32} &w^2_{33} \\ + \end{array} \right] \cdot + \left[\begin{array}{c} + y^1_1 \\ + y^1_2 \\ + y^1_3 \\ + \end{array}\right] + + \left[\begin{array}{c} + b^2_1 \\ + b^2_2 \\ + b^2_3 \\ + \end{array}\right]\right) +\label{_auto6} +\end{equation} +$$ + +and we see that the activation of node \( i \) in layer 2 is + +$$ +\begin{equation} + y^2_i = f_2\Bigr(w^2_{i1}y^1_1 + w^2_{i2}y^1_2 + w^2_{i3}y^1_3 + b^2_i\Bigr) = + f_2\left(\sum_{j=1}^3 w^2_{ij} y_j^1 + b^2_i\right) +\label{_auto7} +\end{equation} +$$ + +which is in accordance with. Note that +This is not just a convenient and compact notation, but also +a useful and intuitive way to think about MLPs: The output is calculated by a series of matrix-vector multiplications +and vector additions that are used as input to the activation functions. For each operation +\( \mathrm{W}_l \vec{y}_{l-1} \) we move forward one layer. + +

diff --git a/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz b/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz index 8258dc201..c86a217a8 100644 Binary files a/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz and b/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz differ diff --git a/doc/pub/NeuralNet/pdf/NeuralNet-beamer-handouts2x3.pdf b/doc/pub/NeuralNet/pdf/NeuralNet-beamer-handouts2x3.pdf index 0b6c244b3..7af14e6c3 100644 Binary files a/doc/pub/NeuralNet/pdf/NeuralNet-beamer-handouts2x3.pdf and b/doc/pub/NeuralNet/pdf/NeuralNet-beamer-handouts2x3.pdf differ diff --git a/doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf b/doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf index 2d108a9f9..0fbe9a574 100644 Binary files a/doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf and b/doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf differ diff --git a/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf b/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf index bf97a014f..6ea228e71 100644 Binary files a/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf and b/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf differ diff --git a/doc/src/Bayesian/Bayesian-bs.html b/doc/src/Bayesian/Bayesian-bs.html new file mode 100644 index 000000000..cb8b0f833 --- /dev/null +++ b/doc/src/Bayesian/Bayesian-bs.html @@ -0,0 +1,139 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of Bayesian theory + + + + + + + + + + + + + + + + +

+
+ + Data Analysis and Machine Learning: Elements of Bayesian theory +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + + + +
+

Data Analysis and Machine Learning: Elements of Bayesian theory

+ +

+ + +

+Morten Hjorth-Jensen [1, 2] +
+ +

+ + +

[1] Department of Physics, University of Oslo
+
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
+
+

+

Nov 2, 2017

+
+

+ + +

Read »

+ + +
+ +

+ +

+ + +
+ + + + + + + +
+ © 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license +
+ + + + + + diff --git a/doc/src/Bayesian/Bayesian-reveal.html b/doc/src/Bayesian/Bayesian-reveal.html new file mode 100644 index 000000000..13bd69c33 --- /dev/null +++ b/doc/src/Bayesian/Bayesian-reveal.html @@ -0,0 +1,297 @@ +\ + + + + + + +Data Analysis and Machine Learning: Elements of Bayesian theory + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + +
+ + + + + + + +
+ + + + +

Data Analysis and Machine Learning: Elements of Bayesian theory

+ +

+ + +

+Morten Hjorth-Jensen [1, 2] +
+ +

 
+ + +

[1] Department of Physics, University of Oslo
+
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
+
+

 
+

Nov 2, 2017

+
+

+ +

+ © 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license +
+
+ + +
+

What is Bayesian Statistics

+
+ +

+

+
+ + + +
+
+ + + + + + + + + + + + diff --git a/doc/src/Bayesian/Bayesian-solarized.html b/doc/src/Bayesian/Bayesian-solarized.html new file mode 100644 index 000000000..c8877b119 --- /dev/null +++ b/doc/src/Bayesian/Bayesian-solarized.html @@ -0,0 +1,114 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of Bayesian theory + + + + + + + + + + + + + + + + + + + + + +

