In [1]:
%%writefile Source/fastICA_0.py
import numpy as np
from sklearn import preprocessing
def sym_decorrelation(W):
""" Symmetric decorrelation """
K = np.dot(W, W.T)
s, u = np.linalg.eigh(K)
W = (u @ np.diag(1.0/np.sqrt(s)) @ u.T) @ W
return W
def g_logcosh(wx,alpha):
"""derivatives of logcosh"""
return np.tanh(alpha * wx)
def gprime_logcosh(wx,alpha):
"""second derivatives of logcosh"""
return alpha * (1-np.square(np.tanh(alpha*wx)))
# exp
def g_exp(wx,alpha):
"""derivatives of exp"""
return wx * np.exp(-np.square(wx)/2)
def gprime_exp(wx,alpha):
"""second derivatives of exp"""
return (1-np.square(wx)) * np.exp(-np.square(wx)/2)
def fastICA_0(X, f,alpha=None, n_comp=None,maxit=200, tol=1e-04):
"""FastICA algorithm for several units"""
n,p = X.shape
#check if n_comp is valid
if n_comp is None:
n_comp = min(n,p)
elif n_comp > min(n,p):
print("n_comp is too large")
n_comp = min(n,p)
#centering
#by subtracting the mean of each column of X (array).
X = preprocessing.scale(X,axis = 0,with_std=False)
X = X.T
#whitening
svd = np.linalg.svd(X @ (X.T) / n)
k = np.diag(1/np.sqrt(svd[1])) @ (svd[0].T)
k = k[:n_comp,:]
X1 = k @ X
# initial random weght vector
w_init = np.random.normal(size=(n_comp, n_comp))
W = sym_decorrelation(w_init)
lim = 1
it = 0
# The FastICA algorithm
if f == "logcosh":
while lim > tol and it < maxit :
wx = W @ X1
gwx = g_logcosh(wx,alpha)
g_wx = gprime_logcosh(wx,alpha)
W1 = np.dot(gwx,X1.T)/X1.shape[1] - np.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(W1 @ W.T)) - 1.0))
W = W1
S = W @ X1
A = np.linalg.inv(W @ k)
X_re = A @ S
return{'X':X1.T,'X_re':X_re.T,'A':A.T,'S':S.T}
elif f == "exp":
while lim > tol and it < maxit :
wx = W @ X1
gwx = g_exp(wx,alpha)
g_wx = gprime_exp(wx,alpha)
W1 = np.dot(gwx,X1.T)/X1.shape[1] - np.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(W1 @ W.T)) - 1.0))
W = W1
S = W @ X1
A = np.linalg.inv(W @ k)
X_re = A @ S
return{'X':X1.T,'X_re':X_re.T,'A':A.T,'S':S.T}
else:
print("doesn't support this approximation negentropy function")
Overwriting Source/fastICA_0.py
In [2]:
%%writefile Source/fastICA_1.py
import numpy as np
def sym_decorrelation(W):
""" Symmetric decorrelation """
K = np.dot(W, W.T)
s, u = np.linalg.eigh(K)
W = (u @ np.diag(1.0/np.sqrt(s)) @ u.T) @ W
return W
def fastICA_1(X, f,alpha=None, n_comp=None,maxit=200, tol=1e-04):
"""FastICA algorithm for several units"""
n,p = X.shape
#check if n_comp is valid
if n_comp is None:
n_comp = min(n,p)
elif n_comp > min(n,p):
print("n_comp is too large")
n_comp = min(n,p)
#centering
#by subtracting the mean of each column of X (array).
