Removing some rows from a matrix, Matlab

>> A = magic(4)
A =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
>> b = [ 2     3];
>> A(b,:) = []
A =
    16     2     3    13
     4    14    15     1

More on manipulating 1-D array

Matlab Path

This is how I add a folder to the matlab path on command window:



if(~exist('varycolor'))
    addpath(genpath('~/MatlabAddon'));
end


The if condition checks for the existence of the function 'varycolor'. If it does not exists, it loads the folder where this file is present.

Deleting empty rows in a matrix

>> a = [1,2,3;4,5,6;0,7,8;0,0,0;0,0,0]

a =
     1     2     3
     4     5     6
     0     7     8
     0     0     0
     0     0     0

>> b = a(any(a,2),:)

b =

     1     2     3
     4     5     6
     0     7     8
>> b = a(all(a,2),:)

b =

     1     2     3
     4     5     6

K-Medoid Algorithm in Matlab

According to Wikipedia, k-medoids algorithm is a clustering algorithm related to the k-means algorithm. In contrast to k-means algorithm, k-medoids chooses data points as centres.  I wrote a Matlab program for implementing this algorithm. I am posting it here in the hope that people may find it useful.

function [IDX, Cluster, Err] = kmedoid2(data, NC, maxIter, varargin)
% Performs clustering using Partition Around Medoids (PAM) algorithm
% Initial clusters must be selected from the available data points

% Usage
% [IDX,C,cost] = kmedoid(data, NC, maxIter, [init_cluster])
% 
% Input : 
%       data - input data matrix
%       NC - number of clusters
%       maxIter - Maximum number of iterations
%       init_cluster - Initial cluster centers (optional)
%       init_index - Index of initial clusters
%
% Output :
%       IDX - data point index which became cluster centres
%       C -  Cluster centers
%       Err - cost associated with the clusters for all iterations
% ------------------------------------------

% Size of data
dsize = size(data);

% Number of data points
L = dsize(1);

% No. of features
NF = dsize(2); 

% Cluster size
csize = [NC, NF];

if (L < NC)
    error('Too few data points for making k clusters');
end

if(nargin > 5)
    error('Usage : [IDX,C,error] = kmedoid(data, NC, maxIter, [init_cluster], [init_idx])');
elseif(nargin == 5)
    vsize1 = size(varargin{1});
    vsize2 = length(varargin{2});
    
    if(isequal(vsize1,csize))
        Cluster = varargin{1};
    else
        error('Incorrect size for initial cluster');
    end
    
    if(vsize2 == NC)
        IDX = varargin{2};
    else
        error('Incorrect size for initial cluster index');
    end
elseif(nargin == 4)
   error('You must provide two optional arguments: init_cluster, init_idx');
elseif(nargin == 3) % no initial cluster provided
    IDX = randint(NC,1,L)+1;
    Cluster = data(IDX,:); % Initialize the initial clusters randomly
else
    display('Usage : [IDX,C] = kmedoid(data, NC, maxIter, [init_cluster], [init_idx]');
    error('Function takes at least 3 arguments');
end

%Array for storing cost for each iteration
Err = zeros(maxIter,1);

Z = zeros(NC, NF, L);
for i = 1:L
    Z(:,:,i) = repmat(data(i,:),NC,1);
end


FIRST = 1;
total_cost = 0;


for Iteration = 1:maxIter
    %disp(Iteration);
    
    if(FIRST) 
        % First time, compute the cost associated with the initial cluster
        
        C = repmat(Cluster,[1,1,L]);
        B = sqrt(sum((abs(Z-C).^2),2)); %Euclidean distance
        B1 = squeeze(B);
        [Bmin,Bidx] = min(B1,[],1);

        cost = zeros(1,NC);
        for k = 1:NC
            cost(k) = sum(Bmin(Bidx==k));
        end
        total_cost = sum(cost);
        
        FIRST = 0; % Reset the FIRST flag
        
    else % Not first time
        
        % change one cluster center randomly and see if the cost is
        % decreased. If yes, accept the change, otherwise reject the change

        while(1)
            Tidx = randint(1,1,L)+1; % find a random number betn 1 to L
            if(isempty(find(IDX==Tidx))) % Avoid previously selected centers
                break;
            end
        end
        % randomly change one cluster
        pos = randint(1,1,NC) + 1;
        OLD_IDX = IDX; % Preserve the old index list
        IDX(pos) = Tidx;

        %Assign cluster centers
        PCluster = Cluster;
        Cluster = data(IDX,:);

        % For each data point, find the cluster which is closest to it
        % and compute the cost obtained from this association

        C = repmat(Cluster,[1,1,L]);

        %B = sum(abs(Z-C),2); %Manhattan distance
        B = sqrt(sum((abs(Z-C).^2),2)); %Euclidean distance

        % Row - cluster (NC)
        % Column - each data point 1, 2, ... L
        B1 = squeeze(B);

