Mic92/k-shape
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compare: Mic92:326ff3f667d65bf913512643d8988674dac9fad8
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Author SHA1 Message Date
Jörg Thalheim
326ff3f667 remove dependency on scipy 2016-05-17 12:23:16 +00:00
1 changed files with 88 additions and 30 deletions
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kshape.py
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@ -1,22 +1,72 @@
import math
import numpy as np
from numpy.random import randint
from numpy.random import randint, seed
from numpy.linalg import norm, eigh
from numpy.linalg import norm
from numpy.fft import fft, ifft
from scipy.sparse.linalg import eigs
from scipy.stats import zscore
from scipy.ndimage.interpolation import shift
#from scipy.linalg import eigh
def zscore(a, axis=0, ddof=0):
a = np.asanyarray(a)
mns = a.mean(axis=axis)
sstd = a.std(axis=axis, ddof=ddof)
if axis and mns.ndim < a.ndim:
return ((a - np.expand_dims(mns, axis=axis)) /
np.expand_dims(sstd,axis=axis))
else:
return (a - mns) / sstd
def roll_zeropad(a, shift, axis=None):
a = np.asanyarray(a)
if shift == 0: return a
if axis is None:
n = a.size
reshape = True
else:
n = a.shape[axis]
reshape = False
if np.abs(shift) > n:
res = np.zeros_like(a)
elif shift < 0:
shift += n
zeros = np.zeros_like(a.take(np.arange(n-shift), axis))
res = np.concatenate((a.take(np.arange(n-shift,n), axis), zeros), axis)
else:
zeros = np.zeros_like(a.take(np.arange(n-shift,n), axis))
res = np.concatenate((zeros, a.take(np.arange(n-shift), axis)), axis)
if reshape:
return res.reshape(a.shape)
else:
return res
# TODO vectorized version of _ncc_c
#def _ncc_c(x,y):
# """
# >>> _ncc_c(np.array([[1,2,3,4]]), np.array([[1,2,3,4]]))
# array([[ 0.13333333, 0.36666667, 0.66666667, 1. , 0.66666667,
# 0.36666667, 0.13333333]])
# >>> _ncc_c(np.array([[1,1,1]]), np.array([[1,1,1]]))
# array([[ 0.33333333, 0.66666667, 1. , 0.66666667, 0.33333333]])
# >>> _ncc_c(np.array([[1,2,3]]), np.array([[-1,-1,-1]]))
# array([[-0.15430335, -0.46291005, -0.9258201 , -0.77151675, -0.46291005]])
# """
# x_len = x.shape[1]
# fft_size = 1<<(2*x_len-1).bit_length()
# cc = ifftn(fftn(x, (fft_size,)) * np.conj(fftn(y, (fft_size,))))
# cc = np.concatenate((cc[:, -(x_len-1):], cc[:, :x_len]), axis=1)
# return np.real(cc) / (norm(x) * norm(y))
def _ncc_c(x,y):
"""
>>> ncc_c([1,2,3,4], [1,2,3,4])
>>> _ncc_c([1,2,3,4], [1,2,3,4])
array([ 0.13333333, 0.36666667, 0.66666667, 1. , 0.66666667,
0.36666667, 0.13333333])
>>> ncc_c([1,1,1], [1,1,1])
>>> _ncc_c([1,1,1], [1,1,1])
array([ 0.33333333, 0.66666667, 1. , 0.66666667, 0.33333333])
>>> ncc_c([1,2,3], [-1,-1,-1])
>>> _ncc_c([1,2,3], [-1,-1,-1])
array([-0.15430335, -0.46291005, -0.9258201 , -0.77151675, -0.46291005])
"""
x_len = len(x)
@ -27,26 +77,33 @@ def _ncc_c(x,y):
def _sbd(x, y):
"""
>>> sbd([1,1,1], [1,1,1])
(-2.2204460492503131e-16, array([1, 1, 1]))
>>> sbd([0,1,2], [1,2,3])
