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# danoneata/fisher_vector.py

Last active December 6, 2023 06:25
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Fisher vectors with sklearn
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 import numpy as np import pdb from sklearn.datasets import make_classification from sklearn.mixture import GaussianMixture as GMM def fisher_vector(xx, gmm): """Computes the Fisher vector on a set of descriptors. Parameters ---------- xx: array_like, shape (N, D) or (D, ) The set of descriptors gmm: instance of sklearn mixture.GMM object Gauassian mixture model of the descriptors. Returns ------- fv: array_like, shape (K + 2 * D * K, ) Fisher vector (derivatives with respect to the mixing weights, means and variances) of the given descriptors. Reference --------- J. Krapac, J. Verbeek, F. Jurie. Modeling Spatial Layout with Fisher Vectors for Image Categorization. In ICCV, 2011. http://hal.inria.fr/docs/00/61/94/03/PDF/final.r1.pdf """ xx = np.atleast_2d(xx) N = xx.shape[0] # Compute posterior probabilities. Q = gmm.predict_proba(xx) # NxK # Compute the sufficient statistics of descriptors. Q_sum = np.sum(Q, 0)[:, np.newaxis] / N Q_xx = np.dot(Q.T, xx) / N Q_xx_2 = np.dot(Q.T, xx ** 2) / N # Compute derivatives with respect to mixing weights, means and variances. d_pi = Q_sum.squeeze() - gmm.weights_ d_mu = Q_xx - Q_sum * gmm.means_ d_sigma = ( - Q_xx_2 - Q_sum * gmm.means_ ** 2 + Q_sum * gmm.covariances_ + 2 * Q_xx * gmm.means_) # Merge derivatives into a vector. return np.hstack((d_pi, d_mu.flatten(), d_sigma.flatten())) def main(): # Short demo. K = 64 N = 1000 xx, _ = make_classification(n_samples=N) xx_tr, xx_te = xx[: -100], xx[-100: ] gmm = GMM(n_components=K, covariance_type='diag') gmm.fit(xx_tr) fv = fisher_vector(xx_te, gmm) pdb.set_trace() if __name__ == '__main__': main()

### sobhanhemati commented Nov 27, 2020

Thank you so much for the comprehensive answer.
I really appreciate that.

### PARVATHYAJITHA commented Jun 15, 2021

Hai I'm beginner so i don't know working of fisher vector encoding. Please help to understand this