MATLAB: K-means for stock market timeseries

k-means - timeseries

I am doing my research to test the accuracy of different volatility models in forecasting the stock market volatility using indexes time series. I need to cluster the data normally with K-means into two groups. I already have the time series from different stock markets but all came with the same length. I Just need to cluster each of them into two subsets. Then the first subset will be used to train the models and the second one will be used to test and to forecast the models. I wonder if you can give the direct code or at least how to start the k-means in Matlab.

I seriously look forward to hearing from you very soon.

Regards, Abdelrazzaq.

Best Answer

The function kmeans is part of the Statistics Toolbox in MATLAB. The following code demonstrates how to use k-means to cluster data into two groups and pull out the individual groups.

% Generate random data
nSamples = 100;
sampleWidth = 5;
X = rand(nSamples,sampleWidth); 
trainingSetSize = 20;
% seperate into two groups using euclidean distance
% IDX will be size nsamples x 1 where each element indicates the label at
% that index
IDX = kmeans( X , 2 , 'distance' , 'sqEuclidean');
% separate the data into two groups
G1 = X(IDX == 1 , : );
G2 = X(IDX == 2 , : );

As a result of the k-means clustering, the groups will be self similar and would likely make very bad training and test data for an ML algorithm. A much more suitable function for generating training and test sets is the randsample function in the Statistics toolbox. By uniformly sampling a population at random, this function will provide more diverse training data to your ML algorithm and help improve its robustness.

% Randomly select trainingSetSize samples without replacement
rsIDX = randsample( size(X,1) , trainingSetSize  );
% Create a logical mask for the selected values
tsMASK = false( nSamples , 1 );
tsMASK( rsIDX ) = true;
% Separate the data into training and test samples.
GTraining = X( tsMASK , : );
GTest = X( ~ tsMASK , : ) ;

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MATLAB: KMEANS delivers different results on the same data set

Christian, the kmeans functions uses a randomly-chosen starting configuration:

>> help kmeans
 kmeans K-means clustering.
[snip]
    'Start' - Method used to choose initial cluster centroid positions,
       sometimes known as "seeds".  Choices are:
           'sample'  - Select K observations from X at random (the default)
           'uniform' - Select K points uniformly at random from the range
                       of X.  Not valid for Hamming distance.
           'cluster' - Perform preliminary clustering phase on random 10%
                       subsample of X.  This preliminary phase is itself
                       initialized using 'sample'.
            matrix   - A K-by-P matrix of starting locations.  In this case,
                       you can pass in [] for K, and kmeans infers K from
                       the first dimension of the matrix.  You can also
                       supply a 3D array, implying a value for 'Replicates'
                       from the array's third dimension.

Like many optimizations, the K-Means algorithm can end up with different solutions for different starting points. You can take advantage of the randomness built into the kmeans function by running several replicates from different starting points:

    'Replicates' - Number of times to repeat the clustering, each with a
       new set of initial centroids.  A positive integer, default is 1.

Hope this helps

MATLAB: K-means without iteration

Not sure I follow exactly, but you could use grpstats to compute the coordinatewise means of data for each distinct value of T. You could use pdist2 to compute the distance from each data point to each centroid. You could use min to figure out which centroid is closest to each point (note the second output of the min command).

Best Answer

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MATLAB: KMEANS delivers different results on the same data set

MATLAB: K-means without iteration

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