Principal Component Analysis

This is about what I think I understood about Principal Component Analysis. I will update this blog post later.

The code is in github and it works but I think the eigen values could be wrong. I have to test it further.

These are the two main functions.

    """Compute the covariance matrix for a given dataset.
    """
def estimateCovariance( data ):
    print data
    mean = getmean( data )
    print mean
    dataZeroMean = map(lambda x : x - mean, data )
    print dataZeroMean
    covar = map( lambda x : np.outer(x,x) , dataZeroMean )
    print getmean( covar ) 
    return getmean( covar )

    """Computes the top `k` principal components, corresponding scores, and all eigenvalues.
    """
def pca(data, k=2):
    
    d = estimateCovariance(  data )
    
    eigVals, eigVecs = eigh(d)

    validate( eigVals, eigVecs )
    inds = np.argsort(eigVals)[::-1]
    topComponent = eigVecs[:,inds[:k]]
    print '\nTop Component: \n{0}'.format(topComponent)
    
    correlatedDataScores = map(lambda x : np.dot( x ,topComponent), data )
    print ('\nScores : \n{0}'
       .format('\n'.join(map(str, correlatedDataScores))))
    print '\n eigenvalues: \n{0}'.format(eigVals[inds])
    return topComponent,correlatedDataScores,eigVals[inds]