20,246 research outputs found
Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction
Local learning of sparse image models has proven to be very effective to
solve inverse problems in many computer vision applications. To learn such
models, the data samples are often clustered using the K-means algorithm with
the Euclidean distance as a dissimilarity metric. However, the Euclidean
distance may not always be a good dissimilarity measure for comparing data
samples lying on a manifold. In this paper, we propose two algorithms for
determining a local subset of training samples from which a good local model
can be computed for reconstructing a given input test sample, where we take
into account the underlying geometry of the data. The first algorithm, called
Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme
which can be seen as an out-of-sample extension of the replicator graph
clustering method for local model learning. The second method, called
Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive
alternative for training subset selection. The proposed AGNN and GOC methods
are evaluated in image super-resolution, deblurring and denoising applications
and shown to outperform spectral clustering, soft clustering, and geodesic
distance based subset selection in most settings.Comment: 15 pages, 10 figures and 5 table
Similarity Learning via Kernel Preserving Embedding
Data similarity is a key concept in many data-driven applications. Many
algorithms are sensitive to similarity measures. To tackle this fundamental
problem, automatically learning of similarity information from data via
self-expression has been developed and successfully applied in various models,
such as low-rank representation, sparse subspace learning, semi-supervised
learning. However, it just tries to reconstruct the original data and some
valuable information, e.g., the manifold structure, is largely ignored. In this
paper, we argue that it is beneficial to preserve the overall relations when we
extract similarity information. Specifically, we propose a novel similarity
learning framework by minimizing the reconstruction error of kernel matrices,
rather than the reconstruction error of original data adopted by existing work.
Taking the clustering task as an example to evaluate our method, we observe
considerable improvements compared to other state-of-the-art methods. More
importantly, our proposed framework is very general and provides a novel and
fundamental building block for many other similarity-based tasks. Besides, our
proposed kernel preserving opens up a large number of possibilities to embed
high-dimensional data into low-dimensional space.Comment: Published in AAAI 201
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
We present a graph-based variational algorithm for classification of
high-dimensional data, generalizing the binary diffuse interface model to the
case of multiple classes. Motivated by total variation techniques, the method
involves minimizing an energy functional made up of three terms. The first two
terms promote a stepwise continuous classification function with sharp
transitions between classes, while preserving symmetry among the class labels.
The third term is a data fidelity term, allowing us to incorporate prior
information into the model in a semi-supervised framework. The performance of
the algorithm on synthetic data, as well as on the COIL and MNIST benchmark
datasets, is competitive with state-of-the-art graph-based multiclass
segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science
volume "Pattern Recognition Applications and Methods 2013", part of series on
Advances in Intelligent and Soft Computin
Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization
Nonnegative Matrix Factorization (NMF) has been continuously evolving in
several areas like pattern recognition and information retrieval methods. It
factorizes a matrix into a product of 2 low-rank non-negative matrices that
will define parts-based, and linear representation of nonnegative data.
Recently, Graph regularized NMF (GrNMF) is proposed to find a compact
representation,which uncovers the hidden semantics and simultaneously respects
the intrinsic geometric structure. In GNMF, an affinity graph is constructed
from the original data space to encode the geometrical information. In this
paper, we propose a novel idea which engages a Multiple Kernel Learning
approach into refining the graph structure that reflects the factorization of
the matrix and the new data space. The GrNMF is improved by utilizing the graph
refined by the kernel learning, and then a novel kernel learning method is
introduced under the GrNMF framework. Our approach shows encouraging results of
the proposed algorithm in comparison to the state-of-the-art clustering
algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible
writin
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