Subspace Determination Through Local Intrinsic Dimensional Decomposition

Ruben Becker; Imane Hafnaoui; Michael E. Houle; Pan Li; Arthur Zimek

doi:10.1007/978-3-030-32047-8_25

Subspace Determination Through Local Intrinsic Dimensional Decomposition

Ruben Becker, Imane Hafnaoui, Michael E. Houle, Pan Li, Arthur Zimek

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local neighborhood surrounding a given data point. For each point, the recently-proposed Local Intrinsic Dimension (LID) model is used in identifying the axis directions along which features have the greatest local discriminability, or equivalently, the fewest number of components of LID that capture the local complexity of the data. In this paper, we develop an estimator of LID along axis projections, and provide preliminary evidence that this LID decomposition can indicate axis-aligned data subspaces that support the formation of clusters.

Original language	English
Title of host publication	Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings
Editors	Giuseppe Amato, Claudio Gennaro, Vincent Oria, Miloš Radovanovic
Publisher	Springer
Publication date	2019
Pages	281-289
ISBN (Print)	978-3-030-32046-1
ISBN (Electronic)	978-3-030-32047-8
DOIs	https://doi.org/10.1007/978-3-030-32047-8_25
Publication status	Published - 2019
Event	International Conference on Similarity Search and Applications - New Jersey Institute of Technology (NJIT), Newark, United States Duration: 2. Oct 2019 → 4. Oct 2019 Conference number: 12 http://www.sisap.org/2019/

Conference

Conference	International Conference on Similarity Search and Applications
Number	12
Location	New Jersey Institute of Technology (NJIT)
Country/Territory	United States
City	Newark
Period	02/10/2019 → 04/10/2019
Internet address	http://www.sisap.org/2019/

Series	Lecture Notes in Computer Science
Volume	11807
ISSN	0302-9743

Keywords

Estimation
Intrinsic dimensionality
Subspace

Documents & Links

10.1007/978-3-030-32047-8_25

Open Access VersionAccepted manuscript, 285 KB

Cite this

Becker, R., Hafnaoui, I., Houle, M. E., Li, P., & Zimek, A. (2019). Subspace Determination Through Local Intrinsic Dimensional Decomposition. In G. Amato, C. Gennaro, V. Oria, & M. Radovanovic (Eds.), Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings (pp. 281-289). Springer. Lecture Notes in Computer Science Vol. 11807 https://doi.org/10.1007/978-3-030-32047-8_25

Becker, Ruben ; Hafnaoui, Imane ; Houle, Michael E. ; Li, Pan ; Zimek, Arthur. / Subspace Determination Through Local Intrinsic Dimensional Decomposition. Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings. editor / Giuseppe Amato ; Claudio Gennaro ; Vincent Oria ; Miloš Radovanovic. Springer, 2019. pp. 281-289 (Lecture Notes in Computer Science, Vol. 11807).

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title = "Subspace Determination Through Local Intrinsic Dimensional Decomposition",

abstract = "Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local neighborhood surrounding a given data point. For each point, the recently-proposed Local Intrinsic Dimension (LID) model is used in identifying the axis directions along which features have the greatest local discriminability, or equivalently, the fewest number of components of LID that capture the local complexity of the data. In this paper, we develop an estimator of LID along axis projections, and provide preliminary evidence that this LID decomposition can indicate axis-aligned data subspaces that support the formation of clusters.",

keywords = "Estimation, Intrinsic dimensionality, Subspace",

author = "Ruben Becker and Imane Hafnaoui and Houle, {Michael E.} and Pan Li and Arthur Zimek",

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booktitle = "Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings",

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Becker, R, Hafnaoui, I, Houle, ME, Li, P & Zimek, A 2019, Subspace Determination Through Local Intrinsic Dimensional Decomposition. in G Amato, C Gennaro, V Oria & M Radovanovic (eds), Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings. Springer, Lecture Notes in Computer Science, vol. 11807, pp. 281-289, International Conference on Similarity Search and Applications, Newark, New Jersey, United States, 02/10/2019. https://doi.org/10.1007/978-3-030-32047-8_25

Subspace Determination Through Local Intrinsic Dimensional Decomposition. / Becker, Ruben; Hafnaoui, Imane; Houle, Michael E.; Li, Pan; Zimek, Arthur.

Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings. ed. / Giuseppe Amato; Claudio Gennaro; Vincent Oria; Miloš Radovanovic. Springer, 2019. p. 281-289 (Lecture Notes in Computer Science, Vol. 11807).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Subspace Determination Through Local Intrinsic Dimensional Decomposition

AU - Becker, Ruben

AU - Hafnaoui, Imane

AU - Houle, Michael E.

AU - Li, Pan

AU - Zimek, Arthur

N1 - Conference code: 12

PY - 2019

Y1 - 2019

N2 - Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local neighborhood surrounding a given data point. For each point, the recently-proposed Local Intrinsic Dimension (LID) model is used in identifying the axis directions along which features have the greatest local discriminability, or equivalently, the fewest number of components of LID that capture the local complexity of the data. In this paper, we develop an estimator of LID along axis projections, and provide preliminary evidence that this LID decomposition can indicate axis-aligned data subspaces that support the formation of clusters.

AB - Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local neighborhood surrounding a given data point. For each point, the recently-proposed Local Intrinsic Dimension (LID) model is used in identifying the axis directions along which features have the greatest local discriminability, or equivalently, the fewest number of components of LID that capture the local complexity of the data. In this paper, we develop an estimator of LID along axis projections, and provide preliminary evidence that this LID decomposition can indicate axis-aligned data subspaces that support the formation of clusters.

KW - Estimation

KW - Intrinsic dimensionality

KW - Subspace

U2 - 10.1007/978-3-030-32047-8_25

DO - 10.1007/978-3-030-32047-8_25

M3 - Article in proceedings

SN - 978-3-030-32046-1

T3 - Lecture Notes in Computer Science

SP - 281

EP - 289

BT - Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings

A2 - Amato, Giuseppe

A2 - Gennaro, Claudio

A2 - Oria, Vincent

A2 - Radovanovic, Miloš

PB - Springer

T2 - International Conference on Similarity Search and Applications

Y2 - 2 October 2019 through 4 October 2019

ER -

Becker R, Hafnaoui I, Houle ME, Li P, Zimek A. Subspace Determination Through Local Intrinsic Dimensional Decomposition. In Amato G, Gennaro C, Oria V, Radovanovic M, editors, Similarity Search and Applications - 12th International Conference, SISAP 2019, Newark, NJ, USA, October 2-4, 2019, Proceedings. Springer. 2019. p. 281-289. (Lecture Notes in Computer Science, Vol. 11807). https://doi.org/10.1007/978-3-030-32047-8_25

Subspace Determination Through Local Intrinsic Dimensional Decomposition

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Keywords

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