laydi/scripts/lpls/lpls.py

import sys
from pylab import *
import matplotlib
from scipy import *
from scipy.linalg import inv,norm

sys.path.append("../../fluents/lib")
import select_generators

def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', verbose=True):
    """ L-shaped Partial Least Sqaures Regression by the nipals algorithm.

    (X!Z)->Y
    :input:
        X : data matrix (m, n)
        Y : data matrix (m, l)
        Z : data matrix (n, o)
        alpha : how much z influence (1=max, 0=none)

    :output:
      T : X-scores
      W : X-weights/Z-weights
      P : X-loadings
      Q : Y-loadings
      U : X-Y relation
      L : Z-scores
      K : Z-loads
      B : Regression coefficients X->Y
      b0: Regression coefficient intercept
      evx : X-explained variance
      evy : Y-explained variance
      evz : Z-explained variance

    :Notes:
    
    """
    if mean_ctr:
        xctr, yctr, zctr = mean_ctr
        X, mnX = center(X, xctr)
        Y, mnY = center(Y, yctr)
        Z, mnZ = center(Z, zctr)

    varX = pow(X, 2).sum()
    varY = pow(Y, 2).sum()
    varZ = pow(Z, 2).sum()
    
    m, n = X.shape
    k, l = Y.shape
    u, o = Z.shape

    # initialize 
    U = empty((k, a_max))
    Q = empty((l, a_max))
    T = empty((m, a_max))
    W = empty((n, a_max))
    P = empty((n, a_max))
    K = empty((o, a_max))
    L = empty((u, a_max))
    B = empty((a_max, n, l))
    b0 = empty((a_max, m, l))
    var_x = empty((a_max,))
    var_y = empty((a_max,))
    var_z = empty((a_max,))

    for a in range(a_max):
        if verbose:
            print "\n Working on comp. %s" %a
        u = Y[:,:1]
        diff = 1
        MAX_ITER = 100
        lim = 1e-7
        niter = 0
        while (diff>lim and niter<MAX_ITER):
            niter += 1
            u1 = u.copy()
            w = dot(X.T, u)
            w = w/sqrt(dot(w.T, w))
            l = dot(Z, w)
            k = dot(Z.T, l)
            k = k/sqrt(dot(k.T, k))
            w = alpha*k + (1-alpha)*w
            w = w/sqrt(dot(w.T, w))
            t = dot(X, w)
            c = dot(Y.T, t)
            c = c/sqrt(dot(c.T, c))
            u = dot(Y, c)
            diff = abs(u1 - u).max()
        if verbose:
            print "Converged after %s iterations" %niter
        tt = dot(t.T, t)
        p = dot(X.T, t)/tt
        q = dot(Y.T, t)/tt
        l = dot(Z, w)
        U[:,a] = u.ravel()
        W[:,a] = w.ravel()
        P[:,a] = p.ravel()
        T[:,a] = t.ravel()
        Q[:,a] = q.ravel()
        L[:,a] = l.ravel()
        K[:,a] = k.ravel()

        X = X - dot(t, p.T)
        Y = Y - dot(t, q.T)
        Z = (Z.T - dot(w, l.T)).T

        var_x[a] = pow(X, 2).sum()
        var_y[a] = pow(Y, 2).sum()
        var_z[a] = pow(Z, 2).sum()
        B[a] = dot(dot(W[:,:a+1], inv(dot(P[:,:a+1].T, W[:,:a+1]))), Q[:,:a+1].T)
        b0[a] = mnY - dot(mnX, B[a])
    # variance explained
    evx = 100.0*(1 - var_x/varX)
    evy = 100.0*(1 - var_y/varY)
    evz = 100.0*(1 - var_z/varZ)
    if scale=='loads':
        tnorm = apply_along_axis(norm, 0, T)
        T = T/tnorm
        Q = Q*tnorm
        W = W*tnorm
    return T, W, P, Q, U, L, K, B, b0, evx, evy, evz, mnX, mnY, mnZ

def svd_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], verbose=True):
    """
    NB: In the works ...
    L-shaped Partial Least Sqaures Regression by the svd algorithm.

