kk-MLE: A fast algorithm for learning statistical mixture models

We describe $k$-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization (EM) soft clustering technique that monotonically increases the incomplete (expected complete) likelihood. Given prescribed mixture weights, the hard clustering $k$-MLE algorithm iteratively assigns data to the most likely weighted component and update the component models using Maximum Likelihood Estimators (MLEs). Using the duality between exponential families and Bregman divergences, we prove that the local convergence of the complete likelihood of $k$-MLE follows directly from the convergence of a dual additively weighted Bregman hard clustering. The inner loop of $k$-MLE can be implemented using any $k$-means heuristic like the celebrated Lloyd's batched or Hartigan's greedy swap updates. We then show how to update the mixture weights by minimizing a cross-entropy criterion that implies to update weights by taking the relative proportion of cluster points, and reiterate the mixture parameter update and mixture weight update processes until convergence. Hard EM is interpreted as a special case of $k$-MLE when both the component update and the weight update are performed successively in the inner loop. To initialize $k$-MLE, we propose $k$-MLE++, a careful initialization of $k$-MLE guaranteeing probabilistically a global bound on the best possible complete likelihood.Comment: 31 pages, Extend preliminary paper presented at IEEE ICASSP 201

Perfectly secure steganography: hiding information in the quantum noise of a photograph

We show that the quantum nature of light can be used to hide a secret message within a photograph. Using this physical principle we achieve information-theoretic secure steganography, which had remained elusive until now. The protocol is such that the digital picture in which the secret message is embedded is perfectly undistinguishable from an ordinary photograph. This implies that, on a fundamental level, it is impossible to discriminate a private communication from an exchange of photographs.Comment: 5 pages, 3 figures + appendix : 5 pages, 6 figure

Ensemble of Different Approaches for a Reliable Person Re-identification System

An ensemble of approaches for reliable person re-identification is proposed in this paper. The proposed ensemble is built combining widely used person re-identification systems using different color spaces and some variants of state-of-the-art approaches that are proposed in this paper. Different descriptors are tested, and both texture and color features are extracted from the images; then the different descriptors are compared using different distance measures (e.g., the Euclidean distance, angle, and the Jeffrey distance). To improve performance, a method based on skeleton detection, extracted from the depth map, is also applied when the depth map is available. The proposed ensemble is validated on three widely used datasets (CAVIAR4REID, IAS, and VIPeR), keeping the same parameter set of each approach constant across all tests to avoid overfitting and to demonstrate that the proposed system can be considered a general-purpose person re-identification system. Our experimental results show that the proposed system offers significant improvements over baseline approaches. The source code used for the approaches tested in this paper will be available at https://www.dei.unipd.it/node/2357 and http://robotics.dei.unipd.it/reid/