-
diff --git a/doc/pub/svm/html/._svm-bs001.html b/doc/pub/svm/html/._svm-bs001.html index bfb7ac6b8..6382d89df 100644 --- a/doc/pub/svm/html/._svm-bs001.html +++ b/doc/pub/svm/html/._svm-bs001.html @@ -159,7 +159,7 @@ MathJax.Hub.Config({
A Support Vector Machine (SVM) is a very powerful and versatile -Machine Learning model, capable of performing linear or nonlinear +Machine Learning method, capable of performing linear or nonlinear classification, regression, and even outlier detection. It is one of the most popular models in Machine Learning, and anyone interested in Machine Learning should have it in their toolbox. SVMs are @@ -167,7 +167,9 @@ particularly well suited for classification of complex but small-sized or medium-sized datasets.
-The case with two well-separated classes only can be understood in an intuitive way in terms of lines in a two-dimensional space separating the two classes (see figure below). +The case with two well-separated classes only can be understood in an +intuitive way in terms of lines in a two-dimensional space separating +the two classes (see figure below).
The basic mathematics behind the SVM is however less familiar to most of us. diff --git a/doc/pub/svm/html/._svm-bs003.html b/doc/pub/svm/html/._svm-bs003.html index 4283e0279..f48b78c5a 100644 --- a/doc/pub/svm/html/._svm-bs003.html +++ b/doc/pub/svm/html/._svm-bs003.html @@ -158,7 +158,9 @@ MathJax.Hub.Config({
-The aim of the SVM algorithm is to find a hyperplane in an \( p \)-dimensional space, where \( p \) is the number of features that distinctly classifies the data points. +The aim of the SVM algorithm is to find a hyperplane in a +\( p \)-dimensional space, where \( p \) is the number of features that +distinctly classifies the data points.
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \). @@ -171,12 +173,14 @@ $$ b+w_1x_1+w_2x_2=0, $$ +
where \( b \) is the intercept and \( w_1 \) and \( w_2 \) define the elements of a vector orthogonal to the line \( b+w_1x_1+w_2x_2=0 \). In two dimensions we define the vectors \( \boldsymbol{x} =[x1,x2] \) and \( \boldsymbol{w}=[w1,w2] \). We can then rewrite the above equation as + $$ -\boldsymbol{w}^T\boldsymbol{x}+b=0. +\boldsymbol{x}^T\boldsymbol{w}+b=0. $$
diff --git a/doc/pub/svm/html/svm-bs.html b/doc/pub/svm/html/svm-bs.html index 0ad4b19d0..b7903aa11 100644 --- a/doc/pub/svm/html/svm-bs.html +++ b/doc/pub/svm/html/svm-bs.html @@ -174,7 +174,7 @@ MathJax.Hub.Config({
-
diff --git a/doc/pub/svm/html/svm-reveal.html b/doc/pub/svm/html/svm-reveal.html index eaa2e0cef..a4efba160 100644 --- a/doc/pub/svm/html/svm-reveal.html +++ b/doc/pub/svm/html/svm-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({
-
@@ -163,7 +163,7 @@ MathJax.Hub.Config({
A Support Vector Machine (SVM) is a very powerful and versatile -Machine Learning model, capable of performing linear or nonlinear +Machine Learning method, capable of performing linear or nonlinear classification, regression, and even outlier detection. It is one of the most popular models in Machine Learning, and anyone interested in Machine Learning should have it in their toolbox. SVMs are @@ -171,7 +171,9 @@ particularly well suited for classification of complex but small-sized or medium-sized datasets.
-The case with two well-separated classes only can be understood in an intuitive way in terms of lines in a two-dimensional space separating the two classes (see figure below). +The case with two well-separated classes only can be understood in an +intuitive way in terms of lines in a two-dimensional space separating +the two classes (see figure below).
The basic mathematics behind the SVM is however less familiar to most of us. @@ -281,7 +283,9 @@ plt.show()
-The aim of the SVM algorithm is to find a hyperplane in an \( p \)-dimensional space, where \( p \) is the number of features that distinctly classifies the data points. +The aim of the SVM algorithm is to find a hyperplane in a +\( p \)-dimensional space, where \( p \) is the number of features that +distinctly classifies the data points.
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \). @@ -296,13 +300,15 @@ b+w_1x_1+w_2x_2=0, $$
+
where \( b \) is the intercept and \( w_1 \) and \( w_2 \) define the elements of a vector orthogonal to the line \( b+w_1x_1+w_2x_2=0 \). In two dimensions we define the vectors \( \boldsymbol{x} =[x1,x2] \) and \( \boldsymbol{w}=[w1,w2] \). -We can then rewrite the above equation as +We can then rewrite the above equation as +
$$
-\boldsymbol{w}^T\boldsymbol{x}+b=0.
