Nonlinear Discriminative Dimensionality Reduction of Multiple Datasets

Chen, Jia; Wang, Gang; Giannakis, Georgios B.

doi:10.1109/acssc.2018.8645467

Cited by 1 publication

(2 citation statements)

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“…Upon defining C yy := M k=1 ω k C k yy , it is straightforward to see that (20) reduces to (8). Therefore, one readily deduces that the optimal U in (20) can be obtained by taking the d right eigenvectors of C −1 yy C xx that are associated with the d largest eigenvalues.…”

Section: Discriminative Analytics With Multiple Background Datasetsmentioning

confidence: 99%

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Nonlinear Dimensionality Reduction for Discriminative Analytics of Multiple Datasets

Jia

Wang

Giannakis

2019

IEEE Trans. Signal Process.

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Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. PCA copes with one dataset at a time, but it is challenged when it comes to analyzing multiple datasets jointly. In certain data science settings however, one is often interested in extracting the most discriminative information from one dataset of particular interest (a.k.a. target data) relative to the other(s) (a.k.a. background data). To this end, this paper puts forth a novel approach, termed discriminative (d) PCA, for such discriminative analytics of multiple datasets. Under certain conditions, dPCA is proved to be least-squares optimal in recovering the latent subspace vector unique to the target data relative to background data. To account for nonlinear data correlations, (linear) dPCA models for one or multiple background datasets are generalized through kernelbased learning. Interestingly, all dPCA variants admit an analytical solution obtainable with a single (generalized) eigenvalue decomposition. Finally, substantial dimensionality reduction tests using synthetic and real datasets are provided to corroborate the merits of the proposed methods.Index Terms-Principal component analysis, discriminative analytics, multiple background datasets, kernel learning.

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Section: Discriminative Analytics With Multiple Background Datasetsmentioning

confidence: 99%

“…on Acoustics, Speech, and Signal Processing, Calgary, Canada, April 15-20, 2018 [36], and the 52nd Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, October 28-31, 2018 [8].…”

Section: Introductionmentioning

confidence: 99%