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12
README.md
12
README.md
@ -1,3 +1,15 @@
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## k-Shape
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Python implementation of k-Shape
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### Usage
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```
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from kshape import kshape
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import numpy as np
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from scipy.stats import zscore
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time_series = [[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]
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cluster_num = 2
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clusters = kshape(zscore(time_series), cluster_num)
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```
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8
example.py
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8
example.py
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from kshape import kshape
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import numpy as np
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from scipy.stats import zscore
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time_series = [[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]
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cluster_num = 2
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clusters = kshape(zscore(time_series), cluster_num)
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print(clusters)
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178
kshape.py
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178
kshape.py
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import math
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import numpy as np
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from numpy.random import randint, seed
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from numpy.linalg import norm, eigh
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from numpy.linalg import norm
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from numpy.fft import fft, ifft
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#from scipy.linalg import eigh
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def zscore(a, axis=0, ddof=0):
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a = np.asanyarray(a)
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mns = a.mean(axis=axis)
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sstd = a.std(axis=axis, ddof=ddof)
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if axis and mns.ndim < a.ndim:
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return ((a - np.expand_dims(mns, axis=axis)) /
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np.expand_dims(sstd,axis=axis))
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else:
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return (a - mns) / sstd
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def roll_zeropad(a, shift, axis=None):
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a = np.asanyarray(a)
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if shift == 0: return a
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if axis is None:
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n = a.size
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reshape = True
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else:
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n = a.shape[axis]
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reshape = False
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if np.abs(shift) > n:
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res = np.zeros_like(a)
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elif shift < 0:
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shift += n
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zeros = np.zeros_like(a.take(np.arange(n-shift), axis))
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res = np.concatenate((a.take(np.arange(n-shift,n), axis), zeros), axis)
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else:
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zeros = np.zeros_like(a.take(np.arange(n-shift,n), axis))
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res = np.concatenate((zeros, a.take(np.arange(n-shift), axis)), axis)
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if reshape:
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return res.reshape(a.shape)
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else:
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return res
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# TODO vectorized version of _ncc_c
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#def _ncc_c(x,y):
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# """
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# >>> _ncc_c(np.array([[1,2,3,4]]), np.array([[1,2,3,4]]))
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# array([[ 0.13333333, 0.36666667, 0.66666667, 1. , 0.66666667,
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# 0.36666667, 0.13333333]])
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# >>> _ncc_c(np.array([[1,1,1]]), np.array([[1,1,1]]))
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# array([[ 0.33333333, 0.66666667, 1. , 0.66666667, 0.33333333]])
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# >>> _ncc_c(np.array([[1,2,3]]), np.array([[-1,-1,-1]]))
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# array([[-0.15430335, -0.46291005, -0.9258201 , -0.77151675, -0.46291005]])
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# """
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# x_len = x.shape[1]
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# fft_size = 1<<(2*x_len-1).bit_length()
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# cc = ifftn(fftn(x, (fft_size,)) * np.conj(fftn(y, (fft_size,))))
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# cc = np.concatenate((cc[:, -(x_len-1):], cc[:, :x_len]), axis=1)
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# return np.real(cc) / (norm(x) * norm(y))
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def _ncc_c(x,y):
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"""
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>>> _ncc_c([1,2,3,4], [1,2,3,4])
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array([ 0.13333333, 0.36666667, 0.66666667, 1. , 0.66666667,
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0.36666667, 0.13333333])
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>>> _ncc_c([1,1,1], [1,1,1])
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array([ 0.33333333, 0.66666667, 1. , 0.66666667, 0.33333333])
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>>> _ncc_c([1,2,3], [-1,-1,-1])
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array([-0.15430335, -0.46291005, -0.9258201 , -0.77151675, -0.46291005])
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"""
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x_len = len(x)
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fft_size = 1<<(2*x_len-1).bit_length()
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cc = ifft(fft(x, fft_size) * np.conj(fft(y, fft_size)))
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cc = np.concatenate((cc[-(x_len-1):], cc[:x_len]))
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return np.real(cc) / (norm(x) * norm(y))
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def _sbd(x, y):
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#"""
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#>>> _sbd([1,1,1], [1,1,1])
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#(-2.2204460492503131e-16, array([1, 1, 1]))
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#>>> _sbd([0,1,2], [1,2,3])
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#(0.043817112532485103, array([1, 2, 3]))
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#>>> _sbd([1,2,3], [0,1,2])
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#(0.043817112532485103, array([0, 1, 2]))
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#"""
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ncc = _ncc_c(x, y)
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idx = ncc.argmax()
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dist = 1 - ncc[idx]
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yshift = roll_zeropad(y, (idx + 1) - max(len(x), len(y)))
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return dist, yshift
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#@profile
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def _extract_shape(idx, x, j, cur_center):
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"""
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>>> _extract_shape(np.array([0,1,2]), np.array([[1,2,3], [4,5,6]]), 1, np.array([0,3,4]))
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array([-1., 0., 1.])