Data Analysis and Machine Learning: Elements of Bayesian theory

+ +

+ + +

+Morten Hjorth-Jensen [1, 2] +
+ +

+ + +

[1] Department of Physics, University of Oslo
+
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
+
+

+

Nov 2, 2017

+
+

+









+ +

What is Bayesian Statistics

+
+ +

+ + +

+ + + + + +
+ © 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license +
+ + + + + + diff --git a/doc/src/Bayesian/Bayesian.do.txt b/doc/src/Bayesian/Bayesian.do.txt index be64e5239..06df75d36 100644 --- a/doc/src/Bayesian/Bayesian.do.txt +++ b/doc/src/Bayesian/Bayesian.do.txt @@ -4,7 +4,7 @@ DATE: today !split -===== Introduction ===== +===== What is Bayesian Statistics ===== !bblock !eblock diff --git a/doc/src/Bayesian/Bayesian.html b/doc/src/Bayesian/Bayesian.html new file mode 100644 index 000000000..25a3992ca --- /dev/null +++ b/doc/src/Bayesian/Bayesian.html @@ -0,0 +1,119 @@ + + + + + + + +Data Analysis and Machine Learning: Elements of Bayesian theory + + + + + + + + + + + + + + + + +

Data Analysis and Machine Learning: Elements of Bayesian theory

+ +

+ + +

+Morten Hjorth-Jensen [1, 2] +
+ +

+ + +

[1] Department of Physics, University of Oslo
+
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
+
+

