7,537 research outputs found
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
Kernel discriminant analysis and clustering with parsimonious Gaussian process models
This work presents a family of parsimonious Gaussian process models which
allow to build, from a finite sample, a model-based classifier in an infinite
dimensional space. The proposed parsimonious models are obtained by
constraining the eigen-decomposition of the Gaussian processes modeling each
class. This allows in particular to use non-linear mapping functions which
project the observations into infinite dimensional spaces. It is also
demonstrated that the building of the classifier can be directly done from the
observation space through a kernel function. The proposed classification method
is thus able to classify data of various types such as categorical data,
functional data or networks. Furthermore, it is possible to classify mixed data
by combining different kernels. The methodology is as well extended to the
unsupervised classification case. Experimental results on various data sets
demonstrate the effectiveness of the proposed method
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