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Kernel Bandwidth Estimation for Nonparametric Modeling
, 2009
"... Kernel density estimation is a nonparametric procedure for probability density modeling, which has found several applications in various fields. The smoothness and modeling ability of the functional approximation are controlled by the kernel bandwidth. In this paper, we describe a Bayesian estimati ..."
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Kernel density estimation is a nonparametric procedure for probability density modeling, which has found several applications in various fields. The smoothness and modeling ability of the functional approximation are controlled by the kernel bandwidth. In this paper, we describe a Bayesian estimation method for finding the bandwidth from a given data set. The proposed bandwidth estimation method is applied in three different computational-intelligence methods that rely on kernel density estimation: 1) scale space; 2) mean shift; and 3) quantum clustering. The third method is a novel approach that relies on the principles of quantum mechanics. This method is based on the analogy between data samples and quantum particles and uses the Schrödinger potential as a cost function. The proposed methodology is used for blind-source separation of modulated signals and for terrain segmentation based on topography information.
A Novel Text Classifier Based on Quantum Computation
"... In this article, we propose a novel classifier based on quantum computation theory. Different from existing methods, we consider the classification as an evolutionary process of a physical system and build the classifier by using the basic quantum mechanics equation. The performance of the experimen ..."
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In this article, we propose a novel classifier based on quantum computation theory. Different from existing methods, we consider the classification as an evolutionary process of a physical system and build the classifier by using the basic quantum mechanics equation. The performance of the experiments on two datasets indicates feasibility and potentiality of the quantum classifier. 1
QUANTUM MECHANICS IN COMPUTER VISION: AUTOMATIC OBJECT EXTRACTION
"... An automatic object extraction method is proposed exploiting the rich mathematical structure of quantum mechanics. First, a novel segmentation method based on the solutions of Schrödinger’s equation is proposed. This powerful segmentation method allows us to model complex objects and inherent struct ..."
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An automatic object extraction method is proposed exploiting the rich mathematical structure of quantum mechanics. First, a novel segmentation method based on the solutions of Schrödinger’s equation is proposed. This powerful segmentation method allows us to model complex objects and inherent structures of edge, shape, and texture information along with the grey-level intensity uniformity, all in a single equation. Due to the large amount of segments extracted with the proposed method, the selection of the object segment is performed by maximizing a regularization energy function based on a recently proposed sub-segment analysis indicating the object boundaries. The results of the proposed automatic object extraction method exhibit such a promising accuracy that pushes the frontier in this field to the borders of the input-driven processing only – without the use of “object knowledge ” aided by long-term human memory and intelligence.
Bayesian Estimation of Kernel Bandwidth for
"... Abstract. Kernel density estimation (KDE) has been used in many computational intelligence and computer vision applications. In this paper we propose a Bayesian estimation method for finding the bandwidth in KDE applications. A Gamma density function is fitted to distributions of variances of K-near ..."
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Abstract. Kernel density estimation (KDE) has been used in many computational intelligence and computer vision applications. In this paper we propose a Bayesian estimation method for finding the bandwidth in KDE applications. A Gamma density function is fitted to distributions of variances of K-nearest neighbours data populations while uniform distribution priors are assumed for K. A maximum log-likelihood approach is used to estimate the parameters of the Gamma distribution when fitted to the local data variance. The proposed methodology is applied in three different KDE approaches: kernel sum, mean shift and quantum clustering. The third method relies on the Schrödinger partial differential equation and uses the analogy between the potential function that manifests around particles, as defined in quantum physics, and the probability density function corresponding to data. The proposed algorithm is applied to artificial data and to segment terrain images.
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"... fro ap ct o had es sign by a de con ting rom nto the & 2013 Elsevier Ltd. All rights reserved. 1. ..."
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fro ap ct o had es sign by a de con ting rom nto the & 2013 Elsevier Ltd. All rights reserved. 1.
