412 lines
11 KiB
Python
412 lines
11 KiB
Python
import sys
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from pylab import *
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import matplotlib
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from scipy import *
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from scipy.linalg import inv,norm
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sys.path.append("../../fluents/lib")
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import select_generators
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def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', verbose=True):
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""" L-shaped Partial Least Sqaures Regression by the nipals algorithm.
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(X!Z)->Y
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:input:
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X : data matrix (m, n)
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Y : data matrix (m, l)
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Z : data matrix (n, o)
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:output:
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T : X-scores
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W : X-weights/Z-weights
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P : X-loadings
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Q : Y-loadings
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U : X-Y relation
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L : Z-scores
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K : Z-loads
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B : Regression coefficients X->Y
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b0: Regression coefficient intercept
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evx : X-explained variance
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evy : Y-explained variance
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evz : Z-explained variance
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:Notes:
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"""
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if mean_ctr:
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xctr, yctr, zctr = mean_ctr
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X, mnX = center(X, xctr)
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Y, mnY = center(Y, xctr)
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Z, mnZ = center(Z, zctr)
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varX = pow(X, 2).sum()
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varY = pow(Y, 2).sum()
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varZ = pow(Z, 2).sum()
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m, n = X.shape
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k, l = Y.shape
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u, o = Z.shape
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# initialize
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U = empty((k, a_max))
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Q = empty((l, a_max))
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T = empty((m, a_max))
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W = empty((n, a_max))
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P = empty((n, a_max))
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K = empty((o, a_max))
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L = empty((u, a_max))
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B = empty((a_max, n, l))
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b0 = empty((a_max, m, l))
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var_x = empty((a_max,))
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var_y = empty((a_max,))
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var_z = empty((a_max,))
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for a in range(a_max):
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if verbose:
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print "\n Working on comp. %s" %a
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u = Y[:,:1]
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diff = 1
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MAX_ITER = 100
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lim = 1e-7
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niter = 0
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while (diff>lim and niter<MAX_ITER):
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niter += 1
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u1 = u.copy()
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w = dot(X.T, u)
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w = w/sqrt(dot(w.T, w))
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l = dot(Z, w)
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k = dot(Z.T, l)
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k = k/sqrt(dot(k.T, k))
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w = alpha*k + (1-alpha)*w
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w = w/sqrt(dot(w.T, w))
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t = dot(X, w)
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c = dot(Y.T, t)
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c = c/sqrt(dot(c.T, c))
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u = dot(Y, c)
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diff = abs(u1 - u).max()
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if verbose:
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print "Converged after %s iterations" %niter
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tt = dot(t.T, t)
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p = dot(X.T, t)/tt
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q = dot(Y.T, t)/tt
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l = dot(Z, w)
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U[:,a] = u.ravel()
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W[:,a] = w.ravel()
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P[:,a] = p.ravel()
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T[:,a] = t.ravel()
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Q[:,a] = q.ravel()
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L[:,a] = l.ravel()
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K[:,a] = k.ravel()
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X = X - dot(t, p.T)
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Y = Y - dot(t, q.T)
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Z = (Z.T - dot(w, l.T)).T
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var_x[a] = pow(X, 2).sum()
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var_y[a] = pow(Y, 2).sum()
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var_z[a] = pow(Z, 2).sum()
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B[a] = dot(dot(W[:,:a+1], inv(dot(P[:,:a+1].T, W[:,:a+1]))), Q[:,:a+1].T)
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b0[a] = mnY - dot(mnX, B[a])
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# variance explained
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evx = 100.0*(1 - var_x/varX)
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evy = 100.0*(1 - var_y/varY)
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evz = 100.0*(1 - var_z/varZ)
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if scale=='loads':
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tnorm = apply_along_axis(norm, 0, T)
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T = T/tnorm
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Q = Q*tnorm
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W = W*tnorm
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return T, W, P, Q, U, L, K, B, b0, evx, evy, evz
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def svd_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], verbose=True):
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"""
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NB: In the works ...
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L-shaped Partial Least Sqaures Regression by the svd algorithm.
