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The Parzen Window method: In terms of two vectors and one matrix()
Pattern classification methods assign an object to one of several predefined classes/categories based on features extracted from observed attributes of the object (pattern). When L discriminatory features for the pattern can be accurately determined, the pattern classification problem presents no di...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier Science
2015
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4534349/ https://www.ncbi.nlm.nih.gov/pubmed/26435560 http://dx.doi.org/10.1016/j.patrec.2015.06.002 |
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author | Mussa, Hamse Y. Mitchell, John B.O. Afzal, Avid M. |
author_facet | Mussa, Hamse Y. Mitchell, John B.O. Afzal, Avid M. |
author_sort | Mussa, Hamse Y. |
collection | PubMed |
description | Pattern classification methods assign an object to one of several predefined classes/categories based on features extracted from observed attributes of the object (pattern). When L discriminatory features for the pattern can be accurately determined, the pattern classification problem presents no difficulty. However, precise identification of the relevant features for a classification algorithm (classifier) to be able to categorize real world patterns without errors is generally infeasible. In this case, the pattern classification problem is often cast as devising a classifier that minimizes the misclassification rate. One way of doing this is to consider both the pattern attributes and its class label as random variables, estimate the posterior class probabilities for a given pattern and then assign the pattern to the class/category for which the posterior class probability value estimated is maximum. More often than not, the form of the posterior class probabilities is unknown. The so-called Parzen Window approach is widely employed to estimate class-conditional probability (class-specific probability) densities for a given pattern. These probability densities can then be utilized to estimate the appropriate posterior class probabilities for that pattern. However, the Parzen Window scheme can become computationally impractical when the size of the training dataset is in the tens of thousands and L is also large (a few hundred or more). Over the years, various schemes have been suggested to ameliorate the computational drawback of the Parzen Window approach, but the problem still remains outstanding and unresolved. In this paper, we revisit the Parzen Window technique and introduce a novel approach that may circumvent the aforementioned computational bottleneck. The current paper presents the mathematical aspect of our idea. Practical realizations of the proposed scheme will be given elsewhere. |
format | Online Article Text |
id | pubmed-4534349 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2015 |
publisher | Elsevier Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-45343492015-10-01 The Parzen Window method: In terms of two vectors and one matrix() Mussa, Hamse Y. Mitchell, John B.O. Afzal, Avid M. Pattern Recognit Lett Article Pattern classification methods assign an object to one of several predefined classes/categories based on features extracted from observed attributes of the object (pattern). When L discriminatory features for the pattern can be accurately determined, the pattern classification problem presents no difficulty. However, precise identification of the relevant features for a classification algorithm (classifier) to be able to categorize real world patterns without errors is generally infeasible. In this case, the pattern classification problem is often cast as devising a classifier that minimizes the misclassification rate. One way of doing this is to consider both the pattern attributes and its class label as random variables, estimate the posterior class probabilities for a given pattern and then assign the pattern to the class/category for which the posterior class probability value estimated is maximum. More often than not, the form of the posterior class probabilities is unknown. The so-called Parzen Window approach is widely employed to estimate class-conditional probability (class-specific probability) densities for a given pattern. These probability densities can then be utilized to estimate the appropriate posterior class probabilities for that pattern. However, the Parzen Window scheme can become computationally impractical when the size of the training dataset is in the tens of thousands and L is also large (a few hundred or more). Over the years, various schemes have been suggested to ameliorate the computational drawback of the Parzen Window approach, but the problem still remains outstanding and unresolved. In this paper, we revisit the Parzen Window technique and introduce a novel approach that may circumvent the aforementioned computational bottleneck. The current paper presents the mathematical aspect of our idea. Practical realizations of the proposed scheme will be given elsewhere. Elsevier Science 2015-10-01 /pmc/articles/PMC4534349/ /pubmed/26435560 http://dx.doi.org/10.1016/j.patrec.2015.06.002 Text en © 2015 The Authors http://creativecommons.org/licenses/by/4.0/ This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Mussa, Hamse Y. Mitchell, John B.O. Afzal, Avid M. The Parzen Window method: In terms of two vectors and one matrix() |
title | The Parzen Window method: In terms of two vectors and one matrix() |
title_full | The Parzen Window method: In terms of two vectors and one matrix() |
title_fullStr | The Parzen Window method: In terms of two vectors and one matrix() |
title_full_unstemmed | The Parzen Window method: In terms of two vectors and one matrix() |
title_short | The Parzen Window method: In terms of two vectors and one matrix() |
title_sort | parzen window method: in terms of two vectors and one matrix() |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4534349/ https://www.ncbi.nlm.nih.gov/pubmed/26435560 http://dx.doi.org/10.1016/j.patrec.2015.06.002 |
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