ó Lá†Oc@s¤dZddlZddlZddlZddljZddddd„Z d„Z ddd„Z de fd„ƒYZ d „Zd „Zd „Zd „ZdS( so prpy module lindisc.py Jason Corso (jcorso@acm.org) This module has been programmed to support teaching an introduction to pattern recognition course. Contains implementations of linear discriminants. This file is organized alphabetically by function name. Some pointers on convention: 1. Generally, data is stored in an N x D matrix, where N is the number of samples and D is the dimension. 2. Class information is typically stored in a parallel N x 1 vector. 3. All plotting functions assume the data is 2 dimensions. Please report bugs/fixes/enhancements to jcorso@acm.org when you find/make them. i˙˙˙˙Nic CsĂ|dkrtjƒ}ntj|jƒtjƒtjddddgƒtjtƒtjƒ|dk r ||j dƒ|dk}xyt |j dƒD]a}||s˘tj ||df||dfddtddd dddgd d d d ƒq˘q˘Wnx˘t |j dƒD]}||dkrqtj ||df||dft jddddtƒqtj ||df||dft jddddtƒqWt|||ƒ|S(s2 Debug two-class plotting and draw the linear discriminant. (X,Y) are the data set Z is the normalized data set a is the weight vector, b (if exists) is the bias (a'x + b is the classifier) m is the margin (if exists) h is the figure handle to draw into iö˙˙˙i iitgotholdt markersizeg,@tmarkerfacecolortmarkeredgecolortgtmarkeredgewidthgř?i˙˙˙˙g @N(tNonetplttfiguretnumbertclftaxistgridtTruetshowtsumtrangetshapetplott datatoolstkDrawt plotWVector( tXtYtatbthtZtmtBti((s4/home/csefaculty/jcorso/555code/code/prpy/lindisc.pyt debugPlots&      2&=>cCs&|jƒ}||dkcd9<|S(sN Data normalization procedure: multiple data values by -1 if the class is -1. i˙˙˙˙(tcopy(RRtXhat((s4/home/csefaculty/jcorso/555code/code/prpy/lindisc.pyt normalizeGs c Cstjdƒ}|d k r1| |d|d 0 no margin Basic assumption we have 2D points in a plane, for debugging and visualization. iRi siteration %d %.4f %.4f is %d of %d samples correctR( R#tlenR!R'R)R*R Rt raw_input( RRta0tetaRtnttRRR((s4/home/csefaculty/jcorso/555code/code/prpy/lindisc.pytbatchPerceptrons$  cCs“t||ƒ}t|ƒ}tj|ƒr@tj|ƒ|}ntjj|ƒj|ƒ}|tjj|ƒ}t |||d|d|ƒ}|S(sí Run a least-squares estimation of the discriminant via the pseudo-inverse. X is n by d Y is n by 1 and is -1 or +1 for classes Linear separability is not needed and a "best" answer will still be returned. RR( R#RAR'R,tonesR)tpinvR;R*R (RRRRRERR((s4/home/csefaculty/jcorso/555code/code/prpy/lindisc.pytmseÂs  c CsÁt||ƒ}t|ƒ}d}d}|jƒ}|tjj|ƒ}t|||d|ƒ} d} x7| |kr | d7} |j||dd…fƒ} d|| | |fGH| dkrd} |d7}d||d|dfGHt|||d| d|ƒtj ||df||dfdd t d d ƒ||||dd…fj ƒ}|tjj|ƒ}t ƒ} | d krPqn|d|}qjWt|||d| d|ƒ|S( sÝ Run the single-sample perceptron algorithm on (X,Y) to learn a linear discriminant. Batch Perceptron on D (not normalized) for dimension d and n samples X is n by d Y is n by 1 and is -1 or +1 for classes Assume (linear) separability. sum_{y in incorrect} -a'y for all x in D (column vector) a'x > 0 no margin Basic assumption we have 2D points in a plane, for debugging and visualization. iRiNs/sample %d, val %0.3f, current count is %d of %ds'correction iteration %d %.4f %.4fRtyoRRg,@tq( R#RAR!R'R)R*R R;RRRtsqueezeRB( RRRCRDRRERRFRRtcounttvalts((s4/home/csefaculty/jcorso/555code/code/prpy/lindisc.pyt ssPerceptronŰs4     3$  c Cst||ƒ}t|ƒ}d}d}|jƒ} | tjj| ƒ} t||| d|d|ƒ} d} x}| |krě| d7} | j||dd…fƒ} d|| | |fGH| |krŰd} |d7}d|| d| dfGHt||| d| d|d|ƒtj ||df||dfd d t d d ƒ|| tj tjj||dd…fj ƒƒd ƒ} | || ||dd…fj ƒ} | tjj| ƒ} t ƒ}|dkrŰPqŰn|d|}qpWt||| d| d|d|ƒ| S(s• Run the single-sample relaxation with margin procedure. Single-Sample Relaxation with the margin on D (not normalized) for dimension d and n samples D is n by d + 1 where the last column of D is Y is n by 1 and is -1 or +1 for classes Assume separability with the margin 1/2 sum_{y in incorrect} (a'y - b)^2 / ||y|| for all x in D (column vector) iRRiNs/sample %d, val %0.3f, current count is %d of %ds'correction iteration %d %.4f %.4fRRKRRg,@iRL(R#RAR!R'R)R*R R;RRRtpowerRMRB(RRRCRDRRRERRFRRRNROtdistRP((s4/home/csefaculty/jcorso/555code/code/prpy/lindisc.pyt ssRelaxations6     "3<(  "(R@RtsystnumpyR'tmatplotlib.pyplottpyplotRRR R#RtobjectR6RGRJRQRT(((s4/home/csefaculty/jcorso/555code/code/prpy/lindisc.pyts   ( ( 5  @