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>>> _extract_shape(np.array([0,1,2]), np.array([[-1,2,3], [4,-5,6]]), 1, np.array([0,3,4]))
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array([-0.96836405, 1.02888681, -0.06052275])
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>>> _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]))
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array([-1.2089303 , -0.19618238, 0.19618238, 1.2089303 ])
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>>> _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]))
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array([-1.19623139, -0.26273649, 0.26273649, 1.19623139])
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"""
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_a = []
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for i in range(len(idx)):
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if idx[i] == j:
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if cur_center.sum() == 0:
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opt_x = x[i]
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else:
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_, opt_x = _sbd(cur_center, x[i])
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_a.append(opt_x)
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a = np.array(_a)
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if len(a) == 0:
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return np.zeros((1, x.shape[1]))
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columns = a.shape[1]
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y = zscore(a,axis=1,ddof=1)
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s = np.dot(y.transpose(), y)
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p = np.empty((columns, columns))
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p.fill(1.0/columns)
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p = np.eye(columns) - p
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m = np.dot(np.dot(p, s), p)
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_, vec = eigh(m)
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centroid = vec[:,-1]
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finddistance1 = math.sqrt(((a[0] - centroid) ** 2).sum())
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finddistance2 = math.sqrt(((a[0] + centroid) ** 2).sum())
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if finddistance1 >= finddistance2:
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centroid *= -1
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return zscore(centroid, ddof=1)
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def _kshape(x, k):
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"""
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>>> from numpy.random import seed; seed(0)
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>>> _kshape(np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 2)
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(array([0, 0, 1, 0]), array([[-1.2244258 , -0.35015476, 0.52411628, 1.05046429],
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[-0.8660254 , 0.8660254 , -0.8660254 , 0.8660254 ]]))
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"""
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m = x.shape[0]
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idx = randint(0, k, size=m)
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centroids = np.zeros((k,x.shape[1]))
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distances = np.empty((m, k))
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for _ in range(100):
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old_idx = idx
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for j in range(k):
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centroids[j] = _extract_shape(idx, x, j, centroids[j])
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for i in range(m):
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for j in range(k):
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distances[i,j] = 1 - max(_ncc_c(x[i], centroids[j]))
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idx = distances.argmin(1)
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if np.array_equal(old_idx, idx):
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break
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return idx, centroids
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def kshape(x, k):
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idx, centroids = _kshape(np.array(x), k)
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clusters = []
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for i, centroid in enumerate(centroids):
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series = []
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for j, val in enumerate(idx):
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if i == val:
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series.append(j)
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clusters.append((centroid, series))
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return clusters
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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110
test.py
110
test.py
@ -1,110 +0,0 @@
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import math
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import numpy as np
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from numpy.random import randint
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from numpy.linalg import norm
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from numpy.fft import fft, ifft
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from scipy.sparse.linalg import eigs
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from scipy.stats import zscore
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from scipy.ndimage.interpolation import shift
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def ncc_c(x,y):
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"""
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>>> ncc_c([1,2,3,4], [1,2,3,4])
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array([ 0.13333333, 0.36666667, 0.66666667, 1. , 0.66666667,
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0.36666667, 0.13333333])
