def clusterVal(y, clusterid):
    '''
    CLUSTERVAL Estimate cluster validity using Entropy, Purity, Rand Statistic,
    and Jaccard coefficient.
    
    Usage:
      Entropy, Purity, Rand, Jaccard = clusterval(y, clusterid);
    
    Input:
       y         N-by-1 vector of class labels 
       clusterid N-by-1 vector of cluster indices
    
    Output:
      Entropy    Entropy measure.
      Purity     Purity measure.
      Rand       Rand index.
      Jaccard    Jaccard coefficient.
    '''
    
    import numpy as np    
    
    y = np.asarray(y).ravel(); clusterid = np.asarray(clusterid).ravel()
    C = np.unique(y).size; K = np.unique(clusterid).size; N = y.shape[0]
    EPS = 2.22e-16
    
    p_ij = np.zeros((K,C))          # probability that member of i'th cluster belongs to j'th class
    m_i = np.zeros((K,1))           # total number of objects in i'th cluster
    for k in range(K):
        m_i[k] = (clusterid==k).sum()
        yk = y[clusterid==k]
        for c in range(C):
            m_ij = (yk==c).sum()    # number of objects of j'th class in i'th cluster
            p_ij[k,c] = m_ij.astype(float)/m_i[k]
    entropy = ( (1-(p_ij*np.log2(p_ij+EPS)).sum(axis=1))*m_i.T ).sum() / (N*K) 
    purity = ( p_ij.max(axis=1) ).sum() / K

    f00=0; f01=0; f10=0; f11=0
    for i in range(N):
        for j in range(i):
            if y[i]!=y[j] and clusterid[i]!=clusterid[j]: f00 += 1;     # different class, different cluster    
            elif y[i]==y[j] and clusterid[i]==clusterid[j]: f11 += 1;   # same class, same cluster
            elif y[i]==y[j] and clusterid[i]!=clusterid[j]: f10 += 1;   # same class, different cluster    
            else: f01 +=1;                                              # different class, same cluster
    rand = np.float(f00+f11)/(f00+f01+f10+f11)
    jaccard = np.float(f11)/(f01+f10+f11)

    return entropy, purity, rand, jaccard