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ca.py
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ca.py
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"""Correspondence Analysis (CA)"""
# Author: Hirotaka Niitsuma
# @2018 Hirotaka Niirtsuma
#
# You can use this code olny for self evaluation.
# Cannot use this code for commercial and academical use.
#
# pantent pending
# https://patentscope2.wipo.int/search/ja/detail.jsf?docId=JP225380312
# Japan patent office patent number 2017-007741
import sys
import math
import numpy as np
from scipy.sparse import csr_matrix,csc_matrix,dok_matrix,issparse,coo_matrix
import scipy.sparse
from sklearn import base
from sklearn import utils
from .delayedsparse import delayedspmatrix,delayedspmatrix_t,isdelayedspmatrix
from .delayedsparse import safe_sparse_dot as sdot
from . import extmath2
## http://stackoverflow.com/questions/26248654/numpy-return-0-with-divide-by-zero
def div0( a, b ):
""" ignore / 0, div0( [-1, 0, 1], 0 ) -> [0, 0, 0] """
with np.errstate(divide='ignore', invalid='ignore'):
c = np.true_divide( a, b )
c[ ~ np.isfinite( c )] = 0 # -inf inf NaN
return c
def set_correspondenceanalysis_delayed_mat(model):
model.Ut = delayedspmatrix_t(model.U)
model.V = delayedspmatrix_t(model.Vt)
model.D_a = scipy.sparse.diags(model.D,offsets=0)
model.F2 = delayedspmatrix(lambda x: sdot(sdot( model.U * model.D_a),x),
lambda x: sdot(x,(model.U * model.D_a)),
(model.U.shape[0],model.D_a.shape[1]))
model.G2 =delayedspmatrix(lambda x: sdot( sdot(model.V, model.D_a) ,x),
lambda x: sdot(x,sdot(model.V, model.D_a)),
(model.V[0],model.D_a.shape[1]))
# principal coordinates of rows
#F = D_r_rsq * (U * D_a)
model.F=delayedspmatrix(lambda x: sdot( model.D_r_rsq*(model.U * model.D_a),x),
lambda x: sdot(x,model.D_r_rsq*(model.U * model.D_a)),
(model.D_r_rsq.shape[0],model.D_a.shape[1]))
# principal coordinates of columns
# G = model.D_c_rsq * (V * D_a)
model.G=delayedspmatrix(lambda x: sdot( model.D_c_rsq * sdot(model.V, model.D_a) ,x),
lambda x: sdot(x,model.D_c_rsq * sdot(model.V, model.D_a)),
(model.D_c_rsq.shape[0],model.D_a.shape[1]))
# #model.X = X.A
# X = model.D_r_rsq.dot(U)
# model.X = X
model.X=delayedspmatrix(lambda x: sdot( model.D_r_rsq*model.U ,x),
lambda x: sdot(x,model.D_r_rsq*model.U),
(model.D_r_rsq.shape[0],model.U.shape[1]))
# #model.Y = Y.A
# Y = model.D_c_rsq.dot(V)
# model.Y = Y
model.Y=delayedspmatrix(lambda x: sdot( sdot(model.D_c_rsq,model.V) ,x),
lambda x: sdot(x,sdot(model.D_c_rsq,model.V)),
(model.D_r_rsq.shape[0],model.Vt.shape[0]))
model.mat_name_list=['F','G','U','V','X','Y','F2','G2']
class CA(base.BaseEstimator, base.TransformerMixin):
def __init__(self, n_components=2):
self.n_components = n_components
self.mat_name_list=[]
def fit(self, X, y=None):
if isinstance(X,np.ndarray):
N = np.matrix(X, dtype=float)
else:
N=X
self.shape=N.shape
n_sum_total=N.sum()
n_sum_total_f=float(n_sum_total)
ra = np.array(N.sum(axis=1))[:, 0]/n_sum_total_f ## =pra
