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<HTML><HEAD></HEAD><BODY TEXT="#000000" BGCOLOR="#FFFFFF" LINK="#0000EE" VLINK="#551A8B" ALINK="#FF0000"><CENTER><TABLE BORDER CELLSPACING=0 CELLPADDING=0 HEIGHT="15%" BGCOLOR="#FDF5E6" ><TR><TD><B><FONT SIZE=+4> Adaline, Perceptronand Backpropagation</FONT></B><IMG SRC="../../../images/java_duke_small.gif" HEIGHT=38 WIDTH=49 ALIGN=ABSCENTER></TD></TR></TABLE></CENTER><H3>Introduction</H3><p>Single-layer neural networks can be trained using various learning algorithms.The best-known algorithms are the Adaline, Perceptron and Backpropagationalgorithms for supervised learning. The first two are specific to single-layerneural networks while the third can be generalized to multi-layer perceptrons.</p><H3>Credits</H3><p>The applet was written by <A HREF="http://diwww.epfl.ch/lami/team/michel">OlivierMichel</A>. This page written by <A HREF="http://diwww.epfl.ch/lami/team/herrmann/">AlixHerrmann</A>.</p><H3><HR WIDTH="100%">Presentation</H3><p>Let's consider a single-layer neural network with <I>b</I> inputs and <I>c</I>outputs:</p><UL><LI><I>W</I><SUB>ij</SUB> = weight from input i to unit j in output layer;W<I><SUB>j </SUB></I>is the vector of all the weights of the j-th neuronin the output layer.</LI><LI><I>I</I><SUP>p</SUP> = input vector (pattern p) = (<I>I</I><SUB>1</SUB><SUP>p</SUP>,<I>I</I><SUB>2</SUB><SUP>p</SUP>, ..., <I>I</I><SUB>b</SUB><SUP>p</SUP>).</LI><LI><I>T</I><SUP>p</SUP> = target output vector (pattern p) = (<I>T</I><SUB>1</SUB><SUP>p</SUP>,<I>T</I><SUB>2</SUB><SUP>p</SUP>, ..., <I>T</I><SUB>c</SUB><SUP>p</SUP>).</LI><LI><I>A</I><SUP>p</SUP> = Actual output vector (pattern p) = (<I>A</I><SUB>1</SUB><SUP>p</SUP>,<I>A</I><SUB>2</SUB><SUP>p</SUP>, ..., <I>A</I><SUB>c</SUB><SUP>p</SUP>).</LI><LI><I>g()</I> = sigmoid activation function: <I>g(a )</I> = [1 + exp (-<I>a</I>)]<SUP>-1</SUP></LI></UL><H3><HR WIDTH="100%">Theory</H3><p>Click on each topic to learn more. Then scroll down to the applet.</p><UL><LI><A HREF="theory.html#Supervised_learning">Supervised learning</A></LI><LI><A HREF="theory.html#Adaline">Adaline learning</A></LI><LI><A HREF="theory.html#Perceptron">Perceptron learning</A></LI><LI><A HREF="theory.html#Pocket">Pocket algorithm</A></LI><LI><A HREF="theory.html">Backpropagation</A></LI><LI><A HREF="theory.html#reading">Further reading</A></LI></UL><HR WIDTH="100%"><H3>Applet</H3><p>This applet allows you to compare the different learning algorithms. The network implemented here has two inputs and a single output neuron. In this tutorial, you will train it to classify 2-dimensional data pointsinto two categories.</p><P>Click <A HREF="instructions.html">here</A> to see the instructions. You may find it helpful to open a separate browser window for the instructions,so you can view them at the same time as the applet window.</p><CENTER><TABLE BORDER=2 CELLSPACING=0 CELLPADDING=0 ><TR ALIGN=CENTER VALIGN=CENTER><TD ALIGN=CENTER VALIGN=CENTER NOWRAP BGCOLOR="#C0C0C0"><APPLET code="SimplePerceptronApplet.class" codebase="../classes" width=520 height=400><param name="applet_mode" value="svm"></APPLET></TD></TR><CAPTION ALIGN=BOTTOM></CAPTION></TABLE></CENTER><HR WIDTH="100%"><H3>Questions</H3><OL><LI><B>Ideal case</B>: place 10 red points (class 1) and10 blue points (0) in two similar, distinct, and linearly separable clusters.</LI><UL><LI>Compare the speed of convergence of the four algorithms. Which one is thefastest?</LI><LI>Which values of the learning rate provide the best results ?</LI></UL><LI><B>Different cluster dispersions</B>: Place 20 red points (1) ina very narrow cluster (strongly correlated points) and 5 blue points (0)in a very wide cluster in such a way that the classes are linearly separable.</LI><UL><LI>Compare the performance of the four algorithms on this problem. Which oneis the best?</LI><LI>Which values of the learning rate provide the best results ?</LI><BR> </UL><LI><B>Imperfectly separable case:</B> Place 10 red points to (1) and10 blue points (0) in two similar, linearly separable clusters. Then,place an additional blue point inside the red cluster.</LI><UL><LI>Compare the behavior of the perceptron with the behavior of the pocketalgorithm.</LI><LI>Which values for the learning rate give the best results ?</LI></UL><LI>For which kind of problem is the Adaline algorithm the best ?</LI><LI>For which kind of problem is the Backpropagation algorithm the best ?</LI><LI>For which kind of problem is the Perceptron algorithm the best ?</LI><LI>For which kind of problem is the Pocket algorithm the best ?</LI></OL></BODY></HTML>⌨️ 快捷键说明
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