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| import numpy as np | |
| from .cpd_nonlin import cpd_nonlin | |
| def cpd_auto(K, ncp, vmax, desc_rate=1, **kwargs): | |
| """Main interface | |
| Detect change points automatically selecting their number | |
| K - kernel between each pair of frames in video | |
| ncp - maximum ncp | |
| vmax - special parameter | |
| Optional arguments: | |
| lmin - minimum segment length | |
| lmax - maximum segment length | |
| desc_rate - rate of descriptor sampling (vmax always corresponds to 1x) | |
| Note: | |
| - cps are always calculated in subsampled coordinates irrespective to | |
| desc_rate | |
| - lmin and m should be in agreement | |
| --- | |
| Returns: (cps, costs) | |
| cps - best selected change-points | |
| costs - costs for 0,1,2,...,m change-points | |
| Memory requirement: ~ (3*N*N + N*ncp)*4 bytes ~= 16 * N^2 bytes | |
| That is 1,6 Gb for the N=10000. | |
| """ | |
| m = ncp | |
| (_, scores) = cpd_nonlin(K, m, backtrack=False, **kwargs) | |
| # print("scores ",scores) | |
| N = K.shape[0] | |
| N2 = N*desc_rate # length of the video before subsampling | |
| penalties = np.zeros(m+1) | |
| # Prevent division by zero (in case of 0 changes) | |
| ncp = np.arange(1, m+1) | |
| penalties[1:] = (vmax*ncp/(2.0*N2))*(np.log(float(N2)/ncp)+1) | |
| costs = scores/float(N) + penalties | |
| m_best = np.argmin(costs) | |
| # print("cost ",costs) | |
| # print("m_best ",m_best) | |
| (cps, scores2) = cpd_nonlin(K, m_best, **kwargs) | |
| return (cps, costs) | |
| # ------------------------------------------------------------------------------ | |
| # Extra functions (currently not used) | |
| def estimate_vmax(K_stable): | |
| """K_stable - kernel between all frames of a stable segment""" | |
| n = K_stable.shape[0] | |
| vmax = np.trace(centering(K_stable)/n) | |
| return vmax | |
| def centering(K): | |
| """Apply kernel centering""" | |
| mean_rows = np.mean(K, 1)[:, np.newaxis] | |
| return K - mean_rows - mean_rows.T + np.mean(mean_rows) | |
| def eval_score(K, cps): | |
| """ Evaluate unnormalized empirical score | |
| (sum of kernelized scatters) for the given change-points """ | |
| N = K.shape[0] | |
| cps = [0] + list(cps) + [N] | |
| V1 = 0 | |
| V2 = 0 | |
| for i in range(len(cps)-1): | |
| K_sub = K[cps[i]:cps[i+1], :][:, cps[i]:cps[i+1]] | |
| V1 += np.sum(np.diag(K_sub)) | |
| V2 += np.sum(K_sub) / float(cps[i+1] - cps[i]) | |
| return (V1 - V2) | |
| def eval_cost(K, cps, score, vmax): | |
| """ Evaluate cost function for automatic number of change points selection | |
| K - kernel between all frames | |
| cps - selected change-points | |
| score - unnormalized empirical score (sum of kernelized scatters) | |
| vmax - vmax parameter""" | |
| N = K.shape[0] | |
| penalty = (vmax*len(cps)/(2.0*N))*(np.log(float(N)/len(cps))+1) | |
| return score/float(N) + penalty | |