Second initial import

This commit is contained in:
Arnar Flatberg 2007-10-26 13:36:05 +00:00
parent 67d6d01f7f
commit 5b91e2d809
4 changed files with 596 additions and 23 deletions

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@ -201,16 +201,16 @@ def eigen(A,k=6,M=None,ncv=None,which='LM',
dr=sb.zeros(k+1,typ)
di=sb.zeros(k+1,typ)
zr=sb.zeros((n,k+1),typ)
dr,di,z,info=\
dr,di,zr,info=\
eigextract(rvec,howmny,sselect,sigmar,sigmai,workev,
bmat,which,k,tol,resid,v,iparam,ipntr,
workd,workl,info)
# make eigenvalues complex
d=dr+1.0j*di
d=(dr+1.0j*di)[:k]
# futz with the eigenvectors:
# complex are stored as real,imaginary in consecutive columns
z=zr.astype(typ.upper())
z=zr.astype(typ.upper())[:,:k]
for i in range(k): # fix c.c. pairs
if di[i] > 0 :
z[:,i]=zr[:,i]+1.0j*zr[:,i+1]

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@ -1,5 +1,6 @@
from crossvalidation import lpls_val
from statistics import lpls_qvals
from engines import pca, pcr, pls
from engines import nipals_lpls as lpls
#from tests import *

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@ -2,11 +2,12 @@
The primary use is crossvalidation.
"""
__all__ = ['lpls_val', 'lpls_jk']
__all__ = ['lpls_val', 'pls_jk', 'lpls_jk']
__docformat__ = "restructuredtext en"
from numpy import dot,empty,zeros,sqrt,atleast_2d,argmax,asarray,median,\
array_split
array_split,arange
from numpy.random import shuffle
from engines import nipals_lpls as lpls
@ -93,8 +94,92 @@ def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2],verbose=Tru
return rmsep, Yhat, aopt
def pca_jk(a, aopt, n_blocks=None):
"""Returns jack-knife segements from PCA.
def lpls_jk(X, Y, Z, a_max, nsets=None, xz_alpha=.5, mean_ctr=[2,0,2], verbose=False):
Parameters:
a : {array}
data matrix (n x m)
aopt : {integer}
number of components in model.
nsets : {integer}
number of segments
Returns:
Pcv : {array}
Loadings collected in a three way matrix (n_segments, m, aopt)
Notes:
- The loadings are scaled with the (1/samples)*eigenvalues.
- Crossvalidation method is currently set to random blocks of samples.
- todo: add support for T
- fixme: more efficient to add this in validation loop?
"""
if nsets == None:
nsets = a.shape[0]
Pcv = empty((nsets, a.shape[1], aopt), dtype=a.dtype)
mn_a = .5*(a.mean(0) + a.mean(1)[:,newaxis])
for i, (cal, val) in enumerate(cv_diag(a.shape, nsets)):
old_values = a.take(ind)
new_values = mn_a.take(ind)
a.put(ind, new_values)
dat = pca(a, aopt, mode='fast', scale='loads', center=center)
PP[nn,:,:] = dat['P']
a.put(ind, old_values)
return PP
def pls_jk(X, Y, a_opt, nsets=None, center=True, verbose=False):
""" Returns jack-knife segements of W.
*Parameters*:
X : {array}
Main data matrix (m, n)
Y : {array}
External row data (m, l)
a_opt : {integer}
The number of components to calculate (0, min(m,n))
nsets : (integer), optional
Number of jack-knife segments
center : {boolean}, optional
- -1 : nothing
- 0 : row center
- 1 : column center
- 2 : double center
verbose : {boolean}, optional
Verbosity of console output. For use in debugging.
*Returns*:
Wcv : {array}
Loading-weights jack-knife segements
"""
m, n = X.shape
k, l = Y.shape
assert(m==k)
if nsets == None:
nsets = X.shape[0]
Wcv = empty((nsets, X.shape[1], a_opt), dtype=X.dtype)
for i, (cal, val) in enumerate(cv(k, nsets)):
if verbose:
print "Segement number: %d" %i
dat = pls(X[cal,:], Y[cal,:], a_opt, scale='loads', mode='fast')
Wcv[nn,:,:] = dat['W']
return Wcv
def lpls_jk(X, Y, Z, a_opt, nsets=None, xz_alpha=.5, mean_ctr=[2,0,2], verbose=False):
"""Returns jack-knifed segments of lpls model.