(0.043817112532485103, array([1, 2, 3]))
>>> sbd([1,2,3], [0,1,2])
(0.043817112532485103, array([0, 1, 2]))
"""
#"""
#>>> _sbd([1,1,1], [1,1,1])
#(-2.2204460492503131e-16, array([1, 1, 1]))
#>>> _sbd([0,1,2], [1,2,3])
#(0.043817112532485103, array([1, 2, 3]))
#>>> _sbd([1,2,3], [0,1,2])
#(0.043817112532485103, array([0, 1, 2]))
#"""
ncc = _ncc_c(x, y)
idx = ncc.argmax()
dist = 1 - ncc[idx]
yshift = shift(y, (idx + 1) - max(len(x), len(y)))
yshift = roll_zeropad(y, (idx + 1) - max(len(x), len(y)))
return dist, yshift
#@profile
def _extract_shape(idx, x, j, cur_center):
"""
>>> extract_shape(np.array([0,1,2]), np.array([[1,2,3], [4,5,6]]), 1, np.array([0,3,4]))
array([ -1.00000000e+00, -3.06658683e-19, 1.00000000e+00])
>>> extract_shape(np.array([0,1,2]), np.array([[-1,2,3], [4,-5,6]]), 1, np.array([0,3,4]))
>>> _extract_shape(np.array([0,1,2]), np.array([[1,2,3], [4,5,6]]), 1, np.array([0,3,4]))
array([-1., 0., 1.])
>>> _extract_shape(np.array([0,1,2]), np.array([[-1,2,3], [4,-5,6]]), 1, np.array([0,3,4]))
array([-0.96836405, 1.02888681, -0.06052275])
>>> _extract_shape(np.array([1,0,1,0]), np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 0, np.array([0,0,0,0]))
array([-1.2089303 , -0.19618238, 0.19618238, 1.2089303 ])
>>> _extract_shape(np.array([0,0,1,0]), np.array([[1,2,3,4],[0,1,2,3],[-1,1,-1,1],[1,2,2,3]]), 0, np.array([-1.2089303,-0.19618238,0.19618238,1.2089303]))
array([-1.19623139, -0.26273649, 0.26273649, 1.19623139])
"""
_a = []
for i in range(len(idx)):
@ -69,39 +126,40 @@ def _extract_shape(idx, x, j, cur_center):
p = np.eye(columns) - p
m = np.dot(np.dot(p, s), p)
_, vec = eigs(m, 1)
centroid = np.real(vec[:,0])
_, vec = eigh(m)
centroid = vec[:,-1]
finddistance1 = math.sqrt(((a[0] - centroid) ** 2).sum())
finddistance2 = math.sqrt(((a[0] + centroid) ** 2).sum())
if finddistance1 >= finddistance2:
centroid *= -1
return zscore(centroid, ddof=1)
return zscore(centroid, ddof=1)
def _kshape(x, k):
"""
>>> kshape(np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 2)
(array([0, 0, 1, 0]), array([[-1.19623139, -0.26273649, 0.26273649, 1.19623139],
>>> from numpy.random import seed; seed(0)
>>> _kshape(np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 2)
(array([0, 0, 1, 0]), array([[-1.2244258 , -0.35015476, 0.52411628, 1.05046429],
[-0.8660254 , 0.8660254 , -0.8660254 , 0.8660254 ]]))
"""
m = x.shape[0]
idx = randint(0, k, size=m)
centroids = np.zeros((k,x.shape[1]))
distances = np.empty((m, k))
for _ in range(100):
old_idx = idx
for j in range(k):
res = _extract_shape(idx, x, j, centroids[j])
centroids[j] = res
centroids[j] = _extract_shape(idx, x, j, centroids[j])
for i in range(m):
for j in range(k):
distances[i,j] = 1 - max(_ncc_c(x[i], centroids[j]))
for j in range(k):
distances[i,j] = 1 - max(_ncc_c(x[i], centroids[j]))
idx = distances.argmin(1)
if norm(old_idx - idx) == 0:
if np.array_equal(old_idx, idx):
break
return idx, centroids
def kshape(x, k):