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(X!Z)->Y
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:input:
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X : data matrix (m, n)
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Y : data matrix (m, l)
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Z : data matrix (n, o)
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:output:
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T : X-scores
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W : X-weights/Z-weights
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P : X-loadings
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Q : Y-loadings
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U : X-Y relation
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L : Z-scores
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K : Z-loads
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B : Regression coefficients X->Y
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b0: Regression coefficient intercept
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evx : X-explained variance
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evy : Y-explained variance
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evz : Z-explained variance
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:Notes:
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Not quite there ,,,,,,,,,,,,,,
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"""
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if mean_ctr:
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xctr, yctr, zctr = mean_ctr
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X, mnX = center(X, xctr)
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Y, mnY = center(Y, xctr)
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Z, mnZ = center(Z, zctr)
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varX = pow(X, 2).sum()
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varY = pow(Y, 2).sum()
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varZ = pow(Z, 2).sum()
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m, n = X.shape
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k, l = Y.shape
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u, o = Z.shape
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# initialize
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U = empty((k, a_max))
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Q = empty((l, a_max))
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T = empty((m, a_max))
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W = empty((n, a_max))
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P = empty((n, a_max))
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K = empty((o, a_max))
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L = empty((u, a_max))
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var_x = empty((a_max,))
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var_y = empty((a_max,))
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var_z = empty((a_max,))
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for a in range(a_max):
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if verbose:
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print "\n Working on comp. %s" %a
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xyz = dot(dot(Z,X.T),Y)
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u,s,vt = linalg.svd(xyz, 0)
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w = u[:,o]
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t = dot(X, w)
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tt = dot(t.T, t)
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p = dot(X.T, t)/tt
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q = dot(Y.T, t)/tt
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l = dot(Z.T, w)
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W[:,a] = w.ravel()
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P[:,a] = p.ravel()
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T[:,a] = t.ravel()
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Q[:,a] = q.ravel()
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L[:,a] = l.ravel()
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K[:,a] = k.ravel()
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X = X - dot(t, p.T)
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Y = Y - dot(t, q.T)
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Z = (Z.T - dot(w, l.T)).T
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var_x[a] = pow(X, 2).sum()
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var_y[a] = pow(Y, 2).sum()
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var_z[a] = pow(Z, 2).sum()
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B = dot(dot(W, inv(dot(P.T, W))), Q.T)
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b0 = mnY - dot(mnX, B)
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# variance explained
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evx = 100.0*(1 - var_x/varX)
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evy = 100.0*(1 - var_y/varY)
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evz = 100.0*(1 - var_z/varZ)
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return T, W, P, Q, U, L, K, B, b0, evx, evy, evz
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def lplsr(X, Y, Z, a_max, mean_ctr=[2,0,1]):
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""" Haralds LPLS.
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"""
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if mean_ctr!=None:
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xctr, yctr, zctr = mean_ctr
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X, mnX = center(X, xctr)
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Y, mnY = center(Y, yctr)
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Z, mnZ = center(Z, zctr)
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varX = pow(X, 2).sum()
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varY = pow(Y, 2).sum()
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varZ = pow(Z, 2).sum()
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m, n = X.shape
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k, l = Y.shape
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u, o = Z.shape
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# initialize
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Wy = empty((l, a_max))
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Py = empty((l, a_max))
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Ty = empty((m, a_max))
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Tz = empty((o, a_max))
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Wz = empty((u, a_max))
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Pz = empty((u, a_max))
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var_x = empty((a_max,))
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var_y = empty((a_max,))
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var_z = empty((a_max,))
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# residuals
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Ey = Y.copy()
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Ez = Z.copy()
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Ex = X.copy()
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for i in range(a_max):
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YtXZ = dot(Ey.T, dot(X, Ez.T))
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U, S, V = linalg.svd(YtXZ)
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wy = U[:,0]
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print wy
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wz = V[0,:]
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ty = dot(Ey, wy)
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tz = dot(Ez.T, wz)
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py = dot(Ey.T, ty)/dot(ty.T,ty)
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pz = dot(Ez, tz)/dot(tz.T,tz)
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Wy[:,i] = wy
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Wz[:,i] = wz
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Ty[:,i] = ty
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Tz[:,i] = tz
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Py[:,i] = py
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Pz[:,i] = pz
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Ey = Ey - outer(ty, py.T)
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Ez = (Ez.T - outer(tz, pz.T)).T
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var_y[i] = pow(Ey, 2).sum()
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var_z[i] = pow(Ez, 2).sum()
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tyd = apply_along_axis(norm, 0, Ty)
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tzd = apply_along_axis(norm, 0, Tz)
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Tyu = Ty/tyd
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Tzu = Tz/tzd
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C = dot(dot(Tyu.T, X), Tzu)
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for i in range(a_max):
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Ex = Ex - dot(dot(Ty[:,:i+1],C[:i+1,:i+1]), Tz[:,:i+1].T)
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var_x[i] = pow(Ex,2).sum()
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# variance explained
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print "var_x:"
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print var_x
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print "varX total:"
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print varX
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evx = 100.0*(1 - var_x/varX)
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evy = 100.0*(1 - var_y/varY)
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evz = 100.0*(1 - var_z/varZ)
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return Ty, Tz, Wy, Wz, Py, Pz, C, Ey, Ez, Ex, evx, evy, evz
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def bifpls(X, Y, Z, a_max, alpha):
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"""Swedssihsh LPLS by nipals.
