Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the it...
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Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the iteration function.
Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers ...
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Extended target tracking arises in situations where the resolution of the sensor is high enough to allow multiple returns from the target of interest corresponding to its different parts. Various formulations and solu...
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ISBN:
(纸本)9781632662651
Extended target tracking arises in situations where the resolution of the sensor is high enough to allow multiple returns from the target of interest corresponding to its different parts. Various formulations and solutions may be found in the literature. We concentrate on the data association aspect involved in the tracking problem and propose utilization of a general framework that allows reformulation of many seemingly unrelated problems in a similar way. Consequently, the extended object tracking problem is stated as a single generalized dynamical system with random coefficients and solved using a standard IMM algorithm.
We show that the two uni-directional n-cubes, namely UHC1n and UHC2n proposed by Chou and Du (1990) as interconnection schemes are Hamiltonian. In addition, we show that (1) if n is even, both architectures are vertex...
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We present a nearly linear time algorithm that produces high-quality spectral sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ∈ > 0, we produce a weighted subgraph H =...
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This paper presents a novel framework for simultaneously learning representation and control in continuous Markov decision processes. Our approach builds on the framework of proto-value functions, in which the underly...
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We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, ...
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ISBN:
(纸本)9780262232531
We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph;the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.
We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs c...
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Spectral embedding and spectral clustering are common methods for non-linear dimensionality reduction and clustering of complex high dimensional datasets. In this paper we provide a diffusion based probabilistic analy...
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ISBN:
(纸本)9783540737490
Spectral embedding and spectral clustering are common methods for non-linear dimensionality reduction and clustering of complex high dimensional datasets. In this paper we provide a diffusion based probabilistic analysis of algorithms that use the normalized graph Laplacian. Given the pairwise adjacency matrix of all points in a dataset, we define a random walk on the graph of points and a diffusion distance between any two points. We show that the diffusion distance is equal to the Euclidean distance in the embedded space with all eigenvectors of the normalized graph Laplacian. This identity shows that characteristic relaxation times and processes of the random walk on the graph are the key concept that governs the properties of these spectral clustering and spectral embedding algorithms. Specifically, for spectral clustering to succeed, a necessary condition is that the mean exit times from each cluster need to be significantly larger than the largest (slowest) of all relaxation times inside all of the individual clusters. For complex, multiscale data, this condition may not hold and multiscale methods need to be developed to handle such situations.
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