Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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TL;DR: In this article, the state space is dynamically partitioned into regions where the value function is the same throughout the region, where the state variables can be expressed by piecewise constant representations.
Abstract: We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for complex, structured problems, our approach exploits the natural structure so that optimal solutions can be computed efficiently.
90 citations
TL;DR: A novel algorithm that can be used to boost the performance of face-verification methods that utilize Fisher's criterion is presented and evaluated and Experimental results indicate that the proposed framework greatly improves the face- Verification performance.
Abstract: A novel algorithm that can be used to boost the performance of face-verification methods that utilize Fisher's criterion is presented and evaluated. The algorithm is applied to similarity, or matching error, data and provides a general solution for overcoming the "small sample size" (SSS) problem, where the lack of sufficient training samples causes improper estimation of a linear separation hyperplane between the classes. Two independent phases constitute the proposed method. Initially, a set of weighted piecewise discriminant hyperplanes are used in order to provide a more accurate discriminant decision than the one produced by the traditional linear discriminant analysis (LDA) methodology. The expected classification ability of this method is investigated throughout a series of simulations. The second phase defines proper combinations for person-specific similarity scores and describes an outlier removal process that further enhances the classification ability. The proposed technique has been tested on the M2VTS and XM2VTS frontal face databases. Experimental results indicate that the proposed framework greatly improves the face-verification performance
90 citations
TL;DR: This paper shows that by allowing (if necessary) two cubic pieces in some data intervals rather than one, convexity can always be preserved.
90 citations
TL;DR: In this paper, the authors present a new approach to the construction of piecewise polynomial or rational C k -spline surfaces of arbitrary topological structure, using exclusively parametric smoothness conditions, and to solve the well-known problems at extraordinary points by admitting singular parametrizations.
Abstract: We present a new approach to the construction of piecewise polynomial or rational C k -spline surfaces of arbitrary topological structure. The basic idea is to use exclusively parametric smoothness conditions, and to solve the well-known problems at extraordinary points by admitting singular parametrizations. The smoothness of the spline surfaces is guaranteed by specifying a regular smooth reparametrization explicitly. The resulting space of topologically unrestricted rational B-splines (TURBS) is linear and possesses a natural refinement property. Compared with all known methods the construction principle of TURBS is of striking simplicity and the required polynomial bi-degree is essentially decreased from O(k 2 ) to d=2k+2 .
90 citations
TL;DR: This paper investigates Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments and proves that the existence and uniqueness of the solution of the network holds when some conditions are satisfied.
90 citations