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import numpy as np |
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from .cpd_nonlin import cpd_nonlin |
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def cpd_auto(K, ncp, vmax, desc_rate=1, **kwargs): |
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"""Main interface |
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Detect change points automatically selecting their number |
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K - kernel between each pair of frames in video |
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ncp - maximum ncp |
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vmax - special parameter |
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Optional arguments: |
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lmin - minimum segment length |
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lmax - maximum segment length |
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desc_rate - rate of descriptor sampling (vmax always corresponds to 1x) |
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Note: |
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- cps are always calculated in subsampled coordinates irrespective to |
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desc_rate |
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- lmin and m should be in agreement |
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--- |
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Returns: (cps, costs) |
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cps - best selected change-points |
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costs - costs for 0,1,2,...,m change-points |
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Memory requirement: ~ (3*N*N + N*ncp)*4 bytes ~= 16 * N^2 bytes |
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That is 1,6 Gb for the N=10000. |
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""" |
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m = ncp |
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(_, scores) = cpd_nonlin(K, m, backtrack=False, **kwargs) |
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N = K.shape[0] |
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N2 = N*desc_rate |
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penalties = np.zeros(m+1) |
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ncp = np.arange(1, m+1) |
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penalties[1:] = (vmax*ncp/(2.0*N2))*(np.log(float(N2)/ncp)+1) |
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costs = scores/float(N) + penalties |
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m_best = np.argmin(costs) |
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(cps, scores2) = cpd_nonlin(K, m_best, **kwargs) |
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return (cps, costs) |
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def estimate_vmax(K_stable): |
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"""K_stable - kernel between all frames of a stable segment""" |
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n = K_stable.shape[0] |
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vmax = np.trace(centering(K_stable)/n) |
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return vmax |
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def centering(K): |
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"""Apply kernel centering""" |
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mean_rows = np.mean(K, 1)[:, np.newaxis] |
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return K - mean_rows - mean_rows.T + np.mean(mean_rows) |
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def eval_score(K, cps): |
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""" Evaluate unnormalized empirical score |
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(sum of kernelized scatters) for the given change-points """ |
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N = K.shape[0] |
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cps = [0] + list(cps) + [N] |
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V1 = 0 |
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V2 = 0 |
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for i in range(len(cps)-1): |
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K_sub = K[cps[i]:cps[i+1], :][:, cps[i]:cps[i+1]] |
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V1 += np.sum(np.diag(K_sub)) |
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V2 += np.sum(K_sub) / float(cps[i+1] - cps[i]) |
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return (V1 - V2) |
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def eval_cost(K, cps, score, vmax): |
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""" Evaluate cost function for automatic number of change points selection |
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K - kernel between all frames |
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cps - selected change-points |
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score - unnormalized empirical score (sum of kernelized scatters) |
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vmax - vmax parameter""" |
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N = K.shape[0] |
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penalty = (vmax*len(cps)/(2.0*N))*(np.log(float(N)/len(cps))+1) |
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return score/float(N) + penalty |
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