+\boldsymbol{x}^T\boldsymbol{w}+b=0.
$$
diff --git a/doc/pub/svm/html/svm-solarized.html b/doc/pub/svm/html/svm-solarized.html
index f9d5ef494..722543128 100644
--- a/doc/pub/svm/html/svm-solarized.html
+++ b/doc/pub/svm/html/svm-solarized.html
@@ -110,7 +110,7 @@ MathJax.Hub.Config({
-
@@ -119,7 +119,7 @@ MathJax.Hub.Config({
A Support Vector Machine (SVM) is a very powerful and versatile -Machine Learning model, capable of performing linear or nonlinear +Machine Learning method, capable of performing linear or nonlinear classification, regression, and even outlier detection. It is one of the most popular models in Machine Learning, and anyone interested in Machine Learning should have it in their toolbox. SVMs are @@ -127,7 +127,9 @@ particularly well suited for classification of complex but small-sized or medium-sized datasets.
-The case with two well-separated classes only can be understood in an intuitive way in terms of lines in a two-dimensional space separating the two classes (see figure below). +The case with two well-separated classes only can be understood in an +intuitive way in terms of lines in a two-dimensional space separating +the two classes (see figure below).
The basic mathematics behind the SVM is however less familiar to most of us. @@ -236,7 +238,9 @@ plt.show()
-The aim of the SVM algorithm is to find a hyperplane in an \( p \)-dimensional space, where \( p \) is the number of features that distinctly classifies the data points. +The aim of the SVM algorithm is to find a hyperplane in a +\( p \)-dimensional space, where \( p \) is the number of features that +distinctly classifies the data points.
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \). @@ -249,12 +253,14 @@ $$ b+w_1x_1+w_2x_2=0, $$ +
where \( b \) is the intercept and \( w_1 \) and \( w_2 \) define the elements of a vector orthogonal to the line \( b+w_1x_1+w_2x_2=0 \). In two dimensions we define the vectors \( \boldsymbol{x} =[x1,x2] \) and \( \boldsymbol{w}=[w1,w2] \). We can then rewrite the above equation as + $$ -\boldsymbol{w}^T\boldsymbol{x}+b=0. +\boldsymbol{x}^T\boldsymbol{w}+b=0. $$
diff --git a/doc/pub/svm/html/svm.html b/doc/pub/svm/html/svm.html index 804b3f318..8579530c4 100644 --- a/doc/pub/svm/html/svm.html +++ b/doc/pub/svm/html/svm.html @@ -115,7 +115,7 @@ MathJax.Hub.Config({
-
@@ -124,7 +124,7 @@ MathJax.Hub.Config({
A Support Vector Machine (SVM) is a very powerful and versatile -Machine Learning model, capable of performing linear or nonlinear +Machine Learning method, capable of performing linear or nonlinear classification, regression, and even outlier detection. It is one of the most popular models in Machine Learning, and anyone interested in Machine Learning should have it in their toolbox. SVMs are @@ -132,7 +132,9 @@ particularly well suited for classification of complex but small-sized or medium-sized datasets.
-The case with two well-separated classes only can be understood in an intuitive way in terms of lines in a two-dimensional space separating the two classes (see figure below). +The case with two well-separated classes only can be understood in an +intuitive way in terms of lines in a two-dimensional space separating +the two classes (see figure below).
The basic mathematics behind the SVM is however less familiar to most of us. @@ -241,7 +243,9 @@ plt.show()
-The aim of the SVM algorithm is to find a hyperplane in an \( p \)-dimensional space, where \( p \) is the number of features that distinctly classifies the data points. +The aim of the SVM algorithm is to find a hyperplane in a +\( p \)-dimensional space, where \( p \) is the number of features that +distinctly classifies the data points.