    (X!Z)->Y
    :input:
        X : data matrix (m, n)
        Y : data matrix (m, l)
        Z : data matrix (n, o)

    :output:
      T : X-scores
      W : X-weights/Z-weights
      P : X-loadings
      Q : Y-loadings
      U : X-Y relation
      L : Z-scores
      K : Z-loads
      B : Regression coefficients X->Y
      b0: Regression coefficient intercept
      evx : X-explained variance
      evy : Y-explained variance
      evz : Z-explained variance

    :Notes:
        Not quite there ,,,,,,,,,,,,,,
    
    """
    if mean_ctr:
        xctr, yctr, zctr = mean_ctr
        X, mnX = center(X, xctr)
        Y, mnY = center(Y, xctr)
        Z, mnZ = center(Z, zctr)

    varX = pow(X, 2).sum()
    varY = pow(Y, 2).sum()
    varZ = pow(Z, 2).sum()
    
    m, n = X.shape
    k, l = Y.shape
    u, o = Z.shape

    # initialize 
    U = empty((k, a_max))
    Q = empty((l, a_max))
    T = empty((m, a_max))
    W = empty((n, a_max))
    P = empty((n, a_max))
    K = empty((o, a_max))
    L = empty((u, a_max))
    var_x = empty((a_max,))
    var_y = empty((a_max,))
    var_z = empty((a_max,))
    
    for a in range(a_max):
        if verbose:
            print "\n Working on comp. %s" %a
        xyz = dot(dot(Z,X.T),Y)
        u,s,vt = linalg.svd(xyz, 0)
        w = u[:,o]
        t = dot(X, w)
        tt = dot(t.T, t)
        p = dot(X.T, t)/tt
        q = dot(Y.T, t)/tt
        l = dot(Z.T, w)
        W[:,a] = w.ravel()
        P[:,a] = p.ravel()
        T[:,a] = t.ravel()
        Q[:,a] = q.ravel()
        L[:,a] = l.ravel()
        K[:,a] = k.ravel()
        X = X - dot(t, p.T)
        Y = Y - dot(t, q.T)
        Z = (Z.T - dot(w, l.T)).T
        var_x[a] = pow(X, 2).sum()
        var_y[a] = pow(Y, 2).sum()
        var_z[a] = pow(Z, 2).sum()
    B = dot(dot(W, inv(dot(P.T, W))), Q.T)
    b0 = mnY - dot(mnX, B)
    # variance explained
    evx = 100.0*(1 - var_x/varX)
    evy = 100.0*(1 - var_y/varY)
    evz = 100.0*(1 - var_z/varZ)
    return T, W, P, Q, U, L, K, B, b0, evx, evy, evz


def lplsr(X, Y, Z, a_max, mean_ctr=[2,0,1]):
    """ Haralds LPLS.
    """
    if mean_ctr!=None:
        xctr, yctr, zctr = mean_ctr
        X, mnX = center(X, xctr)
        Y, mnY = center(Y, yctr)
        Z, mnZ = center(Z, zctr)

    varX = pow(X, 2).sum()
    varY = pow(Y, 2).sum()
    varZ = pow(Z, 2).sum()
    m, n = X.shape
    k, l = Y.shape
    u, o = Z.shape

    # initialize
    Wy = empty((l, a_max))
    Py = empty((l, a_max))
    Ty = empty((m, a_max))
    Tz = empty((o, a_max))
    Wz = empty((u, a_max))
    Pz = empty((u, a_max))
    var_x = empty((a_max,))
    var_y = empty((a_max,))
    var_z = empty((a_max,))

