We assume here that our data set can be well separated into two diff --git a/doc/pub/week47/html/._week47-bs017.html b/doc/pub/week47/html/._week47-bs017.html index 2fcbbf36e..b060c32de 100644 --- a/doc/pub/week47/html/._week47-bs017.html +++ b/doc/pub/week47/html/._week47-bs017.html @@ -356,7 +356,10 @@ MathJax.Hub.Config({
Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.
Suppose now that classes overlap in feature space, as shown in the -figure here. One way to deal with this problem before we define the +figure in the handwritten notes for Thursday November 25. +
+ +One way to deal with this problem before we define the so-called kernel approach, is to allow a kind of slack in the sense that we allow some points to be on the wrong side of the margin.
diff --git a/doc/pub/week47/html/._week47-bs019.html b/doc/pub/week47/html/._week47-bs019.html index 4c1638836..844383e47 100644 --- a/doc/pub/week47/html/._week47-bs019.html +++ b/doc/pub/week47/html/._week47-bs019.html @@ -362,8 +362,9 @@ wavelets, splines etc.If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +in the handwritten notes for Thursday November 25. +, we can achieve a better separation by introducing more complex +basis functions. The ideal would be to, via a specific transformation to obtain a separation between the classes which is almost linear.
diff --git a/doc/pub/week47/html/week47-reveal.html b/doc/pub/week47/html/week47-reveal.html index 1e3141286..cced7c324 100644 --- a/doc/pub/week47/html/week47-reveal.html +++ b/doc/pub/week47/html/week47-reveal.html @@ -251,7 +251,7 @@ unlikely that we can separate classes easily by say straight lines. the mathematical description of so-called hyperplanes. Let us start with a two-dimensional case. This will also allow us to introduce our first SVM examples. These will be tailored to the case of two specific -classes, as displayed in the figure here based on the usage of the petal data. +classes, as displayed in the figure here based on the usage of the petal data.We assume here that our data set can be well separated into two @@ -845,7 +845,10 @@ $$
Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.
Suppose now that classes overlap in feature space, as shown in the -figure here. One way to deal with this problem before we define the +figure in the handwritten notes for Thursday November 25. +
+ +One way to deal with this problem before we define the so-called kernel approach, is to allow a kind of slack in the sense that we allow some points to be on the wrong side of the margin.
@@ -959,8 +962,9 @@ wavelets, splines etc.If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +in the handwritten notes for Thursday November 25. +, we can achieve a better separation by introducing more complex +basis functions. The ideal would be to, via a specific transformation to obtain a separation between the classes which is almost linear.
diff --git a/doc/pub/week47/html/week47-solarized.html b/doc/pub/week47/html/week47-solarized.html index 408c50854..12bcb3ae4 100644 --- a/doc/pub/week47/html/week47-solarized.html +++ b/doc/pub/week47/html/week47-solarized.html @@ -350,7 +350,7 @@ unlikely that we can separate classes easily by say straight lines. the mathematical description of so-called hyperplanes. Let us start with a two-dimensional case. This will also allow us to introduce our first SVM examples. These will be tailored to the case of two specific -classes, as displayed in the figure here based on the usage of the petal data. +classes, as displayed in the figure here based on the usage of the petal data.We assume here that our data set can be well separated into two @@ -849,7 +849,10 @@ $$
Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.
Suppose now that classes overlap in feature space, as shown in the -figure here. One way to deal with this problem before we define the +figure in the handwritten notes for Thursday November 25. +
+ +One way to deal with this problem before we define the so-called kernel approach, is to allow a kind of slack in the sense that we allow some points to be on the wrong side of the margin.
@@ -940,8 +943,9 @@ wavelets, splines etc.If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +in the handwritten notes for Thursday November 25. +, we can achieve a better separation by introducing more complex +basis functions. The ideal would be to, via a specific transformation to obtain a separation between the classes which is almost linear.
diff --git a/doc/pub/week47/html/week47.html b/doc/pub/week47/html/week47.html index 408daae09..c3c15e801 100644 --- a/doc/pub/week47/html/week47.html +++ b/doc/pub/week47/html/week47.html @@ -427,7 +427,7 @@ unlikely that we can separate classes easily by say straight lines. the mathematical description of so-called hyperplanes. Let us start with a two-dimensional case. This will also allow us to introduce our first SVM examples. These will be tailored to the case of two specific -classes, as displayed in the figure here based on the usage of the petal data. +classes, as displayed in the figure here based on the usage of the petal data.We assume here that our data set can be well separated into two @@ -926,7 +926,10 @@ $$
Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.
Suppose now that classes overlap in feature space, as shown in the -figure here. One way to deal with this problem before we define the +figure in the handwritten notes for Thursday November 25. +
+ +One way to deal with this problem before we define the so-called kernel approach, is to allow a kind of slack in the sense that we allow some points to be on the wrong side of the margin.
