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This commit is contained in:
Arnar Flatberg 2007-12-16 21:36:40 +00:00
parent 253305b602
commit ac4456474b
2 changed files with 55 additions and 46 deletions

View File

@ -12,7 +12,7 @@ from numpy.random import shuffle
from engines import pls, pca
from engines import nipals_lpls as lpls
def pca_val(a, a_max, nsets=None, center_axis=[0]):
def pca_val(a, a_max, nsets=None, center_axis=[0], method='cv'):
"""Returns error estimate of crossvalidated PCA.
*Parameters*:
@ -25,7 +25,8 @@ def pca_val(a, a_max, nsets=None, center_axis=[0]):
Centering
nsets : {integer}
number of segments
method : {['cv', 'diag']}
*Returns*:
rmsep : {array}
@ -36,8 +37,14 @@ def pca_val(a, a_max, nsets=None, center_axis=[0]):
Estimate of optimal number of components
*Notes*:
- Crossvalidation of PCA is somewhat artificial as we do not have
any external information to predict. There are essentially two approaches
to this, one is to use a projection error, the other is to leave out
elements in the data matrix then record a missing-value estimator error.
- Crossvalidation method is currently set to random blocks of diagonals.
"""
n, m = a.shape
@ -47,29 +54,44 @@ def pca_val(a, a_max, nsets=None, center_axis=[0]):
err = zeros((a_max, n, m), dtype=a.dtype)
err_mn = zeros((a_max, n, m), dtype=a.dtype)
xhat = zeros((a_max, n, m), dtype=a.dtype)
mn_a = .5*(a.mean(0) + a.mean(1)[:,newaxis])
for i, val in enumerate(diag_cv(a.shape, nsets)):
old_values = a.take(val)
new_values = mn_a.take(val)
# impute mean values
b = a.copy()
a.put(val, new_values)
dat = pca(a, a_max, mode='normal', center_axis=center_axis)
Ti, Pi = dat['T'], dat['P']
bc = b - dat['mnx']
bc2 = b - b.mean(0)
for j in xrange(a_max):
# predict the imputed values
a_pred = dot(Ti[:,:j+1], Pi[:,:j+1].T).take(val)
a_true = bc2.take(val)
err[j,:,:].put(val, (a_true - a_pred)**2)
err_mn[j,:,:].put(val, (bc.take(val) - a_pred)**2)
xhat[j,:,:].put(val, a_pred)
# put original values back
a.put(val, old_values)
if method == 'diag':
mn_a = .5*(a.mean(0) + a.mean(1)[:,newaxis])
for i, val in enumerate(diag_cv(a.shape, nsets)):
old_values = a.take(val)
new_values = mn_a.take(val)
# impute with mean values
b = a.copy()
a.put(val, new_values)
dat = pca(a, a_max, mode='normal', center_axis=center_axis)
Ti, Pi = dat['T'], dat['P']
bc = b - dat['mnx']
bc2 = b - b.mean(0)
for j in xrange(a_max):
# estimate the imputed values
a_pred = dot(Ti[:,:j+1], Pi[:,:j+1].T).take(val)
a_true = bc2.take(val)
err[j,:,:].put(val, (a_true - a_pred)**2)
err_mn[j,:,:].put(val, (bc.take(val) - a_pred)**2)
xhat[j,:,:].put(val, a_pred)
# put original values back
a.put(val, old_values)
elif method == 'cv':
for i, (cal, val) in enumerate(cv(n, nsets)):
xval = atleast_2d(x[val,:])
xcal = x[cal, :]
P = pca(xcal, aopt, mode='fast', scale='scores')['P']
e = eye(m)
rmat = zeros((m, m))
for j, p in enumerate(P.T):
d2 = diag(e) - (p**2).ravel()
e = e - dot(p, p.T)
d = diag(e)
es = e/atleast_2d(d)
xhat[j,:,:] = dot(xval, es)
err[i, a] = (dot(xval, es)**2).sum()
rmsep = sqrt(err).mean(1) # take mean over samples
rmsep2 = sqrt(err_mn).mean(1)
aopt = rmsep.mean(-1).argmin()
@ -120,8 +142,8 @@ def pls_val(X, Y, a_max=2, nsets=None, center_axis=[0,0], verbose=False):
if nsets > X.shape[0]:
print "nsets (%d) is larger than number of variables (%d).\nnsets: %d -> %d" %(nsets, m, nsets, m)
nsets = m
if m > n:
# kernel boosting
if n > 5*m:
# boosting (wide x)
Yhat = _w_pls_predict(X, Y, a_max)
Yhat = empty((a_max, k, l), dtype=dt)
@ -259,7 +281,7 @@ def pca_jk(a, aopt, nsets=None, center_axis=[0], method='cv'):
*Notes*:
- Crossvalidation method is currently set to random blocks of samples.
- .
"""
m, n = a.shape
@ -518,8 +540,8 @@ def diag_cv(shape, nsets=9, randomise=True):
if nsets>m or nsets>n:
msg = "You may not use more subsets than max(n_rows, n_cols)"
raise ValueError, msg
msg = "You may not use more subsets than max(n_rows, n_cols)"
nsets = min(m, n)
nsets = min(m, n)
nm = n*m
index = arange(nm)
n_ind = arange(n+1)
@ -533,20 +555,6 @@ def diag_cv(shape, nsets=9, randomise=True):
#training = [j for j in index if j not in validation]
yield list(validation)
def class_error(y_hat, y, method='vanilla'):
""" Not used.
"""
a_opt, k, l = y_hat.shape
y_hat_c = zeros((k, l), dtype='d')
if method == vanilla:
pass
for a in range(a_opt):
for i in range(k):
y_hat_c[a, val, argmax(y_hat[a,val,:])] = 1.0
err = 100*((y_hat_c + y) == 2).sum(1)/y.sum(0).astype('d')
return y_hat_c, err
def prediction_error(y_hat, y, method='squared'):
"""Loss function on multiclass Y.

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@ -84,7 +84,8 @@ def hotelling(Pcv, P, p_center='median', cov_center='median',
if cov_center == 'median':
Cov_p = median(Cov_i)
else cov_center == 'mean':
else:
# cov_center == 'mean'
Cov_p = Cov.mean(0)
reg_cov = (1. - alpha)*Cov_i + alpha*Cov_p
for i in xrange(n):