+

Nov 2, 2017

+
+

+









+ +

What is Bayesian Statistics

+
+ +

+ + +

+ + + + + +
+ © 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license +
+ + + + + + diff --git a/doc/src/Bayesian/reveal.js/.gitignore b/doc/src/Bayesian/reveal.js/.gitignore new file mode 100644 index 000000000..a5df3133d --- /dev/null +++ b/doc/src/Bayesian/reveal.js/.gitignore @@ -0,0 +1,8 @@ +.DS_Store +.svn +log/*.log +tmp/** +node_modules/ +.sass-cache +css/reveal.min.css +js/reveal.min.js diff --git a/doc/src/Bayesian/reveal.js/.travis.yml b/doc/src/Bayesian/reveal.js/.travis.yml new file mode 100644 index 000000000..165d9ae9f --- /dev/null +++ b/doc/src/Bayesian/reveal.js/.travis.yml @@ -0,0 +1,5 @@ +language: node_js +node_js: + - 0.10 +before_script: + - npm install -g grunt-cli \ No newline at end of file diff --git a/doc/src/Bayesian/reveal.js/CONTRIBUTING.md b/doc/src/Bayesian/reveal.js/CONTRIBUTING.md new file mode 100644 index 000000000..c2091e88f --- /dev/null +++ b/doc/src/Bayesian/reveal.js/CONTRIBUTING.md @@ -0,0 +1,23 @@ +## Contributing + +Please keep the [issue tracker](http://github.com/hakimel/reveal.js/issues) limited to **bug reports**, **feature requests** and **pull requests**. + + +### Personal Support +If you have personal support or setup questions the best place to ask those are [StackOverflow](http://stackoverflow.com/questions/tagged/reveal.js). + + +### Bug Reports +When reporting a bug make sure to include information about which browser and operating system you are on as well as the necessary steps to reproduce the issue. If possible please include a link to a sample presentation where the bug can be tested. + + +### Pull Requests +- Should follow the coding style of the file you work in, most importantly: + - Tabs to indent + - Single-quoted strings +- Should be made towards the **dev branch** +- Should be submitted from a feature/topic branch (not your master) + + +### Plugins +Please do not submit plugins as pull requests. They should be maintained in their own separate repository. More information here: https://github.com/hakimel/reveal.js/wiki/Plugin-Guidelines diff --git a/doc/src/Bayesian/reveal.js/Gruntfile.js b/doc/src/Bayesian/reveal.js/Gruntfile.js new file mode 100644 index 000000000..b257e8f32 --- /dev/null +++ b/doc/src/Bayesian/reveal.js/Gruntfile.js @@ -0,0 +1,140 @@ +/* global module:false */ +module.exports = function(grunt) { + var port = grunt.option('port') || 8000; + // Project configuration + grunt.initConfig({ + pkg: grunt.file.readJSON('package.json'), + meta: { + banner: + '/*!\n' + + ' * reveal.js <%= pkg.version %> (<%= grunt.template.today("yyyy-mm-dd, HH:MM") %>)\n' + + ' * http://lab.hakim.se/reveal-js\n' + + ' * MIT licensed\n' + + ' *\n' + + ' * Copyright (C) 2014 Hakim El Hattab, http://hakim.se\n' + + ' */' + }, + + qunit: { + files: [ 'test/*.html' ] + }, + + uglify: { + options: { + banner: '<%= meta.banner %>\n' + }, + build: { + src: 'js/reveal.js', + dest: 'js/reveal.min.js' + } + }, + + cssmin: { + compress: { + files: { + 'css/reveal.min.css': [ 'css/reveal.css' ] + } + } + }, + + sass: { + main: { + files: { + 'css/theme/darkgray.css': 'css/theme/source/darkgray.scss', + 'css/theme/beigesmall.css': 'css/theme/source/beigesmall.scss', + 'css/theme/cbc.css': 'css/theme/source/cbc.scss', + 'css/theme/default.css': 'css/theme/source/default.scss', + 'css/theme/beige.css': 'css/theme/source/beige.scss', + 'css/theme/night.css': 'css/theme/source/night.scss', + 'css/theme/serif.css': 'css/theme/source/serif.scss', + 'css/theme/simple.css': 'css/theme/source/simple.scss', + 'css/theme/sky.css': 'css/theme/source/sky.scss', + 'css/theme/moon.css': 'css/theme/source/moon.scss', + 'css/theme/solarized.css': 'css/theme/source/solarized.scss', + 'css/theme/blood.css': 'css/theme/source/blood.scss' + } + } + }, + + jshint: { + options: { + curly: false, + eqeqeq: true, + immed: true, + latedef: true, + newcap: true, + noarg: true, + sub: true, + undef: true, + eqnull: true, + browser: true, + expr: true, + globals: { + head: false, + module: false, + console: false, + unescape: false + } + }, + files: [ 'Gruntfile.js', 'js/reveal.js' ] + }, + + connect: { + server: { + options: { + port: port, + base: '.' + } + } + }, + + zip: { + 'reveal-js-presentation.zip': [ + 'index.html', + 'css/**', + 'js/**', + 'lib/**', + 'images/**', + 'plugin/**' + ] + }, + + watch: { + main: { + files: [ 'Gruntfile.js', 'js/reveal.js', 'css/reveal.css' ], + tasks: 'default' + }, + theme: { + files: [ 'css/theme/source/*.scss', 'css/theme/template/*.scss' ], + tasks: 'themes' + } + } + + }); + + // Dependencies + grunt.loadNpmTasks( 'grunt-contrib-qunit' ); + grunt.loadNpmTasks( 'grunt-contrib-jshint' ); + grunt.loadNpmTasks( 'grunt-contrib-cssmin' ); + grunt.loadNpmTasks( 'grunt-contrib-uglify' ); + grunt.loadNpmTasks( 'grunt-contrib-watch' ); + grunt.loadNpmTasks( 'grunt-contrib-sass' ); + grunt.loadNpmTasks( 'grunt-contrib-connect' ); + grunt.loadNpmTasks( 