82,668 research outputs found
Efficient Semidefinite Spectral Clustering via Lagrange Duality
We propose an efficient approach to semidefinite spectral clustering (SSC),
which addresses the Frobenius normalization with the positive semidefinite
(p.s.d.) constraint for spectral clustering. Compared with the original
Frobenius norm approximation based algorithm, the proposed algorithm can more
accurately find the closest doubly stochastic approximation to the affinity
matrix by considering the p.s.d. constraint. In this paper, SSC is formulated
as a semidefinite programming (SDP) problem. In order to solve the high
computational complexity of SDP, we present a dual algorithm based on the
Lagrange dual formalization. Two versions of the proposed algorithm are
proffered: one with less memory usage and the other with faster convergence
rate. The proposed algorithm has much lower time complexity than that of the
standard interior-point based SDP solvers. Experimental results on both UCI
data sets and real-world image data sets demonstrate that 1) compared with the
state-of-the-art spectral clustering methods, the proposed algorithm achieves
better clustering performance; and 2) our algorithm is much more efficient and
can solve larger-scale SSC problems than those standard interior-point SDP
solvers.Comment: 13 page
Matching Image Sets via Adaptive Multi Convex Hull
Traditional nearest points methods use all the samples in an image set to
construct a single convex or affine hull model for classification. However,
strong artificial features and noisy data may be generated from combinations of
training samples when significant intra-class variations and/or noise occur in
the image set. Existing multi-model approaches extract local models by
clustering each image set individually only once, with fixed clusters used for
matching with various image sets. This may not be optimal for discrimination,
as undesirable environmental conditions (eg. illumination and pose variations)
may result in the two closest clusters representing different characteristics
of an object (eg. frontal face being compared to non-frontal face). To address
the above problem, we propose a novel approach to enhance nearest points based
methods by integrating affine/convex hull classification with an adapted
multi-model approach. We first extract multiple local convex hulls from a query
image set via maximum margin clustering to diminish the artificial variations
and constrain the noise in local convex hulls. We then propose adaptive
reference clustering (ARC) to constrain the clustering of each gallery image
set by forcing the clusters to have resemblance to the clusters in the query
image set. By applying ARC, noisy clusters in the query set can be discarded.
Experiments on Honda, MoBo and ETH-80 datasets show that the proposed method
outperforms single model approaches and other recent techniques, such as Sparse
Approximated Nearest Points, Mutual Subspace Method and Manifold Discriminant
Analysis.Comment: IEEE Winter Conference on Applications of Computer Vision (WACV),
201
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