X = X - X.mean(axis=0)[None,:]
X = X.T
#whitening
svd = np.linalg.svd(X @ (X.T) / n)
k = np.diag(1/np.sqrt(svd[1])) @ (svd[0].T)
k = k[:n_comp,:]
X1 = k @ X
del X
# approximation negentropy function
if f == "logcosh":
def g(wx,alpha):
return np.tanh(alpha * wx)
def gprime(wx,alpha):
return alpha * (1-np.square(np.tanh(alpha*wx)))
elif f == "exp":
def g(wx,alpha):
return wx * np.exp(-np.square(wx)/2)
def gprime(wx,alpha):
return (1-np.square(wx)) * np.exp(-np.square(wx)/2)
else:
print("doesn't support this approximation negentropy function")
# initial random weght vector
w_init = np.random.normal(size=(n_comp, n_comp))
W = sym_decorrelation(w_init)
lim = 1
it = 0
# The FastICA algorithm
while lim > tol and it < maxit :
wx = W @ X1
gwx = g(wx,alpha)
g_wx = gprime(wx,alpha)
W1 = np.dot(gwx,X1.T)/X1.shape[1] - np.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(W1 @ W.T)) - 1.0))
W = W1
S = W @ X1
A = np.linalg.inv(W @ k)
X_re = A @ S
return{'X':X1.T,'X_re':X_re.T,'A':A.T,'S':S.T}
Overwriting Source/fastICA_1.py
In [3]:
%%writefile Source/fastICA_3.py
import scipy.linalg
import numpy as np
def sym_decorrelation(W):
""" Symmetric decorrelation """
K = np.dot(W, W.T)
s, u = np.linalg.eigh(K)
W = (u @ np.diag(1.0/np.sqrt(s)) @ u.T) @ W
return W
def g_logcosh(wx,alpha):
"""derivatives of logcosh"""
return np.tanh(alpha * wx)
def gprime_logcosh(wx,alpha):
"""second derivatives of logcosh"""
return alpha * (1-np.square(np.tanh(alpha*wx)))
# exp
def g_exp(wx,alpha):
"""derivatives of exp"""
return wx * np.exp(-np.square(wx)/2)
def gprime_exp(wx,alpha):
"""second derivatives of exp"""
return (1-np.square(wx)) * np.exp(-np.square(wx)/2)
def fastICA_3(X, f,alpha=None,n_comp=None,maxit=200, tol=1e-04):
"""FastICA algorithm for several units"""
n,p = X.shape
#check if n_comp is valid
if n_comp is None:
n_comp = min(n,p)
elif n_comp > min(n,p):
print("n_comp is too large")
n_comp = min(n,p)
#centering
#by subtracting the mean of each column of X (array).
X = X - X.mean(axis=0)[None,:]
X = X.T
#whitening
s = np.linalg.svd(X @ (X.T) / n)
D = np.diag(1/np.sqrt(s[1]))
k = D @ (s[0].T)
k = k[:n_comp,:]
X1 = k @ X
# initial random weght vector
w_init = np.random.normal(size=(n_comp, n_comp))
W = sym_decorrelation(w_init)
lim = 1
it = 0
# The FastICA algorithm
while lim > tol and it < maxit :
wx = W @ X1
if f =="logcosh":
gwx = g_logcosh(wx,alpha)
g_wx = gprime_logcosh(wx,alpha)
elif f =="exp":
gwx = g_exp(wx,alpha)
g_wx = gprimeg_exp(wx,alpha)
else:
print("doesn't support this approximation negentropy function")
W1 = np.dot(gwx,X1.T)/X1.shape[1] - np.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(W1 @ W.T))) - 1.0)
W = W1
S = W @ X1
A = scipy.linalg.pinv2(W @ k)
return{'X':X1.T,'A':A.T,'S':S.T}
Overwriting Source/fastICA_3.py
In [4]:
%%writefile Source/fastICA_scipy.py
import scipy
import scipy.linalg
import numpy as np
def sym_decorrelation_scipy(W):
""" Symmetric decorrelation """
K = scipy.dot(W, W.T)
s, u = scipy.linalg.eigh(K)
W = scipy.dot(scipy.dot(scipy.dot(u,np.diag(1.0/np.sqrt(s)) ),u.T),W)
return W
def fastICA_scipy(X, f,alpha=None, n_comp=None,maxit=200, tol=1e-04):
"""FastICA algorithm for several units"""
n,p = X.shape
#check if n_comp is valid
if n_comp is None:
n_comp = min(n,p)
elif n_comp > min(n,p):
print("n_comp is too large")
n_comp = min(n,p)
#centering
#by subtracting the mean of each column of X (array).
