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correcting typos in svm

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mhjensen
2019-11-23 23:00:49 +01:00
parent a99959483f
commit f44378c5e4
11 changed files with 65 additions and 31 deletions
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doc/pub/svm/html/._svm-bs000.html
+1 -1
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@@ -174,7 +174,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 22, 2019</h4></center> <!-- date -->
<center><h4>Nov 23, 2019</h4></center> <!-- date -->
<br>
<p>
doc/pub/svm/html/._svm-bs001.html
+4 -2
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@@ -159,7 +159,7 @@ MathJax.Hub.Config({
<p>
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.
<p>
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).
<p>
The basic mathematics behind the SVM is however less familiar to most of us.
doc/pub/svm/html/._svm-bs003.html
+6 -2
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@@ -158,7 +158,9 @@ MathJax.Hub.Config({
<h2 id="___sec2" class="anchor">What is a hyperplane? </h2>
<p>
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.
<p>
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \).
@@ -171,12 +173,14 @@ $$
b+w_1x_1+w_2x_2=0,
$$
<p>
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
$$
\boldsymbol{w}^T\boldsymbol{x}+b=0.
\boldsymbol{x}^T\boldsymbol{w}+b=0.
$$
<p>
doc/pub/svm/html/svm-bs.html
+1 -1
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@@ -174,7 +174,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 22, 2019</h4></center> <!-- date -->
<center><h4>Nov 23, 2019</h4></center> <!-- date -->
<br>
<p>
doc/pub/svm/html/svm-reveal.html
+12 -6
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@@ -148,7 +148,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>Nov 22, 2019</h4></center> <!-- date -->
<center><h4>Nov 23, 2019</h4></center> <!-- date -->
<br>
<p>
@@ -163,7 +163,7 @@ MathJax.Hub.Config({
<p>
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.
<p>
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).
<p>
The basic mathematics behind the SVM is however less familiar to most of us.
@@ -281,7 +283,9 @@ plt.show()
<h2 id="___sec2">What is a hyperplane? </h2>
<p>
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.
<p>
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,
$$
<p>&nbsp;<br>
<p>
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
<p>&nbsp;<br>
$$
\boldsymbol{w}^T\boldsymbol{x}+b=0.
\boldsymbol{x}^T\boldsymbol{w}+b=0.
$$
<p>&nbsp;<br>
</section>
doc/pub/svm/html/svm-solarized.html
+11 -5
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@@ -110,7 +110,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 22, 2019</h4></center> <!-- date -->
<center><h4>Nov 23, 2019</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -119,7 +119,7 @@ MathJax.Hub.Config({
<p>
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.
<p>
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).
<p>
The basic mathematics behind the SVM is however less familiar to most of us.
@@ -236,7 +238,9 @@ plt.show()
<h2 id="___sec2">What is a hyperplane? </h2>
<p>
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.
<p>
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \).
@@ -249,12 +253,14 @@ $$
b+w_1x_1+w_2x_2=0,
$$
<p>
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
$$
\boldsymbol{w}^T\boldsymbol{x}+b=0.
\boldsymbol{x}^T\boldsymbol{w}+b=0.
$$
<p>
doc/pub/svm/html/svm.html
+11 -5
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@@ -115,7 +115,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 22, 2019</h4></center> <!-- date -->
<center><h4>Nov 23, 2019</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -124,7 +124,7 @@ MathJax.Hub.Config({
<p>
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.
<p>
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).
<p>
The basic mathematics behind the SVM is however less familiar to most of us.
@@ -241,7 +243,9 @@ plt<span style="color: #666666">.</span>show()
<h2 id="___sec2">What is a hyperplane? </h2>
<p>
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.
<p>
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \).
@@ -254,12 +258,14 @@ $$
b+w_1x_1+w_2x_2=0,
$$
<p>
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
$$
\boldsymbol{w}^T\boldsymbol{x}+b=0.
\boldsymbol{x}^T\boldsymbol{w}+b=0.
$$
<p>
doc/pub/svm/ipynb/ipynb-svm-src.tar.gz
BIN
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Binary file not shown.
doc/pub/svm/ipynb/svm.ipynb
+9 -5
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@@ -10,7 +10,7 @@
"<!-- Author: --> \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": [
"$$\n",
"\\boldsymbol{w}^T\\boldsymbol{x}+b=0.\n",
"\\boldsymbol{x}^T\\boldsymbol{w}+b=0.\n",
"$$"
]
},
doc/pub/svm/pdf/svm-minted.pdf
BIN
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doc/src/SupportVMachines/svm.do.txt
+10 -4
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@@ -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