@@ -1017,8 +1020,9 @@ wavelets, splines etc.If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +in the handwritten notes for Thursday November 25. +, we can achieve a better separation by introducing more complex +basis functions. The ideal would be to, via a specific transformation to obtain a separation between the classes which is almost linear.
diff --git a/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz b/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz index ed7421f30..95a2ef164 100644 Binary files a/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz and b/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz differ diff --git a/doc/pub/week47/ipynb/week47.ipynb b/doc/pub/week47/ipynb/week47.ipynb index dba1bdab4..d2671aad7 100644 --- a/doc/pub/week47/ipynb/week47.ipynb +++ b/doc/pub/week47/ipynb/week47.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d297b5a6", + "id": "1708e9eb", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "c3e26ae4", + "id": "aeceb3ed", "metadata": { "editable": true }, @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "3696edde", + "id": "349d5566", "metadata": { "editable": true }, @@ -52,7 +52,7 @@ }, { "cell_type": "markdown", - "id": "3bce99d8", + "id": "276c8d08", "metadata": { "editable": true }, @@ -86,7 +86,7 @@ }, { "cell_type": "markdown", - "id": "775d98d8", + "id": "9b98a19a", "metadata": { "editable": true }, @@ -97,7 +97,7 @@ "the mathematical description of so-called hyperplanes. Let us start\n", "with a two-dimensional case. This will also allow us to introduce our\n", "first SVM examples. These will be tailored to the case of two specific\n", - "classes, as displayed in the figure here based on the usage of the petal data.\n", + "classes, as displayed in the figure here based on the usage of the petal data.\n", "\n", "We assume here that our data set can be well separated into two\n", "domains, where a straight line does the job in the separating the two\n", @@ -108,7 +108,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "7d9df056", + "id": "d12c9e26", "metadata": { "collapsed": false, "editable": true @@ -187,7 +187,7 @@ }, { "cell_type": "markdown", - "id": "c64f1a9a", + "id": "b0002a66", "metadata": { "editable": true }, @@ -207,7 +207,7 @@ }, { "cell_type": "markdown", - "id": "674b12a3", + "id": "8f68e125", "metadata": { "editable": true }, @@ -219,7 +219,7 @@ }, { "cell_type": "markdown", - "id": "43f0a20b", + "id": "c4ff70be", "metadata": { "editable": true }, @@ -232,7 +232,7 @@ }, { "cell_type": "markdown", - "id": "ce09877b", + "id": "245ca618", "metadata": { "editable": true }, @@ -244,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "d9a14fd7", + "id": "9cbde939", "metadata": { "editable": true }, @@ -254,7 +254,7 @@ }, { "cell_type": "markdown", - "id": "ce869655", + "id": "2053f3da", "metadata": { "editable": true }, @@ -267,7 +267,7 @@ }, { "cell_type": "markdown", - "id": "c703f2d0", + "id": "edc8cd0b", "metadata": { "editable": true }, @@ -279,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "9ce7dd30", + "id": "72f2ceeb", "metadata": { "editable": true }, @@ -291,7 +291,7 @@ }, { "cell_type": "markdown", - "id": "b455795b", + "id": "5b6e0a88", "metadata": { "editable": true }, @@ -303,7 +303,7 @@ }, { "cell_type": "markdown", - "id": "010b9238", + "id": "73e2d917", "metadata": { "editable": true }, @@ -313,7 +313,7 @@ }, { "cell_type": "markdown", - "id": "b999e39f", + "id": "6de10722", "metadata": { "editable": true }, @@ -325,7 +325,7 @@ }, { "cell_type": "markdown", - "id": "42e6b71e", + "id": "d55fa0e3", "metadata": { "editable": true }, @@ -336,7 +336,7 @@ }, { "cell_type": "markdown", - "id": "f8c7506b", + "id": "567365ad", "metadata": { "editable": true }, @@ -348,7 +348,7 @@ }, { "cell_type": "markdown", - "id": "902b6664", + "id": "033c5353", "metadata": { "editable": true }, @@ -361,7 +361,7 @@ }, { "cell_type": "markdown", - "id": "54f2aab2", + "id": "dfa1a17c", "metadata": { "editable": true }, @@ -373,7 +373,7 @@ }, { "cell_type": "markdown", - "id": "d2b39bc3", + "id": "d9b56fb1", "metadata": { "editable": true }, @@ -383,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "d8e438d6", + "id": "461d38f0", "metadata": { "editable": true }, @@ -412,7 +412,7 @@ }, { "cell_type": "markdown", - "id": "284ea218", + "id": "325dabde", "metadata": { "editable": true }, @@ -424,7 +424,7 @@ }, { "cell_type": "markdown", - "id": "4d4e8fdc", + "id": "16861109", "metadata": { "editable": true }, @@ -436,7 +436,7 @@ }, { "cell_type": "markdown", - "id": "5cfd3056", + "id": "f2ddedc9", "metadata": { "editable": true }, @@ -451,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "6f935fa6", + "id": "4306bffb", "metadata": { "editable": true }, @@ -463,7 +463,7 @@ }, { "cell_type": "markdown", - "id": "206d9255", + "id": "9a1f970e", "metadata": { "editable": true }, @@ -477,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "5f7c7666", + "id": "686298c8", "metadata": { "editable": true }, @@ -489,7 +489,7 @@ }, { "cell_type": "markdown", - "id": "2d213860", + "id": "c00fa0cb", "metadata": { "editable": true }, @@ -499,7 +499,7 @@ }, { "cell_type": "markdown", - "id": "276c7e93", + "id": "a45a44e2", "metadata": { "editable": true }, @@ -511,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "264b761f", + "id": "cb71bc88", "metadata": { "editable": true }, @@ -521,7 +521,7 @@ }, { "cell_type": "markdown", - "id": "10dd0353", + "id": "0fb319c6", "metadata": { "editable": true }, @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "69606ee8", + "id": "be983759", "metadata": { "editable": true }, @@ -545,7 +545,7 @@ }, { "cell_type": "markdown", - "id": "3c6f4034", + "id": "0863cef7", "metadata": { "editable": true }, @@ -557,7 +557,7 @@ }, { "cell_type": "markdown", - "id": "45ebb87b", + "id": "b689a885", "metadata": { "editable": true }, @@ -567,7 +567,7 @@ }, { "cell_type": "markdown", - "id": "dcddfbd3", + "id": "4a258203", "metadata": { "editable": true }, @@ -579,7 +579,7 @@ }, { "cell_type": "markdown", - "id": "52da5b57", + "id": "ead67e72", "metadata": { "editable": true }, @@ -589,7 +589,7 @@ }, { "cell_type": "markdown", - "id": "4281f447", + "id": "8d4d628c", "metadata": { "editable": true }, @@ -612,7 +612,7 @@ }, { "cell_type": "markdown", - "id": "dd89f6d6", + "id": "347c4a08", "metadata": { "editable": true }, @@ -628,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "894e43d0", + "id": "abb58339", "metadata": { "editable": true }, @@ -640,7 +640,7 @@ }, { "cell_type": "markdown", - "id": "ab462cfa", + "id": "0f707d57", "metadata": { "editable": true }, @@ -652,7 +652,7 @@ }, { "cell_type": "markdown", - "id": "f66b13c2", + "id": "d20d1e37", "metadata": { "editable": true }, @@ -664,7 +664,7 @@ }, { "cell_type": "markdown", - "id": "b09478e1", + "id": "1db90e6c", "metadata": { "editable": true }, @@ -674,7 +674,7 @@ }, { "cell_type": "markdown", - "id": "e63e1ed8", + "id": "f7434597", "metadata": { "editable": true }, @@ -686,7 +686,7 @@ }, { "cell_type": "markdown", - "id": "09d0ab60", + "id": "4d32d348", "metadata": { "editable": true }, @@ -697,7 +697,7 @@ }, { "cell_type": "markdown", - "id": "815f9576", + "id": "d1a75d9f", "metadata": { "editable": true }, @@ -709,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "81dff301", + "id": "69f0b39a", "metadata": { "editable": true }, @@ -722,7 +722,7 @@ }, { "cell_type": "markdown", - "id": "6a5bcc89", + "id": "ba07bab7", "metadata": { "editable": true }, @@ -735,7 +735,7 @@ }, { "cell_type": "markdown", - "id": "2545b335", + "id": "0406de63", "metadata": { "editable": true }, @@ -747,7 +747,7 @@ }, { "cell_type": "markdown", - "id": "7d5bf787", + "id": "ec5cf43e", "metadata": { "editable": true }, @@ -757,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "761895bf", + "id": "b934ace1", "metadata": { "editable": true }, @@ -769,7 +769,7 @@ }, { "cell_type": "markdown", - "id": "15ff9911", + "id": "b658e117", "metadata": { "editable": true }, @@ -779,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "e5666256", + "id": "1858e8b0", "metadata": { "editable": true }, @@ -791,7 +791,7 @@ }, { "cell_type": "markdown", - "id": "9a3d325a", + "id": "95cca23b", "metadata": { "editable": true }, @@ -808,7 +808,7 @@ }, { "cell_type": "markdown", - "id": "2cda88e0", + "id": "05397bd4", "metadata": { "editable": true }, @@ -820,7 +820,7 @@ }, { "cell_type": "markdown", - "id": "70285535", + "id": "982efeca", "metadata": { "editable": true }, @@ -830,7 +830,7 @@ }, { "cell_type": "markdown", - "id": "3d155c0c", + "id": "4b7f2368", "metadata": { "editable": true }, @@ -842,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "65cfa308", + "id": "4e602e73", "metadata": { "editable": true }, @@ -852,7 +852,7 @@ }, { "cell_type": "markdown", - "id": "204f80ec", + "id": "d6c9eab3", "metadata": { "editable": true }, @@ -864,7 +864,7 @@ }, { "cell_type": "markdown", - "id": "89675f53", + "id": "ec87a2b9", "metadata": { "editable": true }, @@ -877,7 +877,7 @@ }, { "cell_type": "markdown", - "id": "6ebe98f7", + "id": "8d12bb81", "metadata": { "editable": true }, @@ -889,7 +889,7 @@ }, { "cell_type": "markdown", - "id": "cb58d54b", + "id": "10d026d5", "metadata": { "editable": true }, @@ -901,7 +901,7 @@ }, { "cell_type": "markdown", - "id": "ac15bc71", + "id": "6a7c46e4", "metadata": { "editable": true }, @@ -911,7 +911,7 @@ }, { "cell_type": "markdown", - "id": "c0f9ca25", + "id": "d211ad3e", "metadata": { "editable": true }, @@ -925,7 +925,7 @@ }, { "cell_type": "markdown", - "id": "5734050e", + "id": "6886ef44", "metadata": { "editable": true }, @@ -935,7 +935,7 @@ }, { "cell_type": "markdown", - "id": "3deaaab1", + "id": "f9e63f33", "metadata": { "editable": true }, @@ -947,7 +947,7 @@ }, { "cell_type": "markdown", - "id": "c1905f47", + "id": "5e7e1f95", "metadata": { "editable": true }, @@ -957,7 +957,7 @@ }, { "cell_type": "markdown", - "id": "4e0423a8", + "id": "06f66e7b", "metadata": { "editable": true }, @@ -969,7 +969,7 @@ }, { "cell_type": "markdown", - "id": "e0dec665", + "id": "e44affd7", "metadata": { "editable": true }, @@ -979,7 +979,7 @@ }, { "cell_type": "markdown", - "id": "e2d57eef", + "id": "f7c924ed", "metadata": { "editable": true }, @@ -991,7 +991,7 @@ }, { "cell_type": "markdown", - "id": "77bc96c6", + "id": "1b52bf51", "metadata": { "editable": true }, @@ -1005,7 +1005,7 @@ }, { "cell_type": "markdown", - "id": "38775bb9", + "id": "5fbb430c", "metadata": { "editable": true }, @@ -1017,7 +1017,7 @@ }, { "cell_type": "markdown", - "id": "2862aca0", + "id": "19e75f8d", "metadata": { "editable": true }, @@ -1029,7 +1029,7 @@ }, { "cell_type": "markdown", - "id": "b356a9e2", + "id": "45f3abca", "metadata": { "editable": true }, @@ -1041,7 +1041,7 @@ }, { "cell_type": "markdown", - "id": "673fbcec", + "id": "e03d742c", "metadata": { "editable": true }, @@ -1053,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "fce13dac", + "id": "013f58b3", "metadata": { "editable": true }, @@ -1065,7 +1065,7 @@ }, { "cell_type": "markdown", - "id": "5cef7ece", + "id": "ac60181e", "metadata": { "editable": true }, @@ -1075,7 +1075,7 @@ }, { "cell_type": "markdown", - "id": "116189a3", + "id": "9f527f31", "metadata": { "editable": true }, @@ -1087,7 +1087,7 @@ }, { "cell_type": "markdown", - "id": "192e3d83", + "id": "3195b77e", "metadata": { "editable": true }, @@ -1097,7 +1097,7 @@ }, { "cell_type": "markdown", - "id": "0367b41a", + "id": "226450c0", "metadata": { "editable": true }, @@ -1109,7 +1109,7 @@ }, { "cell_type": "markdown", - "id": "73055eee", + "id": "c51cc75d", "metadata": { "editable": true }, @@ -1120,7 +1120,7 @@ }, { "cell_type": "markdown", - "id": "1e9a8e7d", + "id": "f532e0cd", "metadata": { "editable": true }, @@ -1132,7 +1132,7 @@ }, { "cell_type": "markdown", - "id": "fec4bd3f", + "id": "b140f6d9", "metadata": { "editable": true }, @@ -1146,7 +1146,7 @@ }, { "cell_type": "markdown", - "id": "83d140dc", + "id": "030ef098", "metadata": { "editable": true }, @@ -1158,7 +1158,7 @@ }, { "cell_type": "markdown", - "id": "1e8bd1a9", + "id": "134e888c", "metadata": { "editable": true }, @@ -1170,7 +1170,7 @@ }, { "cell_type": "markdown", - "id": "f9020497", + "id": "8fb795f5", "metadata": { "editable": true }, @@ -1180,7 +1180,7 @@ }, { "cell_type": "markdown", - "id": "a3777e9e", + "id": "54737881", "metadata": { "editable": true }, @@ -1197,7 +1197,7 @@ }, { "cell_type": "markdown", - "id": "f4b5422e", + "id": "81814011", "metadata": { "editable": true }, @@ -1208,7 +1208,7 @@ }, { "cell_type": "markdown", - "id": "5434dedf", + "id": "cda4b712", "metadata": { "editable": true }, @@ -1221,7 +1221,7 @@ }, { "cell_type": "markdown", - "id": "59d9227f", + "id": "1371d59a", "metadata": { "editable": true }, @@ -1233,7 +1233,7 @@ }, { "cell_type": "markdown", - "id": "e3205aa2", + "id": "fa4889ae", "metadata": { "editable": true }, @@ -1243,7 +1243,7 @@ }, { "cell_type": "markdown", - "id": "b9773b95", + "id": "a78be679", "metadata": { "editable": true }, @@ -1255,7 +1255,7 @@ }, { "cell_type": "markdown", - "id": "472ad856", + "id": "164c6341", "metadata": { "editable": true }, @@ -1265,7 +1265,7 @@ }, { "cell_type": "markdown", - "id": "fbce138f", + "id": "b0af4f60", "metadata": { "editable": true }, @@ -1277,7 +1277,7 @@ }, { "cell_type": "markdown", - "id": "cee42ab7", + "id": "0f2597ec", "metadata": { "editable": true }, @@ -1287,7 +1287,7 @@ }, { "cell_type": "markdown", - "id": "5ae1628c", + "id": "076089c0", "metadata": { "editable": true }, @@ -1299,7 +1299,7 @@ }, { "cell_type": "markdown", - "id": "dbc046c4", + "id": "6eb1c414", "metadata": { "editable": true }, @@ -1309,7 +1309,7 @@ }, { "cell_type": "markdown", - "id": "62b7934c", + "id": "7dbf8128", "metadata": { "editable": true }, @@ -1321,7 +1321,7 @@ }, { "cell_type": "markdown", - "id": "cd3f6f0a", + "id": "a03361ca", "metadata": { "editable": true }, @@ -1331,7 +1331,7 @@ }, { "cell_type": "markdown", - "id": "372433e3", + "id": "2dd830c5", "metadata": { "editable": true }, @@ -1341,7 +1341,9 @@ "Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.\n", "\n", "Suppose now that classes overlap in feature space, as shown in the\n", - "figure here. One way to deal with this problem before we define the\n", + "figure in the [handwritten notes](https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021) for Thursday November 25.