X = X - X.mean(axis=0)[None,:]
X = X.T
#whitening
svd = scipy.linalg.svd(scipy.dot(X,X.T) / n)
k = scipy.dot(np.diag(1/np.sqrt(svd[1])),svd[0].T)
k = k[:n_comp,:]
X1 = scipy.dot(k,X)
del X
# approximation negentropy function
if f == "logcosh":
def g(wx,alpha):
return scipy.tanh(alpha * wx)
def gprime(wx,alpha):
return alpha * (1-np.square(scipy.tanh(alpha*wx)))
elif f == "exp":
def g(wx,alpha):
return wx * np.exp(-np.square(wx)/2)
def gprime(wx,alpha):
return (1-np.square(wx)) * np.exp(-np.square(wx)/2)
else:
print("doesn't support this approximation negentropy function")
# initial random weght vector
w_init = np.random.normal(size=(n_comp, n_comp))
W = sym_decorrelation_scipy(w_init)
lim = 1
it = 0
# The FastICA algorithm
while lim > tol and it < maxit :
wx = scipy.dot(W,X1)
gwx = g(wx,alpha)
g_wx = gprime(wx,alpha)
W1 = scipy.dot(gwx,X1.T)/X1.shape[1] - scipy.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation_scipy(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(scipy.dot(W1,W.T))) - 1.0))
W = W1
S = scipy.dot(W,X1)
A = scipy.linalg.pinv2(scipy.dot(W,k))
X_re = scipy.dot(A,S)
return{'X':X1.T,'X_re':X_re.T,'A':A.T,'S':S.T}
Overwriting Source/fastICA_scipy.py
In [5]:
%%writefile Source/fastICA_jit.py
import scipy.linalg
import numpy as np
from numba import jit
@jit
def sym_decorrelation_jit(W):
""" Symmetric decorrelation """
K = np.dot(W, W.T)
s, u = np.linalg.eigh(K)
W = (u @ np.diag(1.0/np.sqrt(s)) @ u.T) @ W
return W
def g_logcosh_jit(wx,alpha):
"""derivatives of logcosh"""
return np.tanh(alpha * wx)
def gprime_logcosh_jit(wx,alpha):
"""second derivatives of logcosh"""
return alpha * (1-np.square(np.tanh(alpha*wx)))
# exp
def g_exp_jit(wx,alpha):
"""derivatives of exp"""
return wx * np.exp(-np.square(wx)/2)
def gprime_exp_jit(wx,alpha):
"""second derivatives of exp"""
return (1-np.square(wx)) * np.exp(-np.square(wx)/2)
def fastICA_jit(X, f,alpha=None,n_comp=None,maxit=200, tol=1e-04):
"""FastICA algorithm for several units"""
n,p = X.shape
#check if n_comp is valid
if n_comp is None:
n_comp = min(n,p)
elif n_comp > min(n,p):
print("n_comp is too large")
n_comp = min(n,p)
#centering
#by subtracting the mean of each column of X (array).
X = X - X.mean(axis=0)[None,:]
X = X.T
#whitening
s = np.linalg.svd(X @ (X.T) / n)
D = np.diag(1/np.sqrt(s[1]))
k = D @ (s[0].T)
k = k[:n_comp,:]
X1 = k @ X
# initial random weght vector
w_init = np.random.normal(size=(n_comp, n_comp))
W = sym_decorrelation_jit(w_init)
lim = 1
it = 0
# The FastICA algorithm
while lim > tol and it < maxit :
wx = W @ X1
if f =="logcosh":
gwx = g_logcosh_jit(wx,alpha)
g_wx = gprime_logcosh_jit(wx,alpha)
elif f =="exp":
gwx = g_exp_jit(wx,alpha)
g_wx = gprimeg_exp_jit(wx,alpha)
else:
print("doesn't support this approximation negentropy function")
W1 = np.dot(gwx,X1.T)/X1.shape[1] - np.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation_jit(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(W1 @ W.T))) - 1.0)
W = W1
S = W @ X1
A = scipy.linalg.pinv2(W @ k)
return{'X':X1.T,'A':A.T,'S':S.T}
Overwriting Source/fastICA_jit.py
In [6]:
%%writefile Source/fastICA_ne.py
import scipy.linalg
import numpy as np
import numexpr as ne
def sym_decorrelation_ne(W):
""" Symmetric decorrelation """
K = np.dot(W, W.T)
s, u = np.linalg.eigh(K)
return (u @ np.diag(1.0/np.sqrt(s)) @ u.T) @ W
# logcosh
def g_logcosh_ne(wx,alpha):
"""derivatives of logcosh"""
return ne.evaluate('tanh(alpha * wx)')
def gprime_logcosh_ne(wx,alpha):
"""second derivatives of logcosh"""
return alpha * (1-ne.evaluate('tanh(alpha*wx)**2'))
# exp
def g_exp_ne(wx,alpha):
"""derivatives of exp"""
return ne.evaluate('wx * exp(-wx**2/2)')
def gprime_exp_ne(wx,alpha):
"""second derivatives of exp"""
return (1-np.square(wx)) * ne.evaluate('exp(-wx**2/2)')
def fastICA_ne(X, f,alpha=None,n_comp=None,maxit=200, tol=1e-04):
n,p = X.shape
#check if n_comp is valid
if n_comp is None:
n_comp = min(n,p)
elif n_comp > min(n,p):
print("n_comp is too large")
n_comp = min(n,p)
#centering
#by subtracting the mean of each column of X (array).