ca = np.array(N.sum(axis=0))[0, :]/n_sum_total_f ## =pca
self.ra_inv_sqrt = div0(1.0,np.sqrt(ra))
self.ca_inv_sqrt = div0(1.0,np.sqrt(ca))
self.D_r_rsq = scipy.sparse.diags(self.ra_inv_sqrt,offsets=0)
self.D_c_rsq = scipy.sparse.diags(self.ca_inv_sqrt,offsets=0)
r_sq = self.D_r_rsq * ra.reshape((-1,1))
c_sq = ca.reshape((1,-1)) * self.D_c_rsq
S=delayedspmatrix(
lambda x: sdot(self.D_r_rsq, sdot(N,sdot(self.D_c_rsq,x/n_sum_total_f)))-sdot(r_sq,sdot(c_sq,x)),
lambda x: sdot(sdot(sdot(x/n_sum_total_f,self.D_r_rsq),N),self.D_c_rsq)-sdot(sdot(x,r_sq),c_sq),
N.shape
)
self.U, self.D, self.Vt = extmath2.randomized_svd(S, self.n_components)
set_correspondenceanalysis_delayed_mat(self)
return self
def transform(self, X):
utils.validation.check_is_fitted(self, 'D')
return sdot(X,self.Y)
@property
def eigenvalues_(self):
utils.validation.check_is_fitted(self, 'D')
return np.square(self.D).tolist()
def evaled_mats(self):
self.V=(self.Vt).T
#self.V=delayedspmatrix_t(self.Vt)
self.D_r_rsq = scipy.sparse.diags(self.ra_inv_sqrt,offsets=0)
self.D_c_rsq = scipy.sparse.diags(self.ca_inv_sqrt,offsets=0)
self.D_a = scipy.sparse.diags(self.D,offsets=0)
self.F = self.D_r_rsq * (self.U * self.D_a)
self.G = self.D_c_rsq * (self.V * self.D_a)
self.X = self.D_r_rsq.dot(self.U)
self.Y = self.D_c_rsq.dot(self.V)
self.F2 = (self.U * self.D_a)
self.G2 = (self.V * self.D_a)
self.mat_name_list=['F','G','U','V','X','Y','F2','G2']
def save(self,filename):
np.savez(filename,
U=self.U,
D=self.D,
Vt=self.Vt,
ra_inv_sqrt=self.ra_inv_sqrt,
ca_inv_sqrt=self.ca_inv_sqrt
)
def load(self,filename):
loader = np.load(filename)
self.D=loader['D']
self.ra_inv_sqrt=loader['ra_inv_sqrt']
self.ca_inv_sqrt=loader['ca_inv_sqrt']
self.D_r_rsq = scipy.sparse.diags(self.ra_inv_sqrt,offsets=0)
self.D_c_rsq = scipy.sparse.diags(self.ca_inv_sqrt,offsets=0)
self.U=loader['U']
self.Vt=loader['Vt']
self.mat_name_list=['F','G','U','V','X','Y','F2','G2']
set_correspondenceanalysis_delayed_mat(self)
def _test():
c1 = dok_matrix((4, 4), dtype=np.float32)
c1[0,0]=20
c1[1,1]=10
c1[2,2]=33
c1[3,3]=2
c1[0,2]=7
c1[3,0]=5
c1[1,0]=4
#print(.todense())
from Orange.widgets.unsupervised.owcorrespondence import correspondence
c1dense=c1.todense()
#print(c1dense)
ca=correspondence(c1dense)
print(ca.D)
print(ca.U)
cad=CA(3)
cad.fit(c1)
print(cad.D)
print(cad.U)
print(cad.Vt)
print(cad.F)
print(sdot(cad.F, scipy.sparse.diags(np.ones(3))))
print(cad.eigenvalues_)
if __name__ == '__main__':
#_test()
# mat = scipy.sparse.load_npz('tmp.npz')
# dim=min(10,min(mat.shape))
# cad=SparseCorrespondenceAnalysis(mat,dim)
# #print(cad.D)
if len(sys.argv)==2:
X = scipy.sparse.load_npz('tmp.npz')
dim=min(10,min(X.shape))
if sys.argv[1] == 'delay':
print('delayed sparse CA')
ca=CA()
ca.fit(X)
elif sys.argv[1] == 'orange':
print('existing method(Orange lib)')
from Orange.widgets.unsupervised.owcorrespondence import correspondence
X = scipy.sparse.load_npz('tmp.npz')
ca=correspondence(X.todense())