'grunt-zip' ); + + // Default task + grunt.registerTask( 'default', [ 'jshint', 'cssmin', 'uglify', 'qunit' ] ); + + // Theme task + grunt.registerTask( 'themes', [ 'sass' ] ); + + // Package presentation to archive + grunt.registerTask( 'package', [ 'default', 'zip' ] ); + + // Serve presentation locally + grunt.registerTask( 'serve', [ 'connect', 'watch' ] ); + + // Run tests + grunt.registerTask( 'test', [ 'jshint', 'qunit' ] ); + +}; diff --git a/doc/src/Bayesian/reveal.js/LICENSE b/doc/src/Bayesian/reveal.js/LICENSE new file mode 100644 index 000000000..09623076f --- /dev/null +++ b/doc/src/Bayesian/reveal.js/LICENSE @@ -0,0 +1,19 @@ +Copyright (C) 2015 Hakim El Hattab, http://hakim.se + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. \ No newline at end of file diff --git a/doc/src/Bayesian/reveal.js/README.md b/doc/src/Bayesian/reveal.js/README.md new file mode 100644 index 000000000..573b19597 --- /dev/null +++ b/doc/src/Bayesian/reveal.js/README.md @@ -0,0 +1,1052 @@ +# reveal.js [![Build Status](https://travis-ci.org/hakimel/reveal.js.svg?branch=master)](https://travis-ci.org/hakimel/reveal.js) + +A framework for easily creating beautiful presentations using HTML. [Check out the live demo](http://lab.hakim.se/reveal-js/). + +reveal.js comes with a broad range of features including [nested slides](https://github.com/hakimel/reveal.js#markup), [Markdown contents](https://github.com/hakimel/reveal.js#markdown), [PDF export](https://github.com/hakimel/reveal.js#pdf-export), [speaker notes](https://github.com/hakimel/reveal.js#speaker-notes) and a [JavaScript API](https://github.com/hakimel/reveal.js#api). It's best viewed in a modern browser but [fallbacks](https://github.com/hakimel/reveal.js/wiki/Browser-Support) are available to make sure your presentation can still be viewed elsewhere. + + +#### More reading: +- [Installation](#installation): Step-by-step instructions for getting reveal.js running on your computer. +- [Changelog](https://github.com/hakimel/reveal.js/releases): Up-to-date version history. +- [Examples](https://github.com/hakimel/reveal.js/wiki/Example-Presentations): Presentations created with reveal.js, add your own! +- [Browser Support](https://github.com/hakimel/reveal.js/wiki/Browser-Support): Explanation of browser support and fallbacks. +- [Plugins](https://github.com/hakimel/reveal.js/wiki/Plugins,-Tools-and-Hardware): A list of plugins that can be used to extend reveal.js. + +## Online Editor + +Presentations are written using HTML or Markdown but there's also an online editor for those of you who prefer a graphical interface. Give it a try at [http://slides.com](http://slides.com). + + +## Instructions + +### Markup + +Markup hierarchy needs to be ``
`` where the ``
`` represents one slide and can be repeated indefinitely. If you place multiple ``
``'s inside of another ``
`` they will be shown as vertical slides. The first of the vertical slides is the "root" of the others (at the top), and it will be included in the horizontal sequence. For example: + +```html +
+
+
Single Horizontal Slide
+
+
Vertical Slide 1
+
Vertical Slide 2
+
+
+
+``` + +### Markdown + +It's possible to write your slides using Markdown. To enable Markdown, add the ```data-markdown``` attribute to your ```
``` elements and wrap the contents in a ``` +
+``` + +#### External Markdown + +You can write your content as a separate file and have reveal.js load it at runtime. Note the separator arguments which determine how slides are delimited in the external file. The ```data-charset``` attribute is optional and specifies which charset to use when loading the external file. + +When used locally, this feature requires that reveal.js [runs from a local web server](#full-setup). + +```html +
+
+``` + +#### Element Attributes + +Special syntax (in html comment) is available for adding attributes to Markdown elements. This is useful for fragments, amongst other things. + +```html +
+ +
+``` + +#### Slide Attributes + +Special syntax (in html comment) is available for adding attributes to the slide `
` elements generated by your Markdown. + +```html +
+ +
+``` + + +### Configuration + +At the end of your page you need to initialize reveal by running the following code. Note that all config values are optional and will default as specified below. + +```javascript +Reveal.initialize({ + + // Display controls in the bottom right corner + controls: true, + + // Display a presentation progress bar + progress: true, + + // Display the page number of the current slide + slideNumber: false, + + // Push each slide change to the browser history + history: false, + + // Enable keyboard shortcuts for navigation + keyboard: true, + + // Enable the slide overview mode + overview: true, + + // Vertical centering of slides + center: true, + + // Enables touch navigation on devices with touch input + touch: true, + + // Loop the presentation + loop: false, + + // Change the presentation direction to