X = X - X.mean(axis=0)[None,:]
X = X.T
#whitening
s = np.linalg.svd(X @ (X.T) / n)
D = np.diag(1/np.sqrt(s[1]))
k = D @ (s[0].T)
k = k[:n_comp,:]
X1 = k @ X
# initial random weght vector
w_init = np.random.normal(size=(n_comp, n_comp))
W = sym_decorrelation_ne(w_init)
lim = 1
it = 0
# The FastICA algorithm
while lim > tol and it < maxit :
wx = W @ X1
if f =="logcosh":
gwx = g_logcosh_ne(wx,alpha)
g_wx = gprime_logcosh_ne(wx,alpha)
elif f =="exp":
gwx = g_exp_ne(wx,alpha)
g_wx = gprimeg_exp_ne(wx,alpha)
else:
print("doesn't support this approximation negentropy function")
W1 = np.dot(gwx,X1.T)/X1.shape[1] - np.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation_ne(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(W1 @ W.T))) - 1.0)
W = W1
S = W @ X1
A = scipy.linalg.pinv2(W @ k)
return{'X':X1.T,'A':A.T,'S':S.T}
Overwriting Source/fastICA_ne.py
In [7]:
%load_ext cython
In [8]:
%%cython -a
import numpy as np
import scipy.linalg
from numpy import dot
import cython
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
cdef sym_decorrelation_cython(double[:,:] W):
cdef double[:,:] K = dot(W,W.T)
eigen = np.linalg.eigh(K)
cdef double[:,:] dias = np.diag(1.0/np.sqrt(eigen[0]))
cdef double[:,:] u = eigen[1]
return dot(dot(dot(u,dias),u.T),W)
@cython.wraparound(False)
@cython.boundscheck(False)
cdef g_logcosh_cython(double[:,:] wx, double alpha):
"""derivatives of logcosh"""
return np.tanh(np.multiply(alpha,wx))
@cython.wraparound(False)
@cython.boundscheck(False)
cdef gprime_logcosh_cython(double[:,:] wx, double alpha):
"""second derivatives of logcosh"""
return np.multiply(alpha,(1-np.square(np.tanh(np.multiply(alpha,wx)))))
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
cdef g_exp_cython(double[:,:] wx, double alpha):
"""derivatives of exp"""
return wx * np.exp(-np.square(wx)/2)
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
cdef gprime_exp_cython(double[:,:] wx, double alpha):
"""second derivatives of exp"""
return (1-np.square(wx)) * np.exp(-np.square(wx)/2)
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def fastICA_cython(double[:,:] X, str f,double alpha, int n_comp,int maxit, double tol):
"""FastICA algorithm for several units"""
cdef int n = X.shape[0]
cdef int p = X.shape[1]
#check if n_comp is valid
if n_comp is None:
n_comp = min(n,p)
elif n_comp > min(n,p):
print("n_comp is too large")
n_comp = min(n,p)
#centering
#by subtracting the mean of each column of X (array).
X = X - np.mean(X,axis=0)[None,:]
X = X.T
#whitening
svd = np.linalg.svd(dot(X,X.T) / n)
k = dot(np.diag(1/np.sqrt(svd[1])),svd[0].T)
k = k[:n_comp,:]
X1 = dot(k,X)
# initial random weght vector
w_init = np.random.normal(size=(n_comp, n_comp))
W = sym_decorrelation_cython(w_init)
lim = 1
it = 0
# The FastICA algorithm
while lim > tol and it < maxit :
wx = dot(W,X1)
if f == "logcosh":
gwx = g_logcosh_cython(wx,alpha)
g_wx = gprime_logcosh_cython(wx,alpha)
elif f == "exp":
gwx = g_exp_cython(wx,alpha)
g_wx = gprime_exp_cython(wx,alpha)
else:
print("doesn't support this approximation negentropy function")
W1 = np.dot(gwx,X1.T)/X1.shape[1] - np.dot(np.diag(g_wx.mean(axis=1)),W)
W1 = sym_decorrelation_cython(W1)
it = it +1
lim = np.max(np.abs(np.abs(np.diag(dot(W1,W.T))) - 1.0))
W = W1
S = dot(W,X1)
A = scipy.linalg.pinv2(dot(W,k))
X_re = dot(A,S)
return{'X':X1.T,'X_re':X_re.T,'A':A.T,'S':S.T}
Out[8]:
Cython: _cython_magic_8f9944ae9d4ade65cf1b126b673f1abc.pyx
Generated by Cython 0.23.5
Yellow lines hint at Python interaction.
Click on a line that starts with a "+" to see the C code that Cython generated for it.
01:
+02: import numpy as np
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__Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
+03: import scipy.linalg
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__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
+04: from numpy import dot
__pyx_t_1 = PyList_New(1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 4; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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05: import cython
06:
07: @cython.cdivision(True)
08: @cython.wraparound(False)
09: @cython.boundscheck(False)
+10: cdef sym_decorrelation_cython(double[:,:] W):
static PyObject *__pyx_f_46_cython_magic_8f9944ae9d4ade65cf1b126b673f1abc_sym_decorrelation_cython(__Pyx_memviewslice __pyx_v_W) {
__Pyx_memviewslice __pyx_v_K = { 0, 0, { 0 }, { 0 }, { 0 } };
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__Pyx_GIVEREF(__pyx_v_X1);
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__PYX_XDEC_MEMVIEW(&__pyx_t_11, 1);
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Content source: 663project/fastica_lz
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