Dpca: Dimensionality Reduction for Discriminative Analytics of Multiple Large-Scale Datasets

Abstract

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain setups, one wishes to extract the most significant information of one dataset relative to other datasets. Specifically, the interest may be on identifying, namely extracting features that are specific to a single target dataset but not the others. This paper develops a novel approach for such so-termed discriminative data analysis, and establishes its optimality in the least-squares (LS) sense under suitable data modeling assumptions. The criterion reveals linear combinations of variables by maximizing the ratio of the variance of the target data to that of the remainders. The novel approach solves a generalized eigenvalue problem by performing SVD just once. Numerical tests using synthetic and real datasets showcase the merits of the proposed approach relative to its competing alternatives.

Automatic 3D Reconstruction From Unstructured Videos Combining Video Summarization and Structure From Motion

“…Then, the collected pool of short videos is summarized by the application of a discriminant algorithm. In our case, we propose a novel video summarization scheme that is based on a discriminant Principal Component Analysis (d-PCA) as presented in the very recent work in (Wang et al, 2018). Discriminant Principal Analysis has its goal to extract the most significant information from one dataset, that is, the prominent information.…”

“…The method proposed in (Wang et al, 2018) was applied to recognize handwritten digits and frog images. In this paper, we properly modified and extend this approach to extract a small but meaningful number of key frames from a pool of short videos depicting the same scenery.…”

“…A novel video summarization method is adopted in this paper for key frame selection. The method is derived from the recent article in (Wang et al, 2018) applying, however, for recognition of handwritten digits. The goal is to look inside each video cluster, say the C k , and form representative bunches (sub-clusters) within each cluster so that (i) the elements within each bunch (intra-bunch) to share maximum coherency in terms of visual similarity, while (ii) the elements across bunches (inter-bunch) to be as far as possible in terms of visual similarity.…”

“…The new concept proposed is the use of a discriminant Principal Component Analysis (d-PCA) for summarizing the videos. The d-PCA concept (Wang et al, 2018) was introduced very recently for clustering objects so as to maximize the coherency of foreground against the background. Then, a Structure from Motion (SfM) algorithm is introduced to generate the 3D models.…”

Nonlinear Dimensionality Reduction for Discriminative Analytics of Multiple Datasets

“…Conf. 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].…”