منابع مشابه
Adaptive Metric Dimensionality Reduction
We study data-adaptive dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling, which yields a new theoretical explanation for empirically reported improvements gained by preprocessing Euclidean data by PCA (Principal Compone...
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Graph-based dimensionality reduction (DR) methods have 6 been applied successfully in many practical problems such as face 7 recognition, where graph plays a crucial role with the aim of modeling the 8 data distribution or structure. However, the ideal graph is difficult to be 9 known in practice. Usually, one needs to construct graph empirically 10 according to various motivations, priors or a...
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To be tractable and robust to data noise, existing metric learning algorithms commonly rely on PCA as a pre-processing step. How can we know, however, that PCA, or any other specific dimensionality reduction technique, is the method of choice for the problem at hand? The answer is simple: We cannot! To address this issue, in this paper, we develop a Riemannian framework to jointly learn a mappi...
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A recently proposed metric learning algorithm which enforces the optimal discrimination of the different classes is extended and empirically assessed using different kinds of publicly available data. The optimization problem is posed in terms of landmark points and then, a stochastic approach is followed in order to bypass some of the problems of the original algorithm. According to the results...
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The dynamics of proteins can be described as the superposition of motions at a continuum of time scales. In the special case of a protein immersed in an implicit solvent, a stochastic differential equation (SDE) can model the dynamics of the solute protein. Traditional model reduction techniques fail because a priori characterization of the slow variables in these SDEs is nearly impossible. We ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2016
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.10.040