be RTL + rtl: false, + + // Turns fragments on and off globally + fragments: true, + + // Flags if the presentation is running in an embedded mode, + // i.e. contained within a limited portion of the screen + embedded: false, + + // Flags if we should show a help overlay when the questionmark + // key is pressed + help: true, + + // Number of milliseconds between automatically proceeding to the + // next slide, disabled when set to 0, this value can be overwritten + // by using a data-autoslide attribute on your slides + autoSlide: 0, + + // Stop auto-sliding after user input + autoSlideStoppable: true, + + // Enable slide navigation via mouse wheel + mouseWheel: false, + + // Hides the address bar on mobile devices + hideAddressBar: true, + + // Opens links in an iframe preview overlay + previewLinks: false, + + // Transition style + transition: 'default', // none/fade/slide/convex/concave/zoom + + // Transition speed + transitionSpeed: 'default', // default/fast/slow + + // Transition style for full page slide backgrounds + backgroundTransition: 'default', // none/fade/slide/convex/concave/zoom + + // Number of slides away from the current that are visible + viewDistance: 3, + + // Parallax background image + parallaxBackgroundImage: '', // e.g. "'https://s3.amazonaws.com/hakim-static/reveal-js/reveal-parallax-1.jpg'" + + // Parallax background size + parallaxBackgroundSize: '', // CSS syntax, e.g. "2100px 900px" + + // Amount to move parallax background (horizontal and vertical) on slide change + // Number, e.g. 100 + parallaxBackgroundHorizontal: '', + parallaxBackgroundVertical: '' + +}); +``` + + +The configuration can be updated after initialization using the ```configure``` method: + +```javascript +// Turn autoSlide off +Reveal.configure({ autoSlide: 0 }); + +// Start auto-sliding every 5s +Reveal.configure({ autoSlide: 5000 }); +``` + + +### Dependencies + +Reveal.js doesn't _rely_ on any third party scripts to work but a few optional libraries are included by default. These libraries are loaded as dependencies in the order they appear, for example: + +```javascript +Reveal.initialize({ + dependencies: [ + // Cross-browser shim that fully implements classList - https://github.com/eligrey/classList.js/ + { src: 'lib/js/classList.js', condition: function() { return !document.body.classList; } }, + + // Interpret Markdown in
elements + { src: 'plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } }, + { src: 'plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } }, + + // Syntax highlight for elements + { src: 'plugin/highlight/highlight.js', async: true, callback: function() { hljs.initHighlightingOnLoad(); } }, + + // Zoom in and out with Alt+click + { src: 'plugin/zoom-js/zoom.js', async: true }, + + // Speaker notes + { src: 'plugin/notes/notes.js', async: true }, + + // Remote control your reveal.js presentation using a touch device + { src: 'plugin/remotes/remotes.js', async: true }, + + // MathJax + { src: 'plugin/math/math.js', async: true } + ] +}); +``` + +You can add your own extensions using the same syntax. The following properties are available for each dependency object: +- **src**: Path to the script to load +- **async**: [optional] Flags if the script should load after reveal.js has started, defaults to false +- **callback**: [optional] Function to execute when the script has loaded +- **condition**: [optional] Function which must return true for the script to be loaded + + +### Ready Event + +A 'ready' event is fired when reveal.js has loaded all non-async dependencies and is ready to start navigating. To check if reveal.js is already 'ready' you can call `Reveal.isReady()`. + +```javascript +Reveal.addEventListener( 'ready', function( event ) { + // event.currentSlide, event.indexh, event.indexv +} ); +``` + + +### Presentation Size + +All presentations have a normal size, that is the resolution at which they are authored. The framework will automatically scale presentations uniformly based on this size to ensure that everything fits on any given display or viewport. + +See below for a list of configuration options related to sizing, including default values: + +```javascript +Reveal.initialize({ + + ... + + // The "normal" size of the presentation, aspect ratio will be preserved + // when the presentation is scaled to fit different resolutions. Can be + // specified using percentage units. + width: 960, + height: 700, + + // Factor of the display size that should remain empty around the content + margin: 0.1, + + // Bounds for smallest/largest possible scale to apply to content + minScale: 0.2, + maxScale: 1.5 + +}); +``` + + +### Auto-sliding + +Presentations can be configured to progress through slides automatically, without any user input. To enable this you will need to tell the framework how many milliseconds it should wait between slides: + +```javascript +// Slide every five seconds +Reveal.configure({ + autoSlide: 5000 +}); +``` +When this is turned on a control element will appear that enables users to pause and resume auto-sliding. Alternatively, sliding can be paused or resumed by pressing »a« on the keyboard. Sliding is paused automatically as soon as the user starts navigating. You can disable these controls by specifying ```autoSlideStoppable: false``` in your reveal.js config. + +You can also override the slide duration for individual slides and fragments by using the ```data-autoslide``` attribute: + +```html +