    # residuals
    Ey = Y.copy()
    Ez = Z.copy()
    Ex = X.copy()
    for i in range(a_max):
        YtXZ = dot(Ey.T, dot(X, Ez.T))
        U, S, V = linalg.svd(YtXZ)
        wy = U[:,0]
        print wy
        wz = V[0,:]
        ty = dot(Ey, wy)
        tz = dot(Ez.T, wz)
        py = dot(Ey.T, ty)/dot(ty.T,ty)
        pz = dot(Ez, tz)/dot(tz.T,tz)
        Wy[:,i] = wy
        Wz[:,i] = wz
        Ty[:,i] = ty
        Tz[:,i] = tz
        Py[:,i] = py
        Pz[:,i] = pz
        Ey = Ey - outer(ty, py.T)
        Ez = (Ez.T - outer(tz, pz.T)).T
        var_y[i] = pow(Ey, 2).sum()
        var_z[i] = pow(Ez, 2).sum()

    tyd = apply_along_axis(norm, 0, Ty)
    tzd = apply_along_axis(norm, 0, Tz)
    Tyu = Ty/tyd
    Tzu = Tz/tzd
    C = dot(dot(Tyu.T, X), Tzu)
    for i in range(a_max):
        Ex = Ex - dot(dot(Ty[:,:i+1],C[:i+1,:i+1]), Tz[:,:i+1].T)
        var_x[i] = pow(Ex,2).sum()
    # variance explained
    print "var_x:"
    print var_x
    print "varX total:"
    print varX

    evx = 100.0*(1 - var_x/varX)
    evy = 100.0*(1 - var_y/varY)
    evz = 100.0*(1 - var_z/varZ)

    return Ty, Tz, Wy, Wz, Py, Pz, C, Ey, Ez, Ex, evx, evy, evz

def bifpls(X, Y, Z, a_max, alpha):
    """Swedssihsh LPLS by nipals.
    """
    u = X[:,0]
    Ey = Y.copy()
    Ez = Z.copy()
    for i in range(100):
        w = dot(X.T,u)
        w = w/vnorm(w)
        t = dot(X, w)
        q = dot(Ey, t.T)/dot(t.T,t)
        qnorm = vnorm(q)
        q = q/qnorm
        v = dot(Ez, q)
        s = dot(Ez.T, v)/dot(v.T,v)
        v = v*vnorm(s)
        s = s/vnorm(s)
        c = qnorm*(alpha*q + (1-alpha)*s)
        u = dot(Ey, c)/dot(s.T,s)
        p = dot(X.T, t)/dot(t.T,t)
        v2 = dot(Ez, s)/dot(s.T,s)
    Ey = Ey - dot(t, p.T)
    Ez = Ez - dot(v2, c.T)
    # variance explained
    evx = 100.0*(1 - var_x/varX)
    evy = 100.0*(1 - var_y/varY)
    evz = 100.0*(1 - var_z/varZ)

def center(a, axis):
    # 0 = col center, 1 = row center, 2 = double center
    # -1 = nothing
    if len(a.shape)==1:
        mn = a.mean()
        return a - mn, mn
    if a.shape[0]==1 or a.shape[1]==1:
        mn = a.mean()
        return a - mn, mn
    if axis==-1:
        mn = zeros((a.shape[1],))
        return a - mn, mn
    elif axis==0:
        mn = a.mean(0)
        return a - mn, mn
    elif axis==1:
        mn = a.mean(1)[:,newaxis]
        return a - mn , mn
    elif axis==2:
        mn = a.mean(1)[:,newaxis] + a.mean(0) - a.mean()
        return a - mn, mn
    else:
        raise IOError("input error: axis must be in [-1,0,1,2]")

def correlation_loadings(D, T, P, test=True):
    """ Returns correlation loadings.

