diff --git a/is/ubA/ExerciseSheet10.ipynb b/is/ubA/ExerciseSheet10.ipynb index 2ca4158..1e8c218 100644 --- a/is/ubA/ExerciseSheet10.ipynb +++ b/is/ubA/ExerciseSheet10.ipynb @@ -2,46 +2,6 @@ "cells": [ { "cell_type": "markdown", - "metadata": { - "preamble": true - }, - "source": [ - "(Defining latex commands: not to be shown...)\n", - "$$\n", - "\\newcommand{\\norm}[1]{\\left \\| #1 \\right \\|}\n", - "\\DeclareMathOperator{\\minimize}{minimize}\n", - "\\DeclareMathOperator{\\maximize}{maximize}\n", - "\\newcommand{\\real}{\\mathbb{R}}\n", - "\\newcommand{\\blasso}{\\beta^{\\mathrm{LASSO}}}\n", - "\\newcommand{\\bzero}{\\beta^0}\n", - "\\newcommand{\\bLS}{\\hat{\\beta}^{\\mathrm{LS}}}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Exercise 1 (50 points)\n", - "\n", - "Consider the following three-dimensional\n", - "datapoints:\n", - "\n", - "> (1.3,1.6,2.8), (4.3,-.4,5.8), (-0.6,3.7,0.7), (-0.4,.32,5.8),(3.3,-0.4,4.3), (-0.4,3.1,0.9)\n", - "\n", - "Perform principal component analysis by:\n", - "\n", - "+ Calculating the mean, $\\mathbf{c}$, of the data.\n", - "+ Calculating the covariance matrix $\\Sigma=\\frac{1}{6}\\sum_{n=1}^6 \\mathbf{x}(\\mathbf{x})^T - \\mathbf{c}\\mathbf{c}^T$.\n", - "+ Finding the eigenvalues and eigenvectors $\\mathbf{e}_i$ of the covariance matrix.\n", - "+ You should find that only two eigenvalues are large, and therefore that the data can be well represented using two components only. Let $\\mathbf{e}_1$ and $\\mathbf{e}_2$ be the two eigenvectors with largest eigenvalues. Calculate the two-dimensional representation of each datapoint $(\\mathbf{e}_1^T(\\mathbf{x}^n-\\mathbf{c}),\\mathbf{e}_2^T(\\mathbf{x}^n-\\mathbf{c})), n=1,\\dots,6$ \n", - "+ Calculate the reconstruction of each datapoint $\\mathbf{c}+(\\mathbf{e}_1^T(\\mathbf{x}^n-\\mathbf{c}))\\mathbf{e}_1\n", - "+(\\mathbf{e}_2^T(\\mathbf{x}^n-\\mathbf{c}))\\mathbf{e}_2,\n", - "n=1,\\dots,6$\n" - ] - }, - { - "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise 2(50 points)\n", @@ -51,7 +11,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 1, "metadata": { "collapsed": true }, @@ -87,7 +47,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 2, "metadata": { "collapsed": false }, @@ -142,7 +102,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -164,7 +124,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 4, "metadata": { "collapsed": false 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@@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -410,7 +371,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "{'C': 0.9, 'kernel': 'linear'}\n", + "{'kernel': 'linear', 'C': 0.9}\n", "Fitting the classifier to the training set\n" ] } @@ -449,7 +410,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 7, "metadata": { "collapsed": false }, @@ -459,26 +420,26 @@ "output_type": "stream", "text": [ "Predicting people's names on the test set\n", - "done in 0.099s\n", + "done in 0.124s\n", " precision recall f1-score support\n", "\n", - " Ariel Sharon 0.56 0.62 0.59 24\n", - " Colin Powell 0.78 0.32 0.46 56\n", - " Donald Rumsfeld 0.45 0.83 0.59 30\n", - " George W Bush 0.92 0.40 0.56 115\n", - "Gerhard Schroeder 0.83 0.28 0.42 36\n", - " Hugo Chavez 1.00 0.11 0.19 19\n", - " Tony Blair 0.25 0.90 0.39 42\n", + " Ariel Sharon 0.26 0.90 0.40 20\n", + " Colin Powell 1.00 0.20 0.33 56\n", + " Donald Rumsfeld 0.36 0.55 0.44 22\n", + " George W Bush 0.98 0.34 0.51 137\n", + "Gerhard Schroeder 0.59 0.42 0.49 24\n", + " Hugo Chavez 1.00 0.14 0.24 22\n", + " Tony Blair 0.28 0.95 0.43 41\n", "\n", - " avg / total 0.73 0.48 0.49 322\n", + " avg / total 0.78 0.43 0.44 322\n", "\n", - "[[15 0 5 0 0 0 4]\n", - " [10 18 8 0 0 0 20]\n", - " [ 0 0 25 0 1 0 4]\n", - " [ 0 4 14 46 0 0 51]\n", - " [ 2 0 1 1 10 0 22]\n", - " [ 0 1 0 1 1 2 14]\n", - " [ 0 0 2 2 0 0 38]]\n" + "[[18 0 1 0 0 0 1]\n", + " [23 11 2 0 0 0 20]\n", + " [10 0 12 0 0 0 0]\n", + " [13 0 16 47 2 0 59]\n", + " [ 4 0 1 0 10 0 9]\n", + " [ 1 0 0 1 5 3 12]\n", + " [ 1 0 1 0 0 0 39]]\n" ] } ], @@ -497,2048 +458,1986 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1850, 136)\n" - ] - }, - { "data": { "image/png": [ 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a/mr/ubC/mrC.pdf +++ b/mr/ubC/mrC.pdf Binary files differ diff --git a/mr/ubC/mrC.tex b/mr/ubC/mrC.tex index 8ee214a..5e49930 100644 --- a/mr/ubC/mrC.tex +++ b/mr/ubC/mrC.tex @@ -121,7 +121,18 @@ \frac{1}{2}\\\frac{\sqrt{3}}{2}\\0 \end{pmatrix}l,\ ^Bp_3=\begin{pmatrix} -\frac{1}{2}\\\frac{\sqrt{3}}{2}\\0 + \end{pmatrix}l\\ + ^Bp_4=\begin{pmatrix} + -1\\0\\0 + \end{pmatrix}l,\ ^Bp_5=\begin{pmatrix} + -\frac{1}{2}\\-\frac{\sqrt{3}}{2}\\0 + \end{pmatrix}l,\ ^Bp_6=\begin{pmatrix} + \frac{1}{2}\\-\frac{\sqrt{3}}{2}\\0 \end{pmatrix}l$ + \item $T_\Sigma=k_T\sum_{i=1}^6 \omega_i^2$ + \item $\tau_Q=k_Q \begin{pmatrix} + 0\\0\\-\omega_1+\omega_2-\omega_3+\omega_4-\omega_5+\omega_6 + \end{pmatrix}$ \end{enumerate} \end{document}