Jack-knifing is a method to perturb the model paramters, hopefully
@ -113,8 +198,8 @@ def lpls_jk(X, Y, Z, a_max, nsets=None, xz_alpha=.5, mean_ctr=[2,0,2], verbose=F
External row data (m, l)
Z : {array}
External column data (n, o)
a_max : {integer}, optional
Maximum number of components to calculate (0, min(m,n))
a_opt : {integer}, optional
The number of components to calculate (0, min(m,n))
nsets : (integer), optional
Number of jack-knife segments
xz_alpha : {float}, optional
@ -145,11 +230,11 @@ def lpls_jk(X, Y, Z, a_max, nsets=None, xz_alpha=.5, mean_ctr=[2,0,2], verbose=F
assert(n==p)
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')
WWx = empty((nsets, n, a_opt), 'd')
WWz = empty((nsets, o, a_opt), 'd')
#WWy = empty((nsets, l, a_opt), 'd')
for i, (cal, val) in enumerate(cv(k, nsets)):
dat = lpls(X[cal],Y[cal],Z,a_max=a_max,alpha=xz_alpha,mean_ctr=mean_ctr,
dat = lpls(X[cal], Y[cal], Z, a_max=a_opt,alpha=xz_alpha, mean_ctr=mean_ctr,
scale='loads', verbose=verbose)
WWx[i,:,:] = dat['W']
WWz[i,:,:] = dat['L']
@ -219,6 +304,7 @@ def cv(N, K, randomise=True, sequential=False):
*Notes*:
If randomise is true, a copy of index is shuffled before partitioning,
otherwise its order is preserved in training and validation.
Randomise overrides the sequential argument. If randomise is true,
@ -245,13 +331,40 @@ def cv(N, K, randomise=True, sequential=False):
validation = [i for i in index if i % K == k]
yield training, validation
def diag_cv(shape, nsets=9):
"""Generates K (training, validation) index pairs.
Parameters:
N : {integer}
alpha -- scalar, approx. portion of data perturbed
"""
try:
m, n = shape
except:
raise ValueError("shape needs to be a two-tuple")
if nsets>m or nsets>n:
msg = "You may not use more subsets than max(n_rows, n_cols)"
raise ValueError, msg
nm = n*m
index = arange(nm)
n_ind = arange(n)
shuffle(n_ind) # random start diag
start_inds = array_split(n_ind, nsets)
for v in range(nsets):
validation = []
for start in start_inds[v]:
ind = arange(start+v, nm, n+1)
[validation.append(i) for i in ind]
training = [j for j in index if j not in validation]
yield training, validation
def class_error(Yhat, Y, method='vanilla'):
""" Not used.
"""
a_max, k, l = Yhat.shape
a_opt, k, l = Yhat.shape
Yhat_c = zeros((k, l), dtype='d')
for a in range(a_max):
for a in range(a_opt):
for i in range(k):
Yhat_c[a,val,argmax(Yhat[a,val,:])] = 1.0
err = 100*((Yhat_c + Y) == 2).sum(1)/Y.sum(0).astype('d')

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@ -2,14 +2,414 @@
"""
__all__ = ['nipals_lpls']
__all__ = ['pca', 'pcr', 'pls', 'nipals_lpls']
__docformat__ = "restructuredtext en"
from math import sqrt as msqrt
from numpy import dot,empty,zeros,apply_along_axis,newaxis,finfo
from numpy.linalg import inv
from numpy import dot,empty,zeros,apply_along_axis,newaxis,finfo,sqrt,r_,expand_dims,\
minimum
from numpy.linalg import inv, svd
from scipy.sandbox import arpack
def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
""" Principal Component Analysis.
PCA is a low rank bilinear aprroximation to a data matrix that sequentially
extracts orthogonal components of maximum variance.
Parameters:
X : {array}
Data measurement matrix, (samples x variables)
aopt : {integer}
Number of components to use, aopt<=min(samples, variables)
center_axis : {integer}
Center along given axis. If neg.: no centering (-inf,..., matrix modes)
Returns:
T : {array}
Scores, (samples, components)
P : {array}
Loadings, (variables, components)
E : {array}
Residuals, (samples, variables)
evx : {array}
X-explained variance, (components,)
mnx : {array}
X location, (variables,)
aopt : {integer}
The number of components used
ssqx : {list}
Sum of squared residuals in X along each dimesion
[(samples, ), (variables,)]
leverage : {array}
Leverages, (samples,)
OtherParameters:
scale : {string}, optional
Where to put the weights [['scores'], 'loadings']
mode : {string}, optional
Amount of info retained, [['normal'], 'fast', 'detailed']
:SeeAlso:
`center` : Data centering
*Notes*
Uses kernel speed-up if m>>n or m<<n.
