Face Recognition Based on Videos by Using Convex Hulls

International audienceA wide range of face appearance variations can be modeled by using set based recognition approaches effectively, but computational complexity of current methods is highly dependent on the set and class sizes. This paper introduces new video based classification methods designed for reducing the required disk space of data samples and speed up the testing process in large-scale face recognition systems. In the proposed method, image sets collected from videos are approximated with kernelized convex hulls and it was shown that it is sufficient to use only the samples that participate in shaping the image set boundaries in this setting. The kernelized Support Vector Data Description (SVDD) is used to extract those important samples that form the image set boundaries. Moreover, we show that these kernelized hypersphere models can also be used to approximate image sets for classification purposes. Then, we propose a binary hierarchical decision tree approach to improve the speed of the classification system even more. Lastly, we introduce a new video database that includes 285 people with 8 videos of each person since the most popular video data sets used for set based recognition methods include either a few people, or small number of videos per person. The experimental results on varying sized databases show that the proposed methods greatly improve the testing times of the classification system (we obtained speed-ups to a factor of 20) without a significant drop in accuracies

SAGA: Sparse And Geometry-Aware non-negative matrix factorization through non-linear local embedding

International audienceThis paper presents a new non-negative matrix factorization technique which (1) allows the decomposition of the original data on multiple latent factors accounting for the geometrical structure of the manifold embedding the data; (2) provides an optimal representation with a controllable level of sparsity; (3) has an overall linear complexity allowing handling in tractable time large and high dimensional datasets. It operates by coding the data with respect to local neighbors with non-linear weights. This locality is obtained as a consequence of the simultaneous sparsity and convexity constraints. Our method is demonstrated over several experiments, including a feature extraction and classification task, where it achieves better performances than the state-of-the-art factorization methods, with a shorter computational time

Learning vector quantization for proximity data

Hofmann D. Learning vector quantization for proximity data. Bielefeld: Universität Bielefeld; 2016.Prototype-based classifiers such as learning vector quantization (LVQ) often display intuitive and flexible classification and learning rules. However, classical techniques are restricted to vectorial data only, and hence not suited for more complex data structures. Therefore, a few extensions of diverse LVQ variants to more general data which are characterized based on pairwise similarities or dissimilarities only have been proposed recently in the literature. In this contribution, we propose a novel extension of LVQ to similarity data which is based on the kernelization of an underlying probabilistic model: kernel robust soft LVQ (KRSLVQ). Relying on the notion of a pseudo-Euclidean embedding of proximity data, we put this specific approach as well as existing alternatives into a general framework which characterizes different fundamental possibilities how to extend LVQ towards proximity data: the main characteristics are given by the choice of the cost function, the interface to the data in terms of similarities or dissimilarities, and the way in which optimization takes place. In particular the latter strategy highlights the difference of popular kernel approaches versus so-called relational approaches. While KRSLVQ and alternatives lead to state of the art results, these extensions have two drawbacks as compared to their vectorial counterparts: (i) a quadratic training complexity is encountered due to the dependency of the methods on the full proximity matrix; (ii) prototypes are no longer given by vectors but they are represented in terms of an implicit linear combination of data, i.e. interpretability of the prototypes is lost. We investigate different techniques to deal with these challenges: We consider a speed-up of training by means of low rank approximations of the Gram matrix by its Nyström approximation. In benchmarks, this strategy is successful if the considered data are intrinsically low-dimensional. We propose a quick check to efficiently test this property prior to training. We extend KRSLVQ by sparse approximations of the prototypes: instead of the full coefficient vectors, few exemplars which represent the prototypes can be directly inspected by practitioners in the same way as data. We compare different paradigms based on which to infer a sparse approximation: sparsity priors while training, geometric approaches including orthogonal matching pursuit and core techniques, and heuristic approximations based on the coefficients or proximities. We demonstrate the performance of these LVQ techniques for benchmark data, reaching state of the art results. We discuss the behavior of the methods to enhance performance and interpretability as concerns quality, sparsity, and representativity, and we propose different measures how to quantitatively evaluate the performance of the approaches. We would like to point out that we had the possibility to present our findings in international publication organs including three journal articles [6, 9, 2], four conference papers [8, 5, 7, 1] and two workshop contributions [4, 3]. References [1] A. Gisbrecht, D. Hofmann, and B. Hammer. Discriminative dimensionality reduction mappings. Advances in Intelligent Data Analysis, 7619: 126–138, 2012. [2] B. Hammer, D. Hofmann, F.-M. Schleif, and X. Zhu. Learning vector quantization for (dis-)similarities. Neurocomputing, 131: 43–51, 2014. [3] D. Hofmann. Sparse approximations for kernel robust soft lvq. Mittweida Workshop on Computational Intelligence, 2013. [4] D. Hofmann, A. Gisbrecht, and B. Hammer. Discriminative probabilistic prototype based models in kernel space. New Challenges in Neural Computation, TR Machine Learning Reports, 2012. [5] D. Hofmann, A. Gisbrecht, and B. Hammer. Efficient approximations of kernel robust soft lvq. Workshop on Self-Organizing Maps, 198: 183–192, 2012. [6] D. Hofmann, A. Gisbrecht, and B. Hammer. Efficient approximations of robust soft learning vector quantization for non-vectorial data. Neurocomputing, 147: 96–106, 2015. [7] D. Hofmann and B. Hammer. Kernel robust soft learning vector quantization. Artificial Neural Networks in Pattern Recognition, 7477: 14–23, 2012. [8] D. Hofmann and B. Hammer. Sparse approximations for kernel learning vector quantization. European Symposium on Artificial Neural Networks, 549–554, 2013. [9] D. Hofmann, F.-M. Schleif, B. Paaßen, and B. Hammer. Learning interpretable kernelized prototype-based models. Neurocomputing, 141: 84–96, 2014

Local learning by partitioning

In many machine learning applications data is assumed to be locally simple, where examples near each other have similar characteristics such as class labels or regression responses. Our goal is to exploit this assumption to construct locally simple yet globally complex systems that improve performance or reduce the cost of common machine learning tasks. To this end, we address three main problems: discovering and separating local non-linear structure in high-dimensional data, learning low-complexity local systems to improve performance of risk-based learning tasks, and exploiting local similarity to reduce the test-time cost of learning algorithms. First, we develop a structure-based similarity metric, where low-dimensional non-linear structure is captured by solving a non-linear, low-rank representation problem. We show that this problem can be kernelized, has a closed-form solution, naturally separates independent manifolds, and is robust to noise. Experimental results indicate that incorporating this structural similarity in well-studied problems such as clustering, anomaly detection, and classification improves performance. Next, we address the problem of local learning, where a partitioning function divides the feature space into regions where independent functions are applied. We focus on the problem of local linear classification using linear partitioning and local decision functions. Under an alternating minimization scheme, learning the partitioning functions can be reduced to solving a weighted supervised learning problem. We then present a novel reformulation that yields a globally convex surrogate, allowing for efficient, joint training of the partitioning functions and local classifiers. We then examine the problem of learning under test-time budgets, where acquiring sensors (features) for each example during test-time has a cost. Our goal is to partition the space into regions, with only a small subset of sensors needed in each region, reducing the average number of sensors required per example. Starting with a cascade structure and expanding to binary trees, we formulate this problem as an empirical risk minimization and construct an upper-bounding surrogate that allows for sequential decision functions to be trained jointly by solving a linear program. Finally, we present preliminary work extending the notion of test-time budgets to the problem of adaptive privacy