+

After 2 seconds the first fragment will be shown.

+

After 10 seconds the next fragment will be shown.

+

Now, the fragment is displayed for 2 seconds before the next slide is shown.

+
+``` + +Whenever the auto-slide mode is resumed or paused the ```autoslideresumed``` and ```autoslidepaused``` events are fired. + + +### Keyboard Bindings + +If you're unhappy with any of the default keyboard bindings you can override them using the ```keyboard``` config option: + +```javascript +Reveal.configure({ + keyboard: { + 13: 'next', // go to the next slide when the ENTER key is pressed + 27: function() {}, // do something custom when ESC is pressed + 32: null // don't do anything when SPACE is pressed (i.e. disable a reveal.js default binding) + } +}); +``` + +### Lazy Loading + +When working on presentation with a lot of media or iframe content it's important to load lazily. Lazy loading means that reveal.js will only load content for the few slides nearest to the current slide. The number of slides that are preloaded is determined by the `viewDistance` configuration option. + +To enable lazy loading all you need to do is change your "src" attributes to "data-src" as shown below. This is supported for image, video, audio and iframe elements. Lazy loaded iframes will also unload when the containing slide is no longer visible. + +```html +
+ + + +
+``` + + +### API + +The ``Reveal`` object exposes a JavaScript API for controlling navigation and reading state: + +```javascript +// Navigation +Reveal.slide( indexh, indexv, indexf ); +Reveal.left(); +Reveal.right(); +Reveal.up(); +Reveal.down(); +Reveal.prev(); +Reveal.next(); +Reveal.prevFragment(); +Reveal.nextFragment(); + +// Toggle presentation states, optionally pass true/false to force on/off +Reveal.toggleOverview(); +Reveal.togglePause(); +Reveal.toggleAutoSlide(); + +// Change a config value at runtime +Reveal.configure({ controls: true }); + +// Returns the present configuration options +Reveal.getConfig(); + +// Fetch the current scale of the presentation +Reveal.getScale(); + +// Retrieves the previous and current slide elements +Reveal.getPreviousSlide(); +Reveal.getCurrentSlide(); + +Reveal.getIndices(); // { h: 0, v: 0 } } +Reveal.getProgress(); // 0-1 +Reveal.getTotalSlides(); + +// State checks +Reveal.isFirstSlide(); +Reveal.isLastSlide(); +Reveal.isOverview(); +Reveal.isPaused(); +Reveal.isAutoSliding(); +``` + +### Slide Changed Event + +A 'slidechanged' event is fired each time the slide is changed (regardless of state). The event object holds the index values of the current slide as well as a reference to the previous and current slide HTML nodes. + +Some libraries, like MathJax (see [#226](https://github.com/hakimel/reveal.js/issues/226#issuecomment-10261609)), get confused by the transforms and display states of slides. Often times, this can be fixed by calling their update or render function from this callback. + +```javascript +Reveal.addEventListener( 'slidechanged', function( event ) { + // event.previousSlide, event.currentSlide, event.indexh, event.indexv +} ); +``` + +### Presentation State + +The presentation's current state can be fetched by using the `getState` method. A state object contains all of the information required to put the presentation back as it was when `getState` was first called. Sort of like a snapshot. It's a simple object that can easily be stringified and persisted or sent over the wire. + +```javascript +Reveal.slide( 1 ); +// we're on slide 1 + +var state = Reveal.getState(); + +Reveal.slide( 3 ); +// we're on slide 3 + +Reveal.setState( state ); +// we're back on slide 1 +``` + +### Slide States + +If you set ``data-state="somestate"`` on a slide ``
``, "somestate" will be applied as a class on the document element when that slide is opened. This allows you to apply broad style changes to the page based on the active slide. + +Furthermore you can also listen to these changes in state via JavaScript: + +```javascript +Reveal.addEventListener( 'somestate', function() { + // TODO: Sprinkle magic +}, false ); +``` + +### Slide Backgrounds + +Slides are contained within a limited portion of the screen by default to allow them to fit any display and scale uniformly. You can apply full page backgrounds outside of the slide area by adding a ```data-background``` attribute to your ```
``` elements. Four different types of backgrounds are supported: color, image, video and iframe. Below are a few examples. + +```html +
+

