utils/kts_utils.py

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


def calc_scatters(K):
    n = K.shape[0]
    K1 = np.cumsum([0] + list(np.diag(K)))
    K2 = np.zeros((n + 1, n + 1)).astype(np.double())
    K2[1:, 1:] = np.cumsum(np.cumsum(K, 0), 1)  # TODO: use the fact that K - symmetric
    # KK = np.cumsum(K, 0).astype(np.double())
    # K2[1:, 1:] = np.cumsum(KK, 1) # TODO: use the fact that K - symmetric

    scatters = np.zeros((n, n))

    #     code = r"""
    #     for (int i = 0; i < n; i++) {
    #         for (int j = i; j < n; j++) {
    #             scatters(i,j) = K1(j+1)-K1(i) - (K2(j+1,j+1)+K2(i,i)-K2(j+1,i)-K2(i,j+1))/(j-i+1);
    #         }
    #     }
    #     """
    #     weave.inline(code, ['K1','K2','scatters','n'], global_dict = \
    #         {'K1':K1, 'K2':K2, 'scatters':scatters, 'n':n}, type_converters=weave.converters.blitz)

    for i in range(n):
        for j in range(i, n):
            scatters[i, j] = K1[j + 1] - K1[i] - (K2[j + 1, j + 1] + K2[i, i] - K2[j + 1, i] - K2[i, j + 1]) / (
                        j - i + 1)
    return scatters

def cpd_nonlin(K, ncp, lmin=1, lmax=100000, backtrack=True, verbose=True,
               out_scatters=None):
    """ Change point detection with dynamic programming
    K - square kernel matrix
    ncp - number of change points to detect (ncp >= 0)
    lmin - minimal length of a segment
    lmax - maximal length of a segment
    backtrack - when False - only evaluate objective scores (to save memory)

    Returns: (cps, obj)
        cps - detected array of change points: mean is thought to be constant on [ cps[i], cps[i+1] )
        obj_vals - values of the objective function for 0..m changepoints

    """
    m = int(ncp)  # prevent numpy.int64

    (n, n1) = K.shape
    assert (n == n1), "Kernel matrix awaited."

    assert (n >= (m + 1) * lmin)
    assert (n <= (m + 1) * lmax)
    assert (lmax >= lmin >= 1)

    if verbose:
        # print "n =", n
        print("Precomputing scatters...")
    J = calc_scatters(K)

    if out_scatters != None:
        out_scatters[0] = J

    if verbose:
        print("Inferring best change points...")
    I = 1e101 * np.ones((m + 1, n + 1))
    I[0, lmin:lmax] = J[0, lmin - 1:lmax - 1]

    if backtrack:
        p = np.zeros((m + 1, n + 1), dtype=int)
    else:
        p = np.zeros((1, 1), dtype=int)

    #     code = r"""
    #     #define max(x,y) ((x)>(y)?(x):(y))
    #     for (int k=1; k<m+1; k++) {
    #         for (int l=(k+1)*lmin; l<n+1; l++) {
    #             I(k, l) = 1e100; //nearly infinity
    #             for (int t=max(k*lmin,l-lmax); t<l-lmin+1; t++) {
    #                 double c = I(k-1, t) + J(t, l-1);
    #                 if (c < I(k, l)) {
    #                     I(k, l) = c;
    #                     if (backtrack == 1) {
    #                         p(k, l) = t;
    #                     }
    #                 }
    #             }
    #         }
    #     }
    #     """

    #     weave.inline(code, ['m','n','p','I', 'J', 'lmin', 'lmax', 'backtrack'], \
    #         global_dict={'m':m, 'n':n, 'p':p, 'I':I, 'J':J, \
    #         'lmin':lmin, 'lmax':lmax, 'backtrack': int(1) if backtrack else int(0)},
    #         type_converters=weave.converters.blitz)

    for k in range(1, m + 1):
        for l in range((k + 1) * lmin, n + 1):
            I[k, l] = 1e100
            for t in range(max(k * lmin, l - lmax), l - lmin + 1):
                c = I[k - 1, t] + J[t, l - 1]
                if (c < I[k, l]):
                    I[k, l] = c
                    if (backtrack == 1):
                        p[k, l] = t

    # Collect change points
    cps = np.zeros(m, dtype=int)

    if backtrack:
        cur = n
        for k in range(m, 0, -1):
            cps[k - 1] = p[k, cur]
            cur = cps[k - 1]

    scores = I[:, n].copy()
    scores[scores > 1e99] = np.inf
    return cps, scores