Discrimination at the edge of noise: A Hilbert space of stationary Ergodic processes

Ishanu Chattopadhyay

doi:10.1109/ICDMW.2017.129

Discrimination at the edge of noise: A Hilbert space of stationary Ergodic processes

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

Abstract

Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on uncovering a valid complete inner product on the space of ergodic stationary finite valued processes, providing the latter with the structure of a Hilbert space on the real field. This rigorous construction, based on non-standard generalizations of the notions of sum and scalar multiplication of finite dimensional probability vectors, allows us to meaningfully talk about 'angles' between data streams and data sources, and, make precise the notion of orthogonal stochastic processes. In particular, the relative angles appear to be preserved, and identifiable, under severe noise, and will be developed in future as the underlying principle for robust classification, clustering and unsupervised featurization algorithms.

Original language	English
Title of host publication	Proceeding - 17th IEEE International Conference on Data Mining Workshops, ICDMW 2017
Editors	Raju Gottumukkala, George Karypis, Vijay Raghavan, Xindong Wu, Lucio Miele, Srinivas Aluru, Xia Ning, Guozhu Dong
Pages	942-948
Number of pages	7
ISBN (Electronic)	9781538614808
DOIs	https://doi.org/10.1109/ICDMW.2017.129
State	Published - Dec 15 2017
Event	17th IEEE International Conference on Data Mining Workshops, ICDMW 2017 - New Orleans, United States Duration: Nov 18 2017 → Nov 21 2017

Publication series

Name	IEEE International Conference on Data Mining Workshops, ICDMW
Volume	2017-November
ISSN (Print)	2375-9232
ISSN (Electronic)	2375-9259

Conference

Conference	17th IEEE International Conference on Data Mining Workshops, ICDMW 2017
Country/Territory	United States
City	New Orleans
Period	11/18/17 → 11/21/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Keywords

Hilbert Spaces
Inner Product
Noise
Stochastic Processes

ASJC Scopus subject areas

Computer Science Applications
Software

Access to Document

10.1109/ICDMW.2017.129

Cite this

Chattopadhyay, I. (2017). Discrimination at the edge of noise: A Hilbert space of stationary Ergodic processes. In R. Gottumukkala, G. Karypis, V. Raghavan, X. Wu, L. Miele, S. Aluru, X. Ning, & G. Dong (Eds.), Proceeding - 17th IEEE International Conference on Data Mining Workshops, ICDMW 2017 (pp. 942-948). (IEEE International Conference on Data Mining Workshops, ICDMW; Vol. 2017-November). https://doi.org/10.1109/ICDMW.2017.129

Chattopadhyay, Ishanu. / Discrimination at the edge of noise : A Hilbert space of stationary Ergodic processes. Proceeding - 17th IEEE International Conference on Data Mining Workshops, ICDMW 2017. editor / Raju Gottumukkala ; George Karypis ; Vijay Raghavan ; Xindong Wu ; Lucio Miele ; Srinivas Aluru ; Xia Ning ; Guozhu Dong. 2017. pp. 942-948 (IEEE International Conference on Data Mining Workshops, ICDMW).

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abstract = "Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on uncovering a valid complete inner product on the space of ergodic stationary finite valued processes, providing the latter with the structure of a Hilbert space on the real field. This rigorous construction, based on non-standard generalizations of the notions of sum and scalar multiplication of finite dimensional probability vectors, allows us to meaningfully talk about 'angles' between data streams and data sources, and, make precise the notion of orthogonal stochastic processes. In particular, the relative angles appear to be preserved, and identifiable, under severe noise, and will be developed in future as the underlying principle for robust classification, clustering and unsupervised featurization algorithms.",

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Chattopadhyay, I 2017, Discrimination at the edge of noise: A Hilbert space of stationary Ergodic processes. in R Gottumukkala, G Karypis, V Raghavan, X Wu, L Miele, S Aluru, X Ning & G Dong (eds), Proceeding - 17th IEEE International Conference on Data Mining Workshops, ICDMW 2017. IEEE International Conference on Data Mining Workshops, ICDMW, vol. 2017-November, pp. 942-948, 17th IEEE International Conference on Data Mining Workshops, ICDMW 2017, New Orleans, United States, 11/18/17. https://doi.org/10.1109/ICDMW.2017.129

Discrimination at the edge of noise: A Hilbert space of stationary Ergodic processes. / Chattopadhyay, Ishanu.
Proceeding - 17th IEEE International Conference on Data Mining Workshops, ICDMW 2017. ed. / Raju Gottumukkala; George Karypis; Vijay Raghavan; Xindong Wu; Lucio Miele; Srinivas Aluru; Xia Ning; Guozhu Dong. 2017. p. 942-948 (IEEE International Conference on Data Mining Workshops, ICDMW; Vol. 2017-November).

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

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Chattopadhyay I. Discrimination at the edge of noise: A Hilbert space of stationary Ergodic processes. In Gottumukkala R, Karypis G, Raghavan V, Wu X, Miele L, Aluru S, Ning X, Dong G, editors, Proceeding - 17th IEEE International Conference on Data Mining Workshops, ICDMW 2017. 2017. p. 942-948. (IEEE International Conference on Data Mining Workshops, ICDMW). doi: 10.1109/ICDMW.2017.129

Discrimination at the edge of noise: A Hilbert space of stationary Ergodic processes

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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