All CSS color formats are supported, like rgba() or hsl().

+
+
+

This slide will have a full-size background image.

+
+
+

This background image will be sized to 100px and repeated.

+
+
+

Video. Multiple sources can be defined using a comma separated list. Video will loop when the data-background-video-loop attribute is provided.

+
+
+

Embeds a web page as a background. Note that the page won't be interactive.

+
+``` + +Backgrounds transition using a fade animation by default. This can be changed to a linear sliding transition by passing ```backgroundTransition: 'slide'``` to the ```Reveal.initialize()``` call. Alternatively you can set ```data-background-transition``` on any section with a background to override that specific transition. + + +### Parallax Background + +If you want to use a parallax scrolling background, set the first two config properties below when initializing reveal.js (the other two are optional). + +```javascript +Reveal.initialize({ + + // Parallax background image + parallaxBackgroundImage: '', // e.g. "https://s3.amazonaws.com/hakim-static/reveal-js/reveal-parallax-1.jpg" + + // Parallax background size + parallaxBackgroundSize: '', // CSS syntax, e.g. "2100px 900px" - currently only pixels are supported (don't use % or auto) + + // Amount of pixels to move the parallax background per slide step, + // a value of 0 disables movement along the given axis + // These are optional, if they aren't specified they'll be calculated automatically + parallaxBackgroundHorizontal: 200, + parallaxBackgroundVertical: 50 + +}); +``` + +Make sure that the background size is much bigger than screen size to allow for some scrolling. [View example](http://lab.hakim.se/reveal-js/?parallaxBackgroundImage=https%3A%2F%2Fs3.amazonaws.com%2Fhakim-static%2Freveal-js%2Freveal-parallax-1.jpg¶llaxBackgroundSize=2100px%20900px). + + + +### Slide Transitions +The global presentation transition is set using the ```transition``` config value. You can override the global transition for a specific slide by using the ```data-transition``` attribute: + +```html +
+

This slide will override the presentation transition and zoom!

