exercise:27313b016d: Difference between revisions

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(Created page with "<div class="d-none"><math> \newcommand{\indexmark}[1]{#1\markboth{#1}{#1}} \newcommand{\red}[1]{\textcolor{red}{#1}} \newcommand{\NOTE}[1]{$^{\textcolor{red}\clubsuit}$\marginpar{\setstretch{0.5}$^{\scriptscriptstyle\textcolor{red}\clubsuit}$\textcolor{blue}{\bf\tiny #1}}} \newcommand\xoverline[2][0.75]{% \sbox{\myboxA}{$\m@th#2$}% \setbox\myboxB\null% Phantom box \ht\myboxB=\ht\myboxA% \dp\myboxB=\dp\myboxA% \wd\myboxB=#1\wd\myboxA% Scale phantom...")
 
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\usepackage{pgfplots}
Replicate the results of [[guide:6588b14666#SEP-FIG-2|Figure]]. More precisely, run the code from [[guide:6588b14666#PROBL-6-2 |Problem]] for different dimensions <math>d</math> and different distance functions <math>\Delta=\Delta(d)</math>, e.g., <math>\Delta\equiv c > 0</math>, <math>\Delta=2\sqrt{d}</math>, <math>\Delta=d^{0.3}</math> or <math>\Delta=d^{1/4}</math>. Plot the rate of correctly classified data points as a function of the dimension. Simulate also the case <math>\Delta=2d^{0.2}</math> and confirm that this leads to a low correct classification rate which decreases for large dimensions.
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\newcommand{\mathds}{\mathbb}</math></div>
<span id{{=}}"SEP-FIG-4"/>
Replicate the results of [[#SEP-FIG-2|Figure]]. More precisely, run the code from [[#PROBL-6-2 |Problem]] for different dimensions <math>d</math> and different distance functions <math>\Delta=\Delta(d)</math>, e.g., <math>\Delta\equiv c > 0</math>, <math>\Delta=2\sqrt{d}</math>, <math>\Delta=d^{0.3}</math> or <math>\Delta=d^{1/4}</math>. Plot the rate of correctly classified data points as a function of the dimension. Simulate also the case <math>\Delta=2d^{0.2}</math> and confirm that this leads to a low correct classification rate which decreases for large dimensions.
<div class{{=}}"d-flex justify-content-center">
\begin{center}
[[File:tikzebf95.png | 600px | thumb | Average rate of correctly classified data points for <math>\Delta=2d^{0.2}</math>.]]
\begin{tikzpicture}
</div>
\pgfplotsset{scaled x ticks=false}
\begin{axis}
[
axis line style={thick, shorten  > =-5pt, shorten  < =-2pt},
y=100pt,
x=0.0095pt,
axis y line=left,
axis x line=middle,
axis line style={- > },
no markers,
tick align=outside,
major tick length=2pt,
ymin=0.5,
ymax=1.05,
ytick={0.5,0.6,...,1},
xmin=200,xmax=10000,
xtick={500,3000,6000,9000},
every tick label/.append style={font=\tiny},
xlabel=<math>\scriptstyle d</math>,
every axis x label/.style={
  at={(ticklabel* cs:1.07)},
  anchor=west,
},
every axis y label/.style={
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\end{axis}
\end{tikzpicture}
\nopagebreak[4]\begin{fig}\label{SEP-FIG-4}Average rate of correctly classified data points for <math>\Delta=2d^{0.2}</math>.\end{fig}
\end{center}

Latest revision as of 02:24, 2 June 2024

[math] \newcommand{\smallfrac}[2]{\frac{#1}{#2}} \newcommand{\medfrac}[2]{\frac{#1}{#2}} \newcommand{\textfrac}[2]{\frac{#1}{#2}} \newcommand{\tr}{\operatorname{tr}} \newcommand{\e}{\operatorname{e}} \newcommand{\B}{\operatorname{B}} \newcommand{\Bbar}{\overline{\operatorname{B}}} \newcommand{\pr}{\operatorname{pr}} \newcommand{\dd}{\operatorname{d}\hspace{-1pt}} \newcommand{\E}{\operatorname{E}} \newcommand{\V}{\operatorname{V}} \newcommand{\Cov}{\operatorname{Cov}} \newcommand{\Bigsum}[2]{\mathop{\textstyle\sum}_{#1}^{#2}} \newcommand{\ran}{\operatorname{ran}} \newcommand{\card}{\#} \renewcommand{\P}{\operatorname{P}} \renewcommand{\L}{\operatorname{L}} \newcommand{\mathds}{\mathbb}[/math]

Replicate the results of Figure. More precisely, run the code from Problem for different dimensions [math]d[/math] and different distance functions [math]\Delta=\Delta(d)[/math], e.g., [math]\Delta\equiv c \gt 0[/math], [math]\Delta=2\sqrt{d}[/math], [math]\Delta=d^{0.3}[/math] or [math]\Delta=d^{1/4}[/math]. Plot the rate of correctly classified data points as a function of the dimension. Simulate also the case [math]\Delta=2d^{0.2}[/math] and confirm that this leads to a low correct classification rate which decreases for large dimensions.

Average rate of correctly classified data points for [math]\Delta=2d^{0.2}[/math].