If residuals turn rank deficient, a lower number of component than given
in input will be used.
*Examples*:
>>> import scipy,engines
>>> a=scipy.asarray([[1,2,3],[2,4,5]])
>>> dat=engines.pca(a, 2)
>>> dat['evx']
array([0.,99.8561562, 100.])
"""
m, n = X.shape
assert(aopt<=min(m,n))
if center_axis>=0:
X = X - expand_dims(X.mean(center_axis), center_axis)
if m>(n+100) or n>(m+100):
u, s, v = esvd(X, aopt)
else:
u, s, vt = svd(X, 0)
v = vt.T
u = u[:,:aopt]
s = s[:aopt]
v = v[:,:aopt]
# ranktest
tol = 1e-10
eff_rank = sum(s>s[0]*tol)
aopt = minimum(aopt, eff_rank)
T = u*s
s = s[:aopt]
T = T[:,:aopt]
P = v[:,:aopt]
e = s**2
if scale=='loads':
T = T/s
P = P*s
if mode == 'fast':
return {'T':T, 'P':P, 'aopt':aopt}
if mode=='detailed':
E = empty((aopt, m, n))
ssq = []
lev = []
for ai in range(aopt):
E[ai,:,:] = X - dot(T[:,:ai+1], P[:,:ai+1].T)
ssq.append([(E[ai,:,:]**2).mean(0), (E[ai,:,:]**2).mean(1)])
if scale=='loads':
lev.append([((s*T)**2).sum(1), (P**2).sum(1)])
else:
lev.append([(T**2).sum(1), ((s*P)**2).sum(1)])
else:
# residuals
E = X - dot(T, P.T)
sep = E**2
ssq = [sep.sum(0), sep.sum(1)]
# leverages
if scale=='loads':
lev = [(1./m)+(T**2).sum(1), (1./n)+((P/s)**2).sum(1)]
else:
lev = [(1./m)+((T/s)**2).sum(1), (1./n)+(P**2).sum(1)]
# variances
expvarx = r_[0, 100*e.cumsum()/(X*X).sum()]
return {'T': T, 'P': P, 'E': E, 'evx': expvarx, 'leverage': lev, 'ssqx': ssq,
'aopt': aopt, 'eigvals': e}
def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
""" Principal Component Regression.
Performs PCR on given matrix and returns results in a dictionary.
Parameters:
a : array
Data measurement matrix, (samples x variables)
b : array
Data response matrix, (samples x responses)
aopt : int
Number of components to use, aopt<=min(samples, variables)
Returns:
results : dict
keys -- values, T -- scores, P -- loadings, E -- residuals,
levx -- leverages, ssqx -- sum of squares, expvarx -- cumulative
explained variance, aopt -- number of components used
OtherParameters:
mode : str
Amount of info retained, ('fast', 'normal', 'detailed')
center_axis : int
Center along given axis. If neg.: no centering (-inf,..., matrix modes)
SeeAlso:
- pca : other blm
- pls : other blm
- lpls : other blm
*Notes*
-----
Uses kernel speed-up if m>>n or m<<n.
If residuals turn rank deficient, a lower number of component than given
in input will be used. The number of components used is given in results-dict.
Examples
--------
>>> import scipy,engines
>>> a=scipy.asarray([[1,2,3],[2,4,5]])
>>> b=scipy.asarray([[1,1],[2,3]])
>>> dat=engines.pcr(a, 2)
>>> dat['evx']
array([0.,99.8561562, 100.])