        % For each data point, find the nearest cluster
        % size(Bmin) = 1xL
        [Bmin,Bidx] = min(B1,[],1);

        cost = zeros(1,NC);
        for k = 1:NC
            cost(k) = sum(Bmin(Bidx==k));
        end

        previous_cost = total_cost;
        total_cost = sum(cost);


        if(total_cost > previous_cost) % cost increases
            % Bad choice, restore the previous index list
            IDX = OLD_IDX;
            total_cost = previous_cost;
            Cluster = PCluster;
        end
    end
    Err(Iteration) = total_cost;
end

if(nargout == 0)
    disp(IDX);
elseif(nargout > 3)
    error('Function gives only 3 outputs');
end   
    
return  

Save this file as "kmedoid.m". Now we can create clusters for a given data set as follows :

[Idx, C,err] = kmedoid(data, 5, 1000);

Above command iterates for 1000 times to create 5 clusters for a given data.

Idx - the indices of data points selected as cluster centres.
C - cluster centres selected from the data sets
err - cost for each iteration. It can plotted to see if the error is decreasing.

Cycle through Markers in Matlab Plot

figure(2);
markers = 'ox+*sdv^<>ph';
colorset = varycolor(NC);

hold all;
for i = 1 : NC
    plot(C(:,1), C(:,2), 'LineStyle', 'None', 'Marker', markers(i), 'Markersize', 10);
end

Avoid loops in Matlab

Following examples demonstrate how one can avoid for loops in MATLAB to speed up execution :

1. Vector assignment
   
   x = rand(1,100);
   %In spite of :
   for k=1:100
   y(k) = sin(x(k));
   end
   % We can use :
   y(:) = sin(x(:));
   
   
   
2. Subtracting a vector from each row/column of a matrix
   
   a = [1 2 3]
   b = magic(3);
   c = repmat(a,3,1) - b;
   
   
3. Use logical indexing to operate on a part of a matrix. Use "find" command wherever possible.
   
   a = 200:-10:50;
   % replace the value 120 by 0
   a(find(a == 120)) = 0;
   a =   200   190   180   170   160   150   140   130     0   110   100    90    80    70    60    50
   
   Another example :
   
   % [idx1, idx2] = find(angle < 0);
   % idx = [idx2 idx2];
   % for j = 1:length(idx)
   %     angle(idx(j,1),idx(j,2))=360+angle(idx(j,1),idx(j,2));
   % end
   can be replaced by following code :
   
   angle(angle<0) = angle(angle<0)+360;
   
   
   
4. Useful commands for matrices and vectors :
   
   sum, norm, diff, abs, max, min, sort
   
   
   

   Useful link in this direction

   http://www.ee.columbia.edu/~marios/matlab/matlab_tricks.html  

   
   

Index of an array element closest to an arbitrary value

>> x = 1:100:1000;

The index of the array which is closest to say 130 is given by

>> [v,idx] = min(abs(x-130));

The answer is

v = 29, idx = 2

Matlab Plotting within a loop with different colors

Matlab by default has 7 colors. Following code demonstrates how one can invoke plot command within a for loop so that each time it plots a given data set in a different color. Don't worry about the variables that are used in this piece of code. You should notice that we can pass randomized color information to the plot command inside a for loop.


hold on;
for k = 1:length(idx)
ridx = find(idx == k);
color = rand(1,3);
for j = 1:length(ridx);
plot(logdata(:,1,ridx(j)),logdata(:,2,ridx(j)), ...
'Color',color,'LineWidth',2);
end
end
hold off;

Matlab's NN Toolbox

Following program demonstrates the use of a Feed-forward network in Matlab

%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Matlab Example 1
% Learning XOR function using a MLP

% Create a FFN
net = newff([0 1; 0 1], [2 1], {'logsig', 'logsig'},'traingd');

%Training patterns
P = [0 0 1 1; 0 1 0 1];
T = [0 1 1 0];

% Training parameters
net.trainParam.show = 100;
net.trainParam.lr = 0.8;
net.trainParam.epochs = 3000;
net.trainParam.goal = 1e5;

%Train the network
[net,tr] = train(net, P, T);

% Test the network
Y = sim(net, P)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Following program demonstrates the use of RBFN in matlab to learn a nonlinear function

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MATLAB EXAMPLE 2
% Radial Basis Function Network (RBFN)
clear all;

% Data set for training

x = [0:4:200];
yd = sqrt(x);
spread = 20;

% Create a RBF network

net = newrb(x, yd, 1e-5,20);

%test data
P = [0:0.01:200];
T = sqrt(P);
T1 = sim(net, P);

%mean square error
mse(T1-T)
figure(2)
plot(P,T,'r', P, T1, 'b--');
legend('Desired output', 'Actual Output');
xlabel('Input');
ylabel('Output');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Matlab Editor : Rapid programming

Matlab has introduced something called "cells" to speed up writing/testing programs. Just go through this Flash animation to know more about cells.

http://www.mathworks.com/support/2007a/matlab/7.4/demos/RapidCodeIterationUsingCells_viewlet_swf.html


I had been avoiding Matlab for a long time. Its being a proprietory software. But I must admit, its simply great. They just need to reduce the price.