A deep matrix factorization method for learning attribute representations

Semi-Non-negative Matrix Factorization is a technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our original data matrix contains rather complex hierarchical information with implicit lower-level hidden attributes, that classical one level clustering methodologies can not interpret. In this work we propose a novel model, Deep Semi-NMF, that is able to learn such hidden representations that allow themselves to an interpretation of clustering according to different, unknown attributes of a given dataset. We also present a semi-supervised version of the algorithm, named Deep WSF, that allows the use of (partial) prior information for each of the known attributes of a dataset, that allows the model to be used on datasets with mixed attribute knowledge. Finally, we show that our models are able to learn low-dimensional representations that are better suited for clustering, but also classification, outperforming Semi-Non-negative Matrix Factorization, but also other state-of-the-art methodologies variants.Comment: Submitted to TPAMI (16-Mar-2015

Level Playing Field for Million Scale Face Recognition

Face recognition has the perception of a solved problem, however when tested at the million-scale exhibits dramatic variation in accuracies across the different algorithms. Are the algorithms very different? Is access to good/big training data their secret weapon? Where should face recognition improve? To address those questions, we created a benchmark, MF2, that requires all algorithms to be trained on same data, and tested at the million scale. MF2 is a public large-scale set with 672K identities and 4.7M photos created with the goal to level playing field for large scale face recognition. We contrast our results with findings from the other two large-scale benchmarks MegaFace Challenge and MS-Celebs-1M where groups were allowed to train on any private/public/big/small set. Some key discoveries: 1) algorithms, trained on MF2, were able to achieve state of the art and comparable results to algorithms trained on massive private sets, 2) some outperformed themselves once trained on MF2, 3) invariance to aging suffers from low accuracies as in MegaFace, identifying the need for larger age variations possibly within identities or adjustment of algorithms in future testings

Structured learning of metric ensembles with application to person re-identification

Matching individuals across non-overlapping camera networks, known as person re-identification, is a fundamentally challenging problem due to the large visual appearance changes caused by variations of viewpoints, lighting, and occlusion. Approaches in literature can be categoried into two streams: The first stream is to develop reliable features against realistic conditions by combining several visual features in a pre-defined way; the second stream is to learn a metric from training data to ensure strong inter-class differences and intra-class similarities. However, seeking an optimal combination of visual features which is generic yet adaptive to different benchmarks is a unsoved problem, and metric learning models easily get over-fitted due to the scarcity of training data in person re-identification. In this paper, we propose two effective structured learning based approaches which explore the adaptive effects of visual features in recognizing persons in different benchmark data sets. Our framework is built on the basis of multiple low-level visual features with an optimal ensemble of their metrics. We formulate two optimization algorithms, CMCtriplet and CMCstruct, which directly optimize evaluation measures commonly used in person re-identification, also known as the Cumulative Matching Characteristic (CMC) curve.Comment: 16 pages. Extended version of "Learning to Rank in Person Re-Identification With Metric Ensembles", at http://www.cv-foundation.org/openaccess/content_cvpr_2015/html/Paisitkriangkrai_Learning_to_Rank_2015_CVPR_paper.html. arXiv admin note: text overlap with arXiv:1503.0154

Efficient Black-Box Identity Testing for Free Group Algebras

Hrubes and Wigderson [Pavel Hrubes and Avi Wigderson, 2014] initiated the study of noncommutative arithmetic circuits with division computing a noncommutative rational function in the free skew field, and raised the question of rational identity testing. For noncommutative formulas with inverses the problem can be solved in deterministic polynomial time in the white-box model [Ankit Garg et al., 2016; Ivanyos et al., 2018]. It can be solved in randomized polynomial time in the black-box model [Harm Derksen and Visu Makam, 2017], where the running time is polynomial in the size of the formula. The complexity of identity testing of noncommutative rational functions, in general, remains open for noncommutative circuits with inverses. We solve the problem for a natural special case. We consider expressions in the free group algebra F(X,X^{-1}) where X={x_1, x_2, ..., x_n}. Our main results are the following. 1) Given a degree d expression f in F(X,X^{-1}) as a black-box, we obtain a randomized poly(n,d) algorithm to check whether f is an identically zero expression or not. The technical contribution is an Amitsur-Levitzki type theorem [A. S. Amitsur and J. Levitzki, 1950] for F(X, X^{-1}). This also yields a deterministic identity testing algorithm (and even an expression reconstruction algorithm) that is polynomial time in the sparsity of the input expression. 2) Given an expression f in F(X,X^{-1}) of degree D and sparsity s, as black-box, we can check whether f is identically zero or not in randomized poly(n,log s, log D) time. This yields a randomized polynomial-time algorithm when D and s are exponential in n

Coupled Deep Learning for Heterogeneous Face Recognition

Heterogeneous face matching is a challenge issue in face recognition due to large domain difference as well as insufficient pairwise images in different modalities during training. This paper proposes a coupled deep learning (CDL) approach for the heterogeneous face matching. CDL seeks a shared feature space in which the heterogeneous face matching problem can be approximately treated as a homogeneous face matching problem. The objective function of CDL mainly includes two parts. The first part contains a trace norm and a block-diagonal prior as relevance constraints, which not only make unpaired images from multiple modalities be clustered and correlated, but also regularize the parameters to alleviate overfitting. An approximate variational formulation is introduced to deal with the difficulties of optimizing low-rank constraint directly. The second part contains a cross modal ranking among triplet domain specific images to maximize the margin for different identities and increase data for a small amount of training samples. Besides, an alternating minimization method is employed to iteratively update the parameters of CDL. Experimental results show that CDL achieves better performance on the challenging CASIA NIR-VIS 2.0 face recognition database, the IIIT-D Sketch database, the CUHK Face Sketch (CUFS), and the CUHK Face Sketch FERET (CUFSF), which significantly outperforms state-of-the-art heterogeneous face recognition methods.Comment: AAAI 201