"""
try:
k, l = b.shape
except:
b = atleast_2d(b).T
k, l = b.shape
if center_axis>=0:
b = b - expand_dims(b.mean(center_axis), center_axis)
dat = pca(a, aopt=aopt, scale=scale, mode=mode, center_axis=center_axis)
T = dat['T']
weights = apply_along_axis(vnorm, 0, T)**2
if scale=='loads':
Q = dot(b.T, T*weights)
else:
Q = dot(b.T, T/weights)
if mode=='fast':
dat.update({'Q':Q})
return dat
if mode=='detailed':
F = empty((aopt, k, l))
ssqy = []
for i in range(aopt):
F[i,:,:] = b - dot(T[:,:i+1], Q[:,:i+1].T)
ssqy.append([(F[i,:,:]**2).mean(0), (F[i,:,:]**2).mean(1)])
else:
F = b - dot(T, Q.T)
sepy = F**2
ssqy = [sepy.sum(0), sepy.sum(1)]
expvary = r_[0, 100*((T**2).sum(0)*(Q**2).sum(0)/(b**2).sum()).cumsum()[:aopt]]
dat.update({'Q': Q, 'F': F, 'evy': expvary, 'ssqy': ssqy})
return dat
def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
"""Partial Least Squares Regression.
Performs PLS on given matrix and returns results in a dictionary.
*Parameters*:
X : {array}
Data measurement matrix, (samples x variables)
Y : {array}
Data response matrix, (samples x responses)
aopt : {integer}, optional
Number of components to use, aopt<=min(samples, variables)
scale : ['scores', 'loadings'], optional
Which component should get the scale
center_axis : {-1, integer}
Perform centering across given axis, (-1 is no centering)
*Returns*:
T : {array}
X-scores
W : {array}
X-loading-weights
P : {array}
X-loadings
R : {array}
X-loadings-basis
Q : {array}
Y-loadings
B : {array}
Regression coefficients
E : {array}
X-block residuals
F : {array}
Y-block residuals
evx : {array}
X-explained variance
evy : {array}
Y-explained variance
mnx : {array}
X location
mny : {array}
Y location
aopt : {array}
The number of components used
ssqx : {list}, optional
Sum of squared residuals in X along each dimesion
ssqy : {list}
Sum of squared residuals in Y along each dimesion
leverage : {array}
Sample leverages
*OtherParameters*:
mode : ['normal', 'fast', 'detailed'], optional
How much details to compute
*SeeAlso*:
`center` : data centering
*Notes*
- The output with mode='fast' will only return T and W
- If residuals turn rank deficient, a lower number of component than given in input will be used. The number of components used is given in results.
*Examples*
>>> import numpy, engines
>>> a = numpy.asarray([[1,2,3],[2,4,5]])
>>> b = numpy.asarray([[1,1],[2,3]])
>>> dat =engines.pls(a, b, 2)
>>> dat['evx']
array([0.,99.8561562, 100.])
"""
m, n = X.shape
try:
k, l = Y.shape
except:
Y = atleast_2d(Y).T
k, l = Y.shape
assert(m==k)
assert(aopt<min(m, n))
mnx, mny = 0,0
if center_axis>=0:
mnx = expand_dims(X.mean(center_axis), center_axis)
X = X - mnx
mny = expand_dims(Y.mean(center_axis), center_axis)
Y = Y - mny
W = empty((n, aopt))
P = empty((n, aopt))
R = empty((n, aopt))
Q = empty((l, aopt))
T = empty((m, aopt))
B = empty((aopt, n, l))
tt = empty((aopt,))
XY = dot(X.T, Y)
for i in range(aopt):
if XY.shape[1]==1: #pls 1
w = XY.reshape(n, l)
w = w/vnorm(w)
elif n<l: # more yvars than xvars
s, w = arpack.eigen_symmetric(dot(XY, XY.T),k=1, tol=1e-10, maxiter=100)
#w, s, vh = svd(dot(XY, XY.T))
#w = w[:,:1]
else: # more xvars than yvars
s, q = arpack.eigen_symmetric(dot(XY.T, XY), k=1, tol=1e-10, maxiter=100)
#q, s, vh = svd(dot(XY.T, XY))
#q = q[:,:1]
w = dot(XY, q)
w = w/vnorm(w)
r = w.copy()
if i>0:
for j in range(0, i, 1):
