2,941 research outputs found

    Discriminative Features via Generalized Eigenvectors

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    Representing examples in a way that is compatible with the underlying classifier can greatly enhance the performance of a learning system. In this paper we investigate scalable techniques for inducing discriminative features by taking advantage of simple second order structure in the data. We focus on multiclass classification and show that features extracted from the generalized eigenvectors of the class conditional second moments lead to classifiers with excellent empirical performance. Moreover, these features have attractive theoretical properties, such as inducing representations that are invariant to linear transformations of the input. We evaluate classifiers built from these features on three different tasks, obtaining state of the art results

    DPCA: Dimensionality Reduction for Discriminative Analytics of Multiple Large-Scale Datasets

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    Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain setups, one wishes to extract the most significant information of one dataset relative to other datasets. Specifically, the interest may be on identifying, namely extracting features that are specific to a single target dataset but not the others. This paper develops a novel approach for such so-termed discriminative data analysis, and establishes its optimality in the least-squares (LS) sense under suitable data modeling assumptions. The criterion reveals linear combinations of variables by maximizing the ratio of the variance of the target data to that of the remainders. The novel approach solves a generalized eigenvalue problem by performing SVD just once. Numerical tests using synthetic and real datasets showcase the merits of the proposed approach relative to its competing alternatives.Comment: 5 pages, 2 figure

    Kernel Manifold Alignment

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    We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a sort of manifold unfolding plus alignment, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible which allows transfer across-domains and data synthesis. We also present a reduced-rank version for computational efficiency and discuss the generalization performance of KEMA under Rademacher principles of stability. KEMA exhibits very good performance over competing methods in synthetic examples, visual object recognition and recognition of facial expressions tasks
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