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Total Variation Depth for Functional Data Sun, Ying
Description
There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation depth, for functional data. As a measure of depth, its properties are studied theoretically, and the associated outlier detection performance is investigated through simulations. Compared to magnitude outliers, shape outliers are often masked among the rest of samples and harder to identify. We show that the proposed total variation depth has many desirable features and is well suited for outlier detection. In particular, we propose to decompose the total variation depth into two components that are associated with shape and magnitude outlyingness, respectively. This decomposition allows us to develop an effective procedure for outlier detection and useful visualization tools, while naturally accounting for the correlation in functional data. Finally, the proposed methodology is demonstrated using real datasets of curves, images, and video frames. The talk is based on joint work with Huang Huang.
Item Metadata
Title |
Total Variation Depth for Functional Data
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-09-04T16:34
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Description |
There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to
infinite-dimensional objects such as functional data. In this work, we
propose a new notion of depth, the total variation depth, for functional
data. As a measure of depth, its properties are studied theoretically, and the associated outlier detection performance is investigated through
simulations. Compared to magnitude outliers, shape outliers are often
masked among the rest of samples and harder to identify. We show that the proposed total variation depth has many desirable features and is well suited for outlier detection. In particular, we propose to decompose the total variation depth into two components that are associated with shape and magnitude outlyingness, respectively. This decomposition allows us to develop an effective procedure for outlier detection and useful visualization tools, while naturally accounting for the correlation in functional data. Finally, the proposed methodology is demonstrated using real datasets of curves, images, and video frames. The talk is based on joint work with Huang Huang.
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Extent |
30.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: King Abdullah University of Science and Technology
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Series | |
Date Available |
2019-03-10
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0376718
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International