r = r - dot(P[:,j].T, w)*R[:,j][:,newaxis]
t = dot(X, r)
tt[i] = tti = dot(t.T, t).ravel()
p = dot(X.T, t)/tti
q = dot(r.T, XY).T/tti
XY = XY - dot(p, q.T)*tti
T[:,i] = t.ravel()
W[:,i] = w.ravel()
if mode=='fast' and i==aopt-1:
if scale=='loads':
tnorm = sqrt(tt)
T = T/tnorm
W = W*tnorm
return {'T':T, 'W':W}
P[:,i] = p.ravel()
R[:,i] = r.ravel()
Q[:,i] = q.ravel()
B[i] = dot(R[:,:i+1], Q[:,:i+1].T)
qnorm = apply_along_axis(vnorm, 0, Q)
tnorm = sqrt(tt)
pp = (P**2).sum(0)
if mode=='detailed':
E = empty((aopt, m, n))
F = empty((aopt, k, l))
ssqx, ssqy = [], []
leverage = empty((aopt, m))
#h2x = [] #hotellings T^2
#h2y = []
for ai in range(aopt):
E[ai,:,:] = X - dot(T[:,:ai+1], P[:,:ai+1].T)
F[ai,:,:] = Y - dot(T[:,:i], Q[:,:i].T)
ssqx.append([(E[ai,:,:]**2).mean(0), (E[ai,:,:]**2).mean(1)])
ssqy.append([(F[ai,:,:]**2).mean(0), (F[ai,:,:]**2).mean(1)])
leverage[ai,:] = 1./m + ((T[:,:ai+1]/tnorm[:ai+1])**2).sum(1)
#h2y.append(1./k + ((Q[:,:ai+1]/qnorm[:ai+1])**2).sum(1))
else:
# residuals
E = X - dot(T, P.T)
F = Y - dot(T, Q.T)
sepx = E**2
ssqx = [sepx.sum(0), sepx.sum(1)]
sepy = F**2
ssqy = [sepy.sum(0), sepy.sum(1)]
leverage = 1./m + ((T/tnorm)**2).sum(1)
# variances
tp= tt*pp
tq = tt*qnorm*qnorm
expvarx = r_[0, 100*tp/(X*X).sum()]
expvary = r_[0, 100*tq/(Y*Y).sum()]
if scale=='loads':
T = T/tnorm
W = W*tnorm
Q = Q*tnorm
P = P*tnorm
return {'Q': Q, 'P': P, 'T': T, 'W': W, 'R': R, 'E': E, 'F': F, 'B': B,
'evx': expvarx, 'evy': expvary, 'ssqx': ssqx, 'ssqy': ssqy,
'leverage': leverage, 'mnx': mnx, 'mny': mny}
def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', verbose=False):
""" L-shaped Partial Least Sqaures Regression by the nipals algorithm.
@ -39,10 +439,6 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', ve
0 : row center
1 : column center
2 : double center
scale : {'scores', 'loads'}, optional
Option to decide on where the scale goes.
verbose : {boolean}, optional
Verbosity of console output. For use in debugging.
*Returns*:
@ -75,6 +471,13 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', ve
mnz : {array}
Z location
*OtherParameters*:
scale : {'scores', 'loads'}, optional
Option to decide on where the scale goes.
verbose : {boolean}, optional
Verbosity of console output. For use in debugging.
*References*
Saeboe et al., LPLS-regression: a method for improved prediction and
classification through inclusion of background information on
@ -296,3 +699,59 @@ def _scale(a, axis):
raise IOError("input error: axis must be in [-1,0,1]")
return a - sc, sc
def esvd(data, a_max=None):
""" SVD with kernel calculation
Calculate subspaces of X'X or XX' depending on the shape
of the matrix.
Parameters:
data : {array}
Data matrix
a_max : {integer}
Number of components to extract
Returns:
u : {array}
Right hand eigenvectors
s : {array}
Singular values
v : {array}
Left hand eigenvectors
notes:
Uses Anoldi iterations (ARPACK)
"""
m, n = data.shape
if m>=n:
kernel = dot(data.T, data)
if a_max==None:
a_max = n - 1
s, v = arpack.eigen_symmetric(kernel,k=a_max, which='LM',
maxiter=200,tol=1e-5)
s = s[::-1]
v = v[:,::-1]
#u, s, vt = svd(kernel)
#v = vt.T
s = sqrt(s)
u = dot(data, v)/s
else:
kernel = dot(data, data.T)
if a_max==None:
a_max = m -1
s, u = arpack.eigen_symmetric(kernel,k=a_max, which='LM',
maxiter=200,tol=1e-5)
s = s[::-1]
u = u[:,::-1]
#u, s, vt = svd(kernel)
s = sqrt(s)
v = dot(data.T, u)/s
return u, s, v