+
+ +
+

Choose from three transition speeds: default, fast or slow!

+
+``` + +You can also use different in and out transitions for the same slide: + +```html +
+ The train goes on … +
+
+ and on … +
+
+ and stops. +
+
+ (Passengers entering and leaving) +
+
+ And it starts again. +
+``` + + +Note that this does not work with the page and cube transitions. + + +### Internal links + +It's easy to link between slides. The first example below targets the index of another slide whereas the second targets a slide with an ID attribute (```
```): + +```html +Link +Link +``` + +You can also add relative navigation links, similar to the built in reveal.js controls, by appending one of the following classes on any element. Note that each element is automatically given an ```enabled``` class when it's a valid navigation route based on the current slide. + +```html + + + + + + +``` + + +### Fragments +Fragments are used to highlight individual elements on a slide. Every element with the class ```fragment``` will be stepped through before moving on to the next slide. Here's an example: http://lab.hakim.se/reveal-js/#/fragments + +The default fragment style is to start out invisible and fade in. This style can be changed by appending a different class to the fragment: + +```html +
+

grow

+

shrink

+

fade-out

+

visible only once

+

blue only once

+

highlight-red

+

highlight-green

+

highlight-blue

+
+``` + +Multiple fragments can be applied to the same element sequentially by wrapping it, this will fade in the text on the first step and fade it back out on the second. + +```html +
+ + I'll fade in, then out + +
+``` + +The display order of fragments can be controlled using the ```data-fragment-index``` attribute. + +```html +
+

Appears last

+

Appears first

+

Appears second

+
+``` + +### Fragment events + +When a slide fragment is either shown or hidden reveal.js will dispatch an event. + +Some libraries, like MathJax (see #505), get confused by the initially hidden fragment elements. Often times this can be fixed by calling their update or render function from this callback. + +```javascript +Reveal.addEventListener( 'fragmentshown', function( event ) { + // event.fragment = the fragment DOM element +} ); +Reveal.addEventListener( 'fragmenthidden', function( event ) { + // event.fragment = the fragment DOM element +} ); +``` + +### Code syntax highlighting + +By default, Reveal is configured with [highlight.js](http://softwaremaniacs.org/soft/highlight/en/) for code syntax highlighting. Below is an example with clojure code that will be syntax highlighted. When the `data-trim` attribute is present surrounding whitespace is automatically removed. + +```html +
+ 

+(def lazy-fib
+  (concat
+   [0 1]
+   ((fn rfib [a b]
+        (lazy-cons (+ a b) (rfib b (+ a b)))) 0 1)))
+
+
+``` + +### Slide number +If you would like to display the page number of the current slide you can do so using the ```slideNumber``` configuration value. + +```javascript +// Shows the slide number using default formatting +Reveal.configure({ slideNumber: true }); + +// Slide number formatting can be configured using these variables: +// h: current slide's horizontal index +// v: current slide's vertical index +// c: current slide index (flattened) +// t: total number of slides (flattened) +Reveal.configure({ slideNumber: 'c / t' }); + +``` + + +### Overview mode + +Press "Esc" or "o" keys to toggle the overview mode on and off. While you're in this mode, you can still navigate between slides, +as if you were at 1,000 feet above your presentation. The overview mode comes with a few API hooks: + +```javascript +Reveal.addEventListener( 'overviewshown', function( event ) { /* ... */ } ); +Reveal.addEventListener( 'overviewhidden', function( event ) { /* ... */ } ); + +// Toggle the overview mode programmatically +Reveal.toggleOverview(); +``` + +### Fullscreen mode +Just press »F« on your keyboard to show your presentation in fullscreen mode. Press the »ESC« key to exit fullscreen mode. + + +### Embedded media +Embedded HTML5 `