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"""
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u = X[:,0]
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Ey = Y.copy()
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Ez = Z.copy()
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for i in range(100):
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w = dot(X.T,u)
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w = w/vnorm(w)
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t = dot(X, w)
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q = dot(Ey, t.T)/dot(t.T,t)
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qnorm = vnorm(q)
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q = q/qnorm
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v = dot(Ez, q)
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s = dot(Ez.T, v)/dot(v.T,v)
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v = v*vnorm(s)
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s = s/vnorm(s)
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c = qnorm*(alpha*q + (1-alpha)*s)
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u = dot(Ey, c)/dot(s.T,s)
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p = dot(X.T, t)/dot(t.T,t)
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v2 = dot(Ez, s)/dot(s.T,s)
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Ey = Ey - dot(t, p.T)
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Ez = Ez - dot(v2, c.T)
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# variance explained
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evx = 100.0*(1 - var_x/varX)
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evy = 100.0*(1 - var_y/varY)
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evz = 100.0*(1 - var_z/varZ)
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def center(a, axis):
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# 0 = col center, 1 = row center, 2 = double center
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# -1 = nothing
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if axis==-1:
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mn = zeros((a.shape[1],))
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return a - mn, mn
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elif axis==0:
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mn = a.mean(0)
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return a - mn, mn
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elif axis==1:
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mn = a.mean(1)[:,newaxis]
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return a - mn , mn
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elif axis==2:
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mn = a.mean(0) + a.mean(1)[:,newaxis] - a.mean()
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return a - mn, mn
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else:
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raise IOError("input error: axis must be in [-1,0,1,2]")
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def correlation_loadings(D, T, P, test=True):
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""" Returns correlation loadings.
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:input:
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- D: [nsamps, nvars], data (non-centered data)
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- T: [nsamps, a_max], Scores
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- P: [nvars, a_max], Loadings
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:ouput:
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- Rloads: [nvars, a_max], Correlation loadings
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- rmseVars: [nvars], scaling coeff. for each var in D
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:notes:
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- FIXME: Calculation is not valid .... using corrceof instead
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"""
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nsamps, nvars = D.shape
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nsampsT, a_max = T.shape
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nvarsP, a_maxP = P.shape
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if nsamps!=nsampsT: raise IOError("D/T mismatch")
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if a_max!=a_maxP: raise IOError("a_max mismatch")
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if nvars!=nvarsP: raise IOError("D/P mismatch")
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#init
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Rloads = empty((nvars, a_max), 'd')
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stdvar = stats.std(D, 0)
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rmseVars = sqrt(nsamps-1)*stdvar
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# center
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D = D - D.mean(0)
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TT = diag(dot(T.T, T))
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sTT = sqrt(TT)
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for a in range(a_max):
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Rloads[:,a] = sTT[a]*P[:,a]/rmseVars
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R = empty_like(Rloads)
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for a in range(a_max):
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for k in range(nvars):
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r = corrcoef(D[:,k], T[:,a])
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R[k,a] = r[0,1]
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#Rloads = R
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return Rloads, R, rmseVars
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def cv_lpls(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,1]):
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"""Performs crossvalidation to get generalisation error in lpls"""
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cv_iter = select_generators.pls_gen(X, Y, n_blocks=nsets,center=False,index_out=True)
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k, l = Y.shape
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Yhat = empty((a_max,k,l), 'd')
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for i, (xcal,xi,ycal,yi,ind) in enumerate(cv_iter):
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T, W, P, Q, U, L, K, B, b0, evx, evy, evz = nipals_lpls(xcal,ycal,Z,
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a_max=a_max,
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alpha=alpha,
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mean_ctr=mean_ctr,
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verbose=False)
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for a in range(a_max):
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Yhat[a,ind,:] = b0[a][0][0] + dot(xi, B[a])
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Yhat_class = zeros_like(Yhat)
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for a in range(a_max):
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for i in range(k):
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Yhat_class[a,i,argmax(Yhat[a,i,:])]=1.0
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class_err = 100*((Yhat_class+Y)==2).sum(1)/Y.sum(0).astype('d')
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sep = (Y - Yhat)**2
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rmsep = sqrt(sep.mean(1))
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return rmsep, Yhat, class_err
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def jk_lpls(X, Y, Z, a_max, nsets=None, alpha=.5, mean_ctr=[2,0,1]):
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cv_iter = select_generators.pls_gen(X, Y, n_blocks=nsets,center=False,index_out=False)
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m, n = X.shape
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k, l = Y.shape
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o, p = Z.shape
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if nsets==None:
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nsets = m
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WWx = empty((nsets, n, a_max), 'd')
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WWz = empty((nsets, o, a_max), 'd')
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WWy = empty((nsets, l, a_max), 'd')
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for i, (xcal,xi,ycal,yi) in enumerate(cv_iter):
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T, W, P, Q, U, L, K, B, b0, evx, evy, evz = nipals_lpls(xcal,ycal,Z,
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a_max=a_max,
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alpha=alpha,
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mean_ctr=mean_ctr,
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scale='loads',
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verbose=False)
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WWx[i,:,:] = W
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WWz[i,:,:] = L
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WWy[i,:,:] = Q
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return WWx, WWz, WWy
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