On the Evaluation of Tensor-Based Representations for Optimum-Path Forest Classification
Tensor-based representations have been widely pursued in the last years due to the increasing number of high-dimensional datasets, which might be better described by the multilinear algebra. In this paper, we introduced a recent pattern recognition techni
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Instituto de Pesquisas Eldorado, Campinas, Brazil [email protected] Department of Computing, S˜ ao Paulo State University, S˜ ao Paulo, Brazil [email protected], [email protected]
Abstract. Tensor-based representations have been widely pursued in the last years due to the increasing number of high-dimensional datasets, which might be better described by the multilinear algebra. In this paper, we introduced a recent pattern recognition technique called OptimumPath Forest (OPF) in the context of tensor-oriented applications, as well as we evaluated its robustness to space transformations using Multilinear Principal Component Analysis in both face and human action recognition tasks considering image and video datasets. We have shown OPF can obtain more accurate recognition rates in some situations when working on tensor-oriented feature spaces. Keywords: Optimum-Path Forest · Tensors · Gait and face recognition
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Introduction
Methodologies for data representation have been widely pursued in the last decades, being most part of them based on Vector Space Models (VSM). Roughly speaking, given a dataset X e a label set Y, each sample xi ∈ X is represented as an n-dimensional point on that space with a label associated to it, i.e., each sample can be modelled as a pair (xi , yi ), yi ∈ N and i = 1, 2, . . . , |X |. Therefore, a machine learning algorithm aims at finding a decision function f : X → Y that leads to the best feature space partition [1]. Advances in storage technologies have fostered an increasing number of large data repositories, composed mainly of high-resolution images and videos. Such new environments now require more efficient and effective data representation and classification approaches, which shall take into account the highdimensionality nature of the data [5]. Images acquired through cell phones, for instance, may contain thousands of hundreds of pixels, being 2-dimensional data by nature. As such, a specific segment of researchers have devoted a considerable effort to study more natural data representation systems. One of the most actively data description approaches is related to the well-known Tensor Space Model (TSM), in which a dataset sample is represented as a tensor instead of a c Springer International Publishing AG 2016 F. Schwenker et al. (Eds.): ANNPR 2016, LNAI 9896, pp. 117–125, 2016. DOI: 10.1007/978-3-319-46182-3 10
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regular point, being the properties of such space ruled by the multilinear algebra. Roughly speaking, we can consider an image as a 2-order tensor (matrix), a video as a 3-order tensor (cube), and a scalar number is considered an 1-order tensor. Therefore, tensor-based representations can be understood as a generalization of vector-space models. Although one can find a number of tensor-based machine learning works out there, they are responsible for only a few percentage of the published literature. Vasilescu and Terzopoulos [13], for instance, used tensorial models to dimensionality reduction in the context of face-oriented person
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