14,349 research outputs found
A Nonconvex Projection Method for Robust PCA
Robust principal component analysis (RPCA) is a well-studied problem with the
goal of decomposing a matrix into the sum of low-rank and sparse components. In
this paper, we propose a nonconvex feasibility reformulation of RPCA problem
and apply an alternating projection method to solve it. To the best of our
knowledge, we are the first to propose a method that solves RPCA problem
without considering any objective function, convex relaxation, or surrogate
convex constraints. We demonstrate through extensive numerical experiments on a
variety of applications, including shadow removal, background estimation, face
detection, and galaxy evolution, that our approach matches and often
significantly outperforms current state-of-the-art in various ways.Comment: In the proceedings of Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI-19
Distributed Low-rank Subspace Segmentation
Vision problems ranging from image clustering to motion segmentation to
semi-supervised learning can naturally be framed as subspace segmentation
problems, in which one aims to recover multiple low-dimensional subspaces from
noisy and corrupted input data. Low-Rank Representation (LRR), a convex
formulation of the subspace segmentation problem, is provably and empirically
accurate on small problems but does not scale to the massive sizes of modern
vision datasets. Moreover, past work aimed at scaling up low-rank matrix
factorization is not applicable to LRR given its non-decomposable constraints.
In this work, we propose a novel divide-and-conquer algorithm for large-scale
subspace segmentation that can cope with LRR's non-decomposable constraints and
maintains LRR's strong recovery guarantees. This has immediate implications for
the scalability of subspace segmentation, which we demonstrate on a benchmark
face recognition dataset and in simulations. We then introduce novel
applications of LRR-based subspace segmentation to large-scale semi-supervised
learning for multimedia event detection, concept detection, and image tagging.
In each case, we obtain state-of-the-art results and order-of-magnitude speed
ups
Facial emotion recognition using min-max similarity classifier
Recognition of human emotions from the imaging templates is useful in a wide
variety of human-computer interaction and intelligent systems applications.
However, the automatic recognition of facial expressions using image template
matching techniques suffer from the natural variability with facial features
and recording conditions. In spite of the progress achieved in facial emotion
recognition in recent years, the effective and computationally simple feature
selection and classification technique for emotion recognition is still an open
problem. In this paper, we propose an efficient and straightforward facial
emotion recognition algorithm to reduce the problem of inter-class pixel
mismatch during classification. The proposed method includes the application of
pixel normalization to remove intensity offsets followed-up with a Min-Max
metric in a nearest neighbor classifier that is capable of suppressing feature
outliers. The results indicate an improvement of recognition performance from
92.85% to 98.57% for the proposed Min-Max classification method when tested on
JAFFE database. The proposed emotion recognition technique outperforms the
existing template matching methods
Randomized Robust Subspace Recovery for High Dimensional Data Matrices
This paper explores and analyzes two randomized designs for robust Principal
Component Analysis (PCA) employing low-dimensional data sketching. In one
design, a data sketch is constructed using random column sampling followed by
low dimensional embedding, while in the other, sketching is based on random
column and row sampling. Both designs are shown to bring about substantial
savings in complexity and memory requirements for robust subspace learning over
conventional approaches that use the full scale data. A characterization of the
sample and computational complexity of both designs is derived in the context
of two distinct outlier models, namely, sparse and independent outlier models.
The proposed randomized approach can provably recover the correct subspace with
computational and sample complexity that are almost independent of the size of
the data. The results of the mathematical analysis are confirmed through
numerical simulations using both synthetic and real data
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