Infinite Feature Selection: A Graph-based Feature Filtering Approach

We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting...

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Published in:	IEEE transactions on pattern analysis and machine intelligence Vol. 43; no. 12; pp. 4396 - 4410
Main Authors:	Roffo, Giorgio, Melzi, Simone, Castellani, Umberto, Vinciarelli, Alessandro, Cristani, Marco
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.12.2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Computational complexity Correlation Feature extraction Feature selection filter methods Filtration Laplace equations Markov chains Markov processes Mutual information Power series Redundancy
ISSN:	0162-8828, 1939-3539, 2160-9292, 1939-3539
Online Access:	Get full text
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Abstract	We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.
AbstractList	We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process. We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.
Author	Roffo, Giorgio Castellani, Umberto Melzi, Simone Vinciarelli, Alessandro Cristani, Marco
Author_xml	– sequence: 1 givenname: Giorgio orcidid: 0000-0003-4170-914X surname: Roffo fullname: Roffo, Giorgio email: Giorgio.Roffo@glasgow.ac.uk organization: School of Computing Science, University of Glasgow, Glasgow, U.K – sequence: 2 givenname: Simone orcidid: 0000-0003-2790-9591 surname: Melzi fullname: Melzi, Simone email: simone.melzi@univr.it organization: Department of Computer Science, University of Verona, Verona, Italy – sequence: 3 givenname: Umberto surname: Castellani fullname: Castellani, Umberto email: umberto.castellani@univr.it organization: Department of Computer Science, University of Verona, Verona, Italy – sequence: 4 givenname: Alessandro orcidid: 0000-0002-9048-0524 surname: Vinciarelli fullname: Vinciarelli, Alessandro email: Alessandro.Vinciarelli@glasgow.ac.uk organization: School of Computing Science, University of Glasgow, Glasgow, U.K – sequence: 5 givenname: Marco orcidid: 0000-0002-0523-6042 surname: Cristani fullname: Cristani, Marco email: marco.cristani@univr.it organization: Department of Computer Science, University of Verona, Verona, Italy
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Snippet	We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates...
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SubjectTerms	Computational complexity Correlation Feature extraction Feature selection filter methods Filtration Laplace equations Markov chains Markov processes Mutual information Power series Redundancy
Title	Infinite Feature Selection: A Graph-based Feature Filtering Approach
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