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \). @@ -254,12 +258,14 @@ $$ b+w_1x_1+w_2x_2=0, $$ +
where \( b \) is the intercept and \( w_1 \) and \( w_2 \) define the elements of a vector orthogonal to the line \( b+w_1x_1+w_2x_2=0 \). In two dimensions we define the vectors \( \boldsymbol{x} =[x1,x2] \) and \( \boldsymbol{w}=[w1,w2] \). We can then rewrite the above equation as + $$ -\boldsymbol{w}^T\boldsymbol{x}+b=0. +\boldsymbol{x}^T\boldsymbol{w}+b=0. $$
diff --git a/doc/pub/svm/ipynb/ipynb-svm-src.tar.gz b/doc/pub/svm/ipynb/ipynb-svm-src.tar.gz index 5ee1bf504..b7c9245f6 100644 Binary files a/doc/pub/svm/ipynb/ipynb-svm-src.tar.gz and b/doc/pub/svm/ipynb/ipynb-svm-src.tar.gz differ diff --git a/doc/pub/svm/ipynb/svm.ipynb b/doc/pub/svm/ipynb/svm.ipynb index e5c37dc32..181342b04 100644 --- a/doc/pub/svm/ipynb/svm.ipynb +++ b/doc/pub/svm/ipynb/svm.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Nov 22, 2019**\n", + "Date: **Nov 23, 2019**\n", "\n", "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -19,14 +19,16 @@ "## Support Vector Machines, overarching aims\n", "\n", "A Support Vector Machine (SVM) is a very powerful and versatile\n", - "Machine Learning model, capable of performing linear or nonlinear\n", + "Machine Learning method, capable of performing linear or nonlinear\n", "classification, regression, and even outlier detection. It is one of\n", "the most popular models in Machine Learning, and anyone interested in\n", "Machine Learning should have it in their toolbox. SVMs are\n", "particularly well suited for classification of complex but small-sized or\n", "medium-sized datasets. \n", "\n", - "The case with two well-separated classes only can be understood in an intuitive way in terms of lines in a two-dimensional space separating the two classes (see figure below). \n", + "The case with two well-separated classes only can be understood in an\n", + "intuitive way in terms of lines in a two-dimensional space separating\n", + "the two classes (see figure below).\n", "\n", "The basic mathematics behind the SVM is however less familiar to most of us. \n", "It relies on the definition of hyperplanes and the\n", @@ -138,7 +140,9 @@ "source": [ "## What is a hyperplane?\n", "\n", - "The aim of the SVM algorithm is to find a hyperplane in an $p$-dimensional space, where $p$ is the number of features that distinctly classifies the data points. \n", + "The aim of the SVM algorithm is to find a hyperplane in a\n", + "$p$-dimensional space, where $p$ is the number of features that\n", + "distinctly classifies the data points.\n", "\n", "In a $p$-dimensional space, a hyperplane is what we call an affine subspace of dimension of $p-1$.\n", "As an example, in two dimension, a hyperplane is simply as straight line while in three dimensions it is \n", @@ -171,7 +175,7 @@ "metadata": {}, "source": [ "$$\n", - "\\boldsymbol{w}^T\\boldsymbol{x}+b=0.\n", + "\\boldsymbol{x}^T\\boldsymbol{w}+b=0.\n", "$$" ] }, diff --git a/doc/pub/svm/pdf/svm-minted.pdf b/doc/pub/svm/pdf/svm-minted.pdf index 3c8036925..3f1b41988 100644 Binary files a/doc/pub/svm/pdf/svm-minted.pdf and b/doc/pub/svm/pdf/svm-minted.pdf differ diff --git a/doc/src/SupportVMachines/svm.do.txt b/doc/src/SupportVMachines/svm.do.txt index f1417f311..ee7906ce9 100644 --- a/doc/src/SupportVMachines/svm.do.txt +++ b/doc/src/SupportVMachines/svm.do.txt @@ -6,14 +6,16 @@ DATE: today ===== Support Vector Machines, overarching aims ===== A Support Vector Machine (SVM) is a very powerful and versatile -Machine Learning model, capable of performing linear or nonlinear +Machine Learning method, capable of performing linear or nonlinear classification, regression, and even outlier detection. It is one of the most popular models in Machine Learning, and anyone interested in Machine Learning should have it in their toolbox. SVMs are particularly well suited for classification of complex but small-sized or medium-sized datasets. -The case with two well-separated classes only can be understood in an intuitive way in terms of lines in a two-dimensional space separating the two classes (see figure below). +The case with two well-separated classes only can be understood in an +intuitive way in terms of lines in a two-dimensional space separating +the two classes (see figure below). The basic mathematics behind the SVM is however less familiar to most of us. It relies on the definition of hyperplanes and the @@ -118,7 +120,9 @@ plt.show() !split ===== What is a hyperplane? ===== -The aim of the SVM algorithm is to find a hyperplane in an $p$-dimensional space, where $p$ is the number of features that distinctly classifies the data points. +The aim of the SVM algorithm is to find a hyperplane in a +$p$-dimensional space, where $p$ is the number of features that +distinctly classifies the data points. In a $p$-dimensional space, a hyperplane is what we call an affine subspace of dimension of $p-1$. As an example, in two dimension, a hyperplane is simply as straight line while in three dimensions it is @@ -130,13 +134,15 @@ In two dimensions, with the variables $x_1$ and $x_2$, the hyperplane is defined b+w_1x_1+w_2x_2=0, \] !et + where $b$ is the intercept and $w_1$ and $w_2$ define the elements of a vector orthogonal to the line $b+w_1x_1+w_2x_2=0$. In two dimensions we define the vectors $\bm{x} =[x1,x2]$ and $\bm{w}=[w1,w2]$. We can then rewrite the above equation as + !bt \[ -\bm{w}^T\bm{x}+b=0. +\bm{x}^T\bm{w}+b=0. \] !et