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>>> ncc_c([1,1,1], [1,1,1])
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array([ 0.33333333, 0.66666667, 1. , 0.66666667, 0.33333333])
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>>> ncc_c([1,2,3], [-1,-1,-1])
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array([-0.15430335, -0.46291005, -0.9258201 , -0.77151675, -0.46291005])
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"""
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x_len = len(x)
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fft_size = 1<<(2*x_len-1).bit_length()
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cc = ifft(fft(x, fft_size) * np.conj(fft(y, fft_size)))
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cc = np.concatenate((cc[-(x_len-1):], cc[:x_len]))
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return np.real(cc) / (norm(x) * norm(y))
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def sbd(x, y):
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"""
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>>> sbd([1,1,1], [1,1,1])
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(-2.2204460492503131e-16, array([1, 1, 1]))
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>>> sbd([0,1,2], [1,2,3])
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(0.043817112532485103, array([1, 2, 3]))
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>>> sbd([1,2,3], [0,1,2])
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(0.043817112532485103, array([0, 1, 2]))
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"""
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ncc = ncc_c(x, y)
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idx = ncc.argmax()
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dist = 1 - ncc[idx]
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yshift = shift(y, (idx + 1) - max(len(x), len(y)))
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return dist, yshift
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def extract_shape(idx, x, j, cur_center):
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"""
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>>> extract_shape(np.array([0,1,2]), np.array([[1,2,3], [4,5,6]]), 1, np.array([0,3,4]))
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array([ -1.00000000e+00, -3.06658683e-19, 1.00000000e+00])
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>>> extract_shape(np.array([0,1,2]), np.array([[-1,2,3], [4,-5,6]]), 1, np.array([0,3,4]))
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array([-0.96836405, 1.02888681, -0.06052275])
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"""
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_a = []
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for i in range(len(idx)):
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if idx[i] == j:
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if cur_center.sum() == 0:
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opt_x = x[i]
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else:
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_, opt_x = sbd(cur_center, x[i])
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_a.append(opt_x)
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a = np.array(_a)
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if len(a) == 0:
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return np.zeros((1, x.shape[1]))
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columns = a.shape[1]
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y = zscore(a,axis=1,ddof=1)
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s = np.dot(y.transpose(), y)
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p = np.empty((columns, columns))
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p.fill(1.0/columns)
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p = np.eye(columns) - p
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m = np.dot(np.dot(p, s), p)
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_, vec = eigs(m, 1)
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centroid = np.real(vec[:,0])
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finddistance1 = math.sqrt(((a[0] - centroid) ** 2).sum())
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finddistance2 = math.sqrt(((a[0] + centroid) ** 2).sum())
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if finddistance1 >= finddistance2:
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centroid *= -1
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return zscore(centroid, ddof=1)
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def kshape(x, k):
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"""
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>>> kshape(np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 2)
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(array([0, 0, 1, 0]), array([[-1.19623139, -0.26273649, 0.26273649, 1.19623139],
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[-0.8660254 , 0.8660254 , -0.8660254 , 0.8660254 ]]))
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"""
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m = x.shape[0]
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idx = randint(0, k, size=m)
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centroids = np.zeros((k,x.shape[1]))
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distances = np.empty((m, k))
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for _ in range(100):
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old_idx = idx
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for j in range(k):
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res = extract_shape(idx, x, j, centroids[j])
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centroids[j] = res
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for i in range(m):
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for j in range(k):
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distances[i,j] = 1 - max(ncc_c(x[i], centroids[j]))
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idx = distances.argmin(1)
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if norm(old_idx - idx) == 0:
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break
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return idx, centroids
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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