\n", + "\n", + "One way to deal with this problem before we define the\n", "so-called **kernel approach**, is to allow a kind of slack in the sense\n", "that we allow some points to be on the wrong side of the margin.\n", "\n", @@ -1351,7 +1353,7 @@ }, { "cell_type": "markdown", - "id": "3b0cb06e", + "id": "0dc3f9af", "metadata": { "editable": true }, @@ -1363,7 +1365,7 @@ }, { "cell_type": "markdown", - "id": "fd1d9050", + "id": "a9b8b493", "metadata": { "editable": true }, @@ -1373,7 +1375,7 @@ }, { "cell_type": "markdown", - "id": "0b22eabb", + "id": "39194508", "metadata": { "editable": true }, @@ -1385,7 +1387,7 @@ }, { "cell_type": "markdown", - "id": "f38b37d2", + "id": "903b1b09", "metadata": { "editable": true }, @@ -1401,7 +1403,7 @@ }, { "cell_type": "markdown", - "id": "4560c89b", + "id": "db69e6ee", "metadata": { "editable": true }, @@ -1413,7 +1415,7 @@ }, { "cell_type": "markdown", - "id": "8255a80f", + "id": "197fb7da", "metadata": { "editable": true }, @@ -1425,7 +1427,7 @@ }, { "cell_type": "markdown", - "id": "8dbf6a88", + "id": "a254ef6c", "metadata": { "editable": true }, @@ -1435,7 +1437,7 @@ }, { "cell_type": "markdown", - "id": "dc353570", + "id": "20f993a9", "metadata": { "editable": true }, @@ -1447,7 +1449,7 @@ }, { "cell_type": "markdown", - "id": "6565e7ac", + "id": "a381c227", "metadata": { "editable": true }, @@ -1459,7 +1461,7 @@ }, { "cell_type": "markdown", - "id": "05e47e0a", + "id": "7ab15cb1", "metadata": { "editable": true }, @@ -1471,7 +1473,7 @@ }, { "cell_type": "markdown", - "id": "d55883da", + "id": "31416bbc", "metadata": { "editable": true }, @@ -1481,7 +1483,7 @@ }, { "cell_type": "markdown", - "id": "39f7b542", + "id": "9c827b1e", "metadata": { "editable": true }, @@ -1493,7 +1495,7 @@ }, { "cell_type": "markdown", - "id": "141d2a34", + "id": "840e9948", "metadata": { "editable": true }, @@ -1503,7 +1505,7 @@ }, { "cell_type": "markdown", - "id": "787755c1", + "id": "3e1d7923", "metadata": { "editable": true }, @@ -1515,7 +1517,7 @@ }, { "cell_type": "markdown", - "id": "ddd7223d", + "id": "8182840e", "metadata": { "editable": true }, @@ -1525,7 +1527,7 @@ }, { "cell_type": "markdown", - "id": "de1e5717", + "id": "8304578d", "metadata": { "editable": true }, @@ -1537,7 +1539,7 @@ }, { "cell_type": "markdown", - "id": "0d5ad78d", + "id": "a6268362", "metadata": { "editable": true }, @@ -1548,7 +1550,7 @@ }, { "cell_type": "markdown", - "id": "c112457b", + "id": "21b23ee4", "metadata": { "editable": true }, @@ -1560,7 +1562,7 @@ }, { "cell_type": "markdown", - "id": "363c1a47", + "id": "9655b95d", "metadata": { "editable": true }, @@ -1572,7 +1574,7 @@ }, { "cell_type": "markdown", - "id": "06a0a3ed", + "id": "f4567799", "metadata": { "editable": true }, @@ -1582,7 +1584,7 @@ }, { "cell_type": "markdown", - "id": "98083d0f", + "id": "4b9b4e69", "metadata": { "editable": true }, @@ -1594,7 +1596,7 @@ }, { "cell_type": "markdown", - "id": "6e494443", + "id": "d6b6e35e", "metadata": { "editable": true }, @@ -1609,8 +1611,9 @@ "wavelets, splines etc.\n", "\n", "If our feature space is not easy to separate, as shown in the figure\n", - "here, we can achieve a better separation by introducing more complex\n", - "basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to \n", + "in the [handwritten notes](https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021) for Thursday November 25.\n", + ", we can achieve a better separation by introducing more complex\n", + "basis functions. The ideal would be to, via a specific transformation to \n", "obtain a separation between the classes which is almost linear. \n", "\n", "The change of basis, from $x\\rightarrow z=\\phi(x)$ leads to the same type of equations to be solved, except that\n", @@ -1620,7 +1623,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "42524afe", + "id": "a1a38dbc", "metadata": { "collapsed": false, "editable": true @@ -1677,7 +1680,7 @@ }, { "cell_type": "markdown", - "id": "8a04c098", + "id": "74f17cd6", "metadata": { "editable": true }, @@ -1689,7 +1692,7 @@ }, { "cell_type": "markdown", - "id": "8a837902", + "id": "59a7758f", "metadata": { "editable": true }, @@ -1701,7 +1704,7 @@ }, { "cell_type": "markdown", - "id": "5ff37c0d", + "id": "7511cc97", "metadata": { "editable": true }, @@ -1711,7 +1714,7 @@ }, { "cell_type": "markdown", - "id": "59243c73", + "id": "c18aae49", "metadata": { "editable": true }, @@ -1723,7 +1726,7 @@ }, { "cell_type": "markdown", - "id": "aa20b129", + "id": "6f577c4b", "metadata": { "editable": true }, @@ -1733,7 +1736,7 @@ }, { "cell_type": "markdown", - "id": "3b67b193", + "id": "01d040cc", "metadata": { "editable": true }, @@ -1745,7 +1748,7 @@ }, { "cell_type": "markdown", - "id": "28823267", + "id": "a165ba6e", "metadata": { "editable": true }, @@ -1756,7 +1759,7 @@ }, { "cell_type": "markdown", - "id": "c90b67ca", + "id": "7bf9de65", "metadata": { "editable": true }, @@ -1768,7 +1771,7 @@ }, { "cell_type": "markdown", - "id": "e4fcdba6", + "id": "8c870963", "metadata": { "editable": true }, @@ -1778,7 +1781,7 @@ }, { "cell_type": "markdown", - "id": "715664f9", + "id": "14d72bac", "metadata": { "editable": true }, @@ -1790,7 +1793,7 @@ }, { "cell_type": "markdown", - "id": "7b853f11", + "id": "7e9c91fa", "metadata": { "editable": true }, @@ -1808,7 +1811,7 @@ }, { "cell_type": "markdown", - "id": "803a45ce", + "id": "36551459", "metadata": { "editable": true }, @@ -1819,7 +1822,7 @@ }, { "cell_type": "markdown", - "id": "61310ff9", + "id": "1f558a05", "metadata": { "editable": true }, @@ -1831,7 +1834,7 @@ }, { "cell_type": "markdown", - "id": "66491438", + "id": "279ab53a", "metadata": { "editable": true }, @@ -1841,7 +1844,7 @@ }, { "cell_type": "markdown", - "id": "e8d2d136", + "id": "672fd6fa", "metadata": { "editable": true }, @@ -1858,7 +1861,7 @@ }, { "cell_type": "markdown", - "id": "f7952451", + "id": "42031f08", "metadata": { "editable": true }, @@ -1872,7 +1875,7 @@ }, { "cell_type": "markdown", - "id": "b19b5113", + "id": "7a16af05", "metadata": { "editable": true }, @@ -1887,7 +1890,7 @@ }, { "cell_type": "markdown", - "id": "4caf5a80", + "id": "bcf0d58c", "metadata": { "editable": true }, @@ -1899,7 +1902,7 @@ }, { "cell_type": "markdown", - "id": "633e3356", + "id": "d4c81398", "metadata": { "editable": true }, @@ -1927,7 +1930,7 @@ }, { "cell_type": "markdown", - "id": "76ac96ea", + "id": "16082e86", "metadata": { "editable": true }, @@ -1939,7 +1942,7 @@ }, { "cell_type": "markdown", - "id": "74510d78", + "id": "0b8c3336", "metadata": { "editable": true }, @@ -1954,7 +1957,7 @@ }, { "cell_type": "markdown", - "id": "faac8dc8", + "id": "ee66be99", "metadata": { "editable": true }, @@ -1965,7 +1968,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "91ea69e9", + "id": "ae55fede", "metadata": { "collapsed": false, "editable": true @@ -2164,7 +2167,7 @@ }, { "cell_type": "markdown", - "id": "d0b7f9cf", + "id": "33d09931", "metadata": { "editable": true }, @@ -2176,7 +2179,7 @@ }, { "cell_type": "markdown", - "id": "9463bbe9", + "id": "18af658e", "metadata": { "editable": true }, @@ -2191,7 +2194,7 @@ }, { "cell_type": "markdown", - "id": "7b64fd8d", + "id": "762e6754", "metadata": { "editable": true }, @@ -2208,7 +2211,7 @@ }, { "cell_type": "markdown", - "id": "8b168bf3", + "id": "6699af37", "metadata": { "editable": true }, @@ -2229,7 +2232,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "fe97004b", + "id": "91eb98c8", "metadata": { "collapsed": false, "editable": true @@ -2242,7 +2245,7 @@ }, { "cell_type": "markdown", - "id": "9ebe52b7", + "id": "0e8869fe", "metadata": { "editable": true }, @@ -2252,7 +2255,7 @@ }, { "cell_type": "markdown", - "id": "ea4caa80", + "id": "d2089bcc", "metadata": { "editable": true }, @@ -2264,7 +2267,7 @@ }, { "cell_type": "markdown", - "id": "447ad01e", + "id": "f6016f93", "metadata": { "editable": true }, @@ -2279,7 +2282,7 @@ }, { "cell_type": "markdown", - "id": "9917fc9c", + "id": "5befddeb", "metadata": { "editable": true }, @@ -2289,7 +2292,7 @@ }, { "cell_type": "markdown", - "id": "4ec0b02c", + "id": "b181577e", "metadata": { "editable": true }, @@ -2308,7 +2311,7 @@ }, { "cell_type": "markdown", - "id": "23f12ebb", + "id": "76afd26b", "metadata": { "editable": true }, @@ -2318,7 +2321,7 @@ }, { "cell_type": "markdown", - "id": "e53e01bb", + "id": "d6e70295", "metadata": { "editable": true }, @@ -2330,7 +2333,7 @@ }, { "cell_type": "markdown", - "id": "953de6d5", + "id": "ae1478ad", "metadata": { "editable": true }, @@ -2340,7 +2343,7 @@ }, { "cell_type": "markdown", - "id": "1addd2bf", + "id": "d1af3e76", "metadata": { "editable": true }, @@ -2352,7 +2355,7 @@ }, { "cell_type": "markdown", - "id": "818d1345", + "id": "e8fdf43e", "metadata": { "editable": true }, @@ -2362,7 +2365,7 @@ }, { "cell_type": "markdown", - "id": "7da978de", + "id": "950f39e6", "metadata": { "editable": true }, @@ -2374,7 +2377,7 @@ }, { "cell_type": "markdown", - "id": "d4d1d665", + "id": "62c0750c", "metadata": { "editable": true }, @@ -2385,7 +2388,7 @@ }, { "cell_type": "markdown", - "id": "ebf7b0d8", + "id": "05f7db4e", "metadata": { "editable": true }, @@ -2397,7 +2400,7 @@ }, { "cell_type": "markdown", - "id": "aa66eb96", + "id": "be905e5c", "metadata": { "editable": true }, @@ -2409,7 +2412,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "bcb69ce9", + "id": "84671cc1", "metadata": { "collapsed": false, "editable": true @@ -2433,7 +2436,7 @@ }, { "cell_type": "markdown", - "id": "60a3d131", + "id": "1c9d5533", "metadata": { "editable": true }, @@ -2445,7 +2448,7 @@ }, { "cell_type": "markdown", - "id": "09a979c4", + "id": "a5abe159", "metadata": { "editable": true }, @@ -2455,7 +2458,7 @@ }, { "cell_type": "markdown", - "id": "e93c0928", + "id": "9e154bb6", "metadata": { "editable": true }, @@ -2470,7 +2473,7 @@ }, { "cell_type": "markdown", - "id": "906a462a", + "id": "bca0471a", "metadata": { "editable": true }, @@ -2486,7 +2489,7 @@ }, { "cell_type": "markdown", - "id": "ce4e7093", + "id": "28cb541d", "metadata": { "editable": true }, @@ -2511,7 +2514,7 @@ }, { "cell_type": "markdown", - "id": "030684fc", + "id": "b7fa1d7d", "metadata": { "editable": true }, @@ -2540,7 +2543,7 @@ }, { "cell_type": "markdown", - "id": "8e1d2370", + "id": "003a23ee", "metadata": { "editable": true }, @@ -2556,7 +2559,7 @@ }, { "cell_type": "markdown", - "id": "5ceec6b5", + "id": "58b9a8f0", "metadata": { "editable": true }, @@ -2581,7 +2584,7 @@ }, { "cell_type": "markdown", - "id": "5336ae51", + "id": "bf2dbf12", "metadata": { "editable": true }, @@ -2628,7 +2631,7 @@ }, { "cell_type": "markdown", - "id": "69d7807b", + "id": "2c79eaf4", "metadata": { "editable": true }, @@ -2664,7 +2667,7 @@ }, { "cell_type": "markdown", - "id": "a5788fcf", + "id": "25c294d5", "metadata": { "editable": true }, @@ -2687,7 +2690,7 @@ }, { "cell_type": "markdown", - "id": "fda2577a", + "id": "ee41415f", "metadata": { "editable": true }, @@ -2710,7 +2713,7 @@ }, { "cell_type": "markdown", - "id": "aa0f65b6", + "id": "5e1f3792", "metadata": { "editable": true }, @@ -2730,7 +2733,7 @@ }, { "cell_type": "markdown", - "id": "a387c41a", + "id": "2343a871", "metadata": { "editable": true }, @@ -2746,7 +2749,7 @@ }, { "cell_type": "markdown", - "id": "b4412a32", + "id": "b8119c66", "metadata": { "editable": true }, @@ -2774,7 +2777,7 @@ }, { "cell_type": "markdown", - "id": "09fe89d1", + "id": "9dc83fc3", "metadata": { "editable": true }, @@ -2796,7 +2799,7 @@ }, { "cell_type": "markdown", - "id": "a1625399", + "id": "c7ab7d9e", "metadata": { "editable": true }, @@ -2821,7 +2824,7 @@ }, { "cell_type": "markdown", - "id": "a60af950", + "id": "4f361b65", "metadata": { "editable": true }, @@ -2839,7 +2842,7 @@ }, { "cell_type": "markdown", - "id": "717ff832", + "id": "e40ad98c", "metadata": { "editable": true }, @@ -2867,7 +2870,7 @@ }, { "cell_type": "markdown", - "id": "69120211", + "id": "c6f64d3f", "metadata": { "editable": true }, @@ -2881,7 +2884,7 @@ }, { "cell_type": "markdown", - "id": "cf743a91", + "id": "68b28771", "metadata": { "editable": true }, @@ -2907,7 +2910,7 @@ }, { "cell_type": "markdown", - "id": "2b1c821d", + "id": "b9271af0", "metadata": { "editable": true }, @@ -2936,7 +2939,7 @@ }, { "cell_type": "markdown", - "id": "d07a08c1", + "id": "966ba86e", "metadata": { "editable": true }, @@ -2953,7 +2956,7 @@ }, { "cell_type": "markdown", - "id": "21760d88", + "id": "c9e3653b", "metadata": { "editable": true }, @@ -2975,7 +2978,7 @@ }, { "cell_type": "markdown", - "id": "a215b485", + "id": "73a5b537", "metadata": { "editable": true }, @@ -2993,7 +2996,7 @@ }, { "cell_type": "markdown", - "id": "e0e5b2f2", + "id": "4b8c7811", "metadata": { "editable": true }, @@ -3016,7 +3019,7 @@ }, { "cell_type": "markdown", - "id": "883ff967", + "id": "89427e4d", "metadata": { "editable": true }, @@ -3035,7 +3038,7 @@ }, { "cell_type": "markdown", - "id": "a8c66672", + "id": "a79b7a09", "metadata": { "editable": true }, @@ -3051,7 +3054,7 @@ }, { "cell_type": "markdown", - "id": "38867651", + "id": "8f9545b1", "metadata": { "editable": true }, @@ -3066,7 +3069,7 @@ }, { "cell_type": "markdown", - "id": "31d4a91e", + "id": "f1d71860", "metadata": { "editable": true }, @@ -3090,7 +3093,7 @@ }, { "cell_type": "markdown", - "id": "d8eb36e7", + "id": "0ea2d42d", "metadata": { "editable": true }, @@ -3102,7 +3105,7 @@ }, { "cell_type": "markdown", - "id": "03f66dfa", + "id": "b9d0e1d1", "metadata": { "editable": true }, @@ -3120,7 +3123,7 @@ }, { "cell_type": "markdown", - "id": "15a58ad9", + "id": "d7065d67", "metadata": { "editable": true }, @@ -3130,7 +3133,7 @@ }, { "cell_type": "markdown", - "id": "8fee60a6", + "id": "cbf630db", "metadata": { "editable": true }, @@ -3148,7 +3151,7 @@ }, { "cell_type": "markdown", - "id": "bd6b9ab1", + "id": "baa89cde", "metadata": { "editable": true }, @@ -3158,7 +3161,7 @@ }, { "cell_type": "markdown", - "id": "2f1d5ba5", + "id": "e90da2c5", "metadata": { "editable": true }, @@ -3177,7 +3180,7 @@ }, { "cell_type": "markdown", - "id": "cda96c2d", + "id": "c35f1e14", "metadata": { "editable": true }, @@ -3189,7 +3192,7 @@ }, { "cell_type": "markdown", - "id": "17566561", + "id": "f68ce169", "metadata": { "editable": true }, @@ -3203,7 +3206,7 @@ }, { "cell_type": "markdown", - "id": "161d5743", + "id": "1652008b", "metadata": { "editable": true }, @@ -3218,7 +3221,7 @@ }, { "cell_type": "markdown", - "id": "707e8fcb", + "id": "cf9a080a", "metadata": { "editable": true }, @@ -3236,7 +3239,7 @@ }, { "cell_type": "markdown", - "id": "d1fff888", + "id": "c859d123", "metadata": { "editable": true }, @@ -3250,7 +3253,7 @@ }, { "cell_type": "markdown", - "id": "ae35a3c3", + "id": "a1c9078b", "metadata": { "editable": true }, @@ -3268,7 +3271,7 @@ }, { "cell_type": "markdown", - "id": "de8a68fe", + "id": "bdfcc47e", "metadata": { "editable": true }, @@ -3292,7 +3295,7 @@ }, { "cell_type": "markdown", - "id": "6fce707b", + "id": "b07f0554", "metadata": { "editable": true }, @@ -3330,7 +3333,7 @@ }, { "cell_type": "markdown", - "id": "1b2d107e", + "id": "b04dfdb3", "metadata": { "editable": true }, @@ -3353,7 +3356,7 @@ }, { "cell_type": "markdown", - "id": "649355d5", + "id": "cd2fa1fa", "metadata": { "editable": true }, @@ -3389,7 +3392,7 @@ }, { "cell_type": "markdown", - "id": "1bd0b6d2", + "id": "f81f5278", "metadata": { "editable": true }, @@ -3410,7 +3413,7 @@ }, { "cell_type": "markdown", - "id": "d3d56d06", + "id": "0090aea4", "metadata": { "editable": true }, @@ -3432,7 +3435,7 @@ }, { "cell_type": "markdown", - "id": "281ec76c", + "id": "05cf9456", "metadata": { "editable": true }, @@ -3452,7 +3455,7 @@ }, { "cell_type": "markdown", - "id": "16eb46ae", + "id": "7e4f0953", "metadata": { "editable": true }, @@ -3467,7 +3470,7 @@ }, { "cell_type": "markdown", - "id": "d6880678", + "id": "a9c33826", "metadata": { "editable": true }, @@ -3485,7 +3488,7 @@ }, { "cell_type": "markdown", - "id": "f85f760a", + "id": "752e5038", "metadata": { "editable": true }, @@ -3515,7 +3518,7 @@ }, { "cell_type": "markdown", - "id": "469842c0", + "id": "f7764abd", "metadata": { "editable": true }, @@ -3544,7 +3547,7 @@ }, { "cell_type": "markdown", - "id": "66388087", + "id": "27480bd3", "metadata": { "editable": true }, @@ -3575,7 +3578,7 @@ }, { "cell_type": "markdown", - "id": "e26957e8", + "id": "749b7131", "metadata": { "editable": true }, @@ -3598,7 +3601,7 @@ }, { "cell_type": "markdown", - "id": "31886d45", + "id": "ee1256ed", "metadata": { "editable": true }, @@ -3616,7 +3619,7 @@ }, { "cell_type": "markdown", - "id": "36603525", + "id": "a9168474", "metadata": { "editable": true }, @@ -3639,7 +3642,7 @@ }, { "cell_type": "markdown", - "id": "63bf1e9a", + "id": "ad7bb318", "metadata": { "editable": true }, @@ -3660,7 +3663,7 @@ }, { "cell_type": "markdown", - "id": "c5b98e9b", + "id": "554ca5d8", "metadata": { "editable": true }, @@ -3676,7 +3679,7 @@ }, { "cell_type": "markdown", - "id": "518e3444", + "id": "7226e95f", "metadata": { "editable": true }, diff --git a/doc/src/week47/week47.do.txt b/doc/src/week47/week47.do.txt index 2137f86c7..e318554a6 100644 --- a/doc/src/week47/week47.do.txt +++ b/doc/src/week47/week47.do.txt @@ -52,7 +52,7 @@ The theory behind support vector machines (SVM hereafter) is based on the mathematical description of so-called hyperplanes. Let us start with a two-dimensional case. This will also allow us to introduce our first SVM examples. These will be tailored to the case of two specific -classes, as displayed in the figure here based on the usage of the petal data. +classes, as displayed in the figure here based on the usage of the petal data. We assume here that our data set can be well separated into two domains, where a straight line does the job in the separating the two @@ -561,7 +561,10 @@ Below we discuss how to find the optimal values of $\lambda_i$. Before we procee Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined. Suppose now that classes overlap in feature space, as shown in the -figure here. One way to deal with this problem before we define the +figure in the "handwritten notes":"https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021" for Thursday November 25. + + +One way to deal with this problem before we define the so-called _kernel approach_, is to allow a kind of slack in the sense that we allow some points to be on the wrong side of the margin. @@ -658,8 +661,9 @@ space using other basis expansions such as higher-order polynomials, wavelets, splines etc. If our feature space is not easy to separate, as shown in the figure -here, we can achieve a better separation by introducing more complex -basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to +in the "handwritten notes":"https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021" for Thursday November 25. +, we can achieve a better separation by introducing more complex +basis functions. The ideal would be to, via a specific transformation to obtain a separation between the classes which is almost linear. The change of basis, from $x\rightarrow z=\phi(x)$ leads to the same type of equations to be solved, except that