    :input:
        - D: [nsamps, nvars], data (non-centered data)
        - T: [nsamps, a_max], Scores
        - P: [nvars, a_max], Loadings
    :ouput:
        - Rloads: [nvars, a_max], Correlation loadings
        - rmseVars: [nvars], scaling coeff. for each var in D

    :notes:
        - FIXME: Calculation is not valid .... using corrceof instead 
    """
    nsamps, nvars = D.shape
    nsampsT, a_max = T.shape
    nvarsP, a_maxP = P.shape
    if nsamps!=nsampsT: raise IOError("D/T mismatch")
    if a_max!=a_maxP: raise IOError("a_max mismatch")
    if nvars!=nvarsP: raise IOError("D/P mismatch")

    #init
    Rloads = empty((nvars, a_max), 'd')
    stdvar = stats.std(D, 0)
    rmseVars = sqrt(nsamps-1)*stdvar

    # center
    D = D - D.mean(0)
    TT = diag(dot(T.T, T))
    sTT = sqrt(TT)
    for a in range(a_max):
        Rloads[:,a] = sTT[a]*P[:,a]/rmseVars
    R = empty_like(Rloads)
    for a in range(a_max):
        for k in range(nvars):
            r = corrcoef(D[:,k], T[:,a])
            R[k,a] = r[0,1]
    #Rloads = R
    return Rloads, R, rmseVars



def cv_lpls(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,1]):
    """Performs crossvalidation to get generalisation error in lpls"""

    # if double centering of x or y:
    #     row-center prior to cross validation (as this is independent of subsets)
    if mean_ctr[0]==2:
        mnx_row = X.mean(1)[:,newaxis]
        X = X - mnx_row
        mean_ctr[0] = 0
    else:
        mnx_row = 0
    if mean_ctr[1]==2:
        if Y.shape[1]!=1:
            mny_row = Y.mean(1)[:,newaxis]
            Y = Y - mny_row
    else:
        mny_row = 0
    
    cv_iter = select_generators.pls_gen(X, Y, n_blocks=nsets,center=False,index_out=True)
    k, l = Y.shape
    Yhat = empty((a_max,k,l), 'd')
    for i, (xcal,xi,ycal,yi,ind) in enumerate(cv_iter):
        T, W, P, Q, U, L, K, B, b0, evx, evy, evz, mnx, mny, mnz = nipals_lpls(xcal,ycal,Z,
                                                                               a_max=a_max,
                                                                               alpha=alpha,
                                                                               mean_ctr=mean_ctr,
                                                                               verbose=False)
        
        for a in range(a_max):
            xc = xi - mnx
            Yhat[a,ind,:] = mny + dot(xc, B[a])
        
    Yhat_class = zeros_like(Yhat)
    for a in range(a_max):
        for i in range(k):
            Yhat_class[a,i,argmax(Yhat[a,i,:])] = 1.0
    class_err = 100*((Yhat_class+Y)==2).sum(1)/Y.sum(0).astype('d')
    
    sep = (Y - Yhat)**2
    rmsep = sqrt(sep.mean(1))
    return rmsep, Yhat, class_err

def jk_lpls(X, Y, Z, a_max, nsets=None, xz_alpha=.5, mean_ctr=[2,0,1]):
    cv_iter = select_generators.pls_gen(X, Y, n_blocks=nsets,center=False,index_out=False)
    m, n = X.shape
    k, l = Y.shape
    o, p = Z.shape
    if nsets==None:
        nsets = m
    WWx = empty((nsets, n, a_max), 'd')
    WWz = empty((nsets, o, a_max), 'd')
    WWy = empty((nsets, l, a_max), 'd')
    for i, (xcal,xi,ycal,yi) in enumerate(cv_iter):
        T, W, P, Q, U, L, K, B, b0, evx, evy, evz,mnx,mny,mnz = nipals_lpls(xcal,ycal,Z,
                                                                            a_max=a_max,
                                                                            alpha=xz_alpha,
                                                                            mean_ctr=mean_ctr,
                                                                            scale='loads',
                                                                            verbose=False)
        WWx[i,:,:] = W
        WWz[i,:,:] = L
        WWy[i,:,:] = Q

    return WWx, WWz, WWy