1,618 research outputs found
Subspace Clustering Based Tag Sharing for Inductive Tag Matrix Refinement with Complex Errors
Annotating images with tags is useful for indexing and retrieving images.
However, many available annotation data include missing or inaccurate
annotations. In this paper, we propose an image annotation framework which
sequentially performs tag completion and refinement. We utilize the subspace
property of data via sparse subspace clustering for tag completion. Then we
propose a novel matrix completion model for tag refinement, integrating visual
correlation, semantic correlation and the novelly studied property of complex
errors. The proposed method outperforms the state-of-the-art approaches on
multiple benchmark datasets even when they contain certain levels of annotation
noise.Comment: 4 page
Structured Priors for Sparse-Representation-Based Hyperspectral Image Classification
Pixel-wise classification, where each pixel is assigned to a predefined
class, is one of the most important procedures in hyperspectral image (HSI)
analysis. By representing a test pixel as a linear combination of a small
subset of labeled pixels, a sparse representation classifier (SRC) gives rather
plausible results compared with that of traditional classifiers such as the
support vector machine (SVM). Recently, by incorporating additional structured
sparsity priors, the second generation SRCs have appeared in the literature and
are reported to further improve the performance of HSI. These priors are based
on exploiting the spatial dependencies between the neighboring pixels, the
inherent structure of the dictionary, or both. In this paper, we review and
compare several structured priors for sparse-representation-based HSI
classification. We also propose a new structured prior called the low rank
group prior, which can be considered as a modification of the low rank prior.
Furthermore, we will investigate how different structured priors improve the
result for the HSI classification.Comment: IEEE Geoscience and Remote Sensing Lette
Locally Linear Embedding Clustering Algorithm for Natural Imagery
The ability to characterize the color content of natural imagery is an
important application of image processing. The pixel by pixel coloring of
images may be viewed naturally as points in color space, and the inherent
structure and distribution of these points affords a quantization, through
clustering, of the color information in the image. In this paper, we present a
novel topologically driven clustering algorithm that permits segmentation of
the color features in a digital image. The algorithm blends Locally Linear
Embedding (LLE) and vector quantization by mapping color information to a lower
dimensional space, identifying distinct color regions, and classifying pixels
together based on both a proximity measure and color content. It is observed
that these techniques permit a significant reduction in color resolution while
maintaining the visually important features of images
Two-Manifold Problems
Recently, there has been much interest in spectral approaches to learning
manifolds---so-called kernel eigenmap methods. These methods have had some
successes, but their applicability is limited because they are not robust to
noise. To address this limitation, we look at two-manifold problems, in which
we simultaneously reconstruct two related manifolds, each representing a
different view of the same data. By solving these interconnected learning
problems together and allowing information to flow between them, two-manifold
algorithms are able to succeed where a non-integrated approach would fail: each
view allows us to suppress noise in the other, reducing bias in the same way
that an instrumental variable allows us to remove bias in a {linear}
dimensionality reduction problem. We propose a class of algorithms for
two-manifold problems, based on spectral decomposition of cross-covariance
operators in Hilbert space. Finally, we discuss situations where two-manifold
problems are useful, and demonstrate that solving a two-manifold problem can
aid in learning a nonlinear dynamical system from limited data
Self-Expressive Decompositions for Matrix Approximation and Clustering
Data-aware methods for dimensionality reduction and matrix decomposition aim
to find low-dimensional structure in a collection of data. Classical approaches
discover such structure by learning a basis that can efficiently express the
collection. Recently, "self expression", the idea of using a small subset of
data vectors to represent the full collection, has been developed as an
alternative to learning. Here, we introduce a scalable method for computing
sparse SElf-Expressive Decompositions (SEED). SEED is a greedy method that
constructs a basis by sequentially selecting incoherent vectors from the
dataset. After forming a basis from a subset of vectors in the dataset, SEED
then computes a sparse representation of the dataset with respect to this
basis. We develop sufficient conditions under which SEED exactly represents low
rank matrices and vectors sampled from a unions of independent subspaces. We
show how SEED can be used in applications ranging from matrix approximation and
denoising to clustering, and apply it to numerous real-world datasets. Our
results demonstrate that SEED is an attractive low-complexity alternative to
other sparse matrix factorization approaches such as sparse PCA and
self-expressive methods for clustering.Comment: 11 pages, 7 figure
Accelerated Sparse Subspace Clustering
State-of-the-art algorithms for sparse subspace clustering perform spectral
clustering on a similarity matrix typically obtained by representing each data
point as a sparse combination of other points using either basis pursuit (BP)
or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in
practice while the performance of OMP-based schemes are unsatisfactory,
especially in settings where data points are highly similar. In this paper, we
propose a novel algorithm that exploits an accelerated variant of orthogonal
least-squares to efficiently find the underlying subspaces. We show that under
certain conditions the proposed algorithm returns a subspace-preserving
solution. Simulation results illustrate that the proposed method compares
favorably with BP-based method in terms of running time while being
significantly more accurate than OMP-based schemes
Tensor Laplacian Regularized Low-Rank Representation for Non-uniformly Distributed Data Subspace Clustering
Low-Rank Representation (LRR) highly suffers from discarding the locality
information of data points in subspace clustering, as it may not incorporate
the data structure nonlinearity and the non-uniform distribution of
observations over the ambient space. Thus, the information of the observational
density is lost by the state-of-art LRR models, as they take a constant number
of adjacent neighbors into account. This, as a result, degrades the subspace
clustering accuracy in such situations. To cope with deficiency, in this paper,
we propose to consider a hypergraph model to facilitate having a variable
number of adjacent nodes and incorporating the locality information of the
data. The sparsity of the number of subspaces is also taken into account. To do
so, an optimization problem is defined based on a set of regularization terms
and is solved by developing a tensor Laplacian-based algorithm. Extensive
experiments on artificial and real datasets demonstrate the higher accuracy and
precision of the proposed method in subspace clustering compared to the
state-of-the-art methods. The outperformance of this method is more revealed in
presence of inherent structure of the data such as nonlinearity, geometrical
overlapping, and outliers
Sketched SVD: Recovering Spectral Features from Compressive Measurements
We consider a streaming data model in which n sensors observe individual
streams of data, presented in a turnstile model. Our goal is to analyze the
singular value decomposition (SVD) of the matrix of data defined implicitly by
the stream of updates. Each column i of the data matrix is given by the stream
of updates seen at sensor i. Our approach is to sketch each column of the
matrix, forming a "sketch matrix" Y, and then to compute the SVD of the sketch
matrix. We show that the singular values and right singular vectors of Y are
close to those of X, with small relative error. We also believe that this bound
is of independent interest in non-streaming and non-distributed data collection
settings.
Assuming that the data matrix X is of size Nxn, then with m linear
measurements of each column of X, we obtain a smaller matrix Y with dimensions
mxn. If m = O(k \epsilon^{-2} (log(1/\epsilon) + log(1/\delta)), where k
denotes the rank of X, then with probability at least 1-\delta, the singular
values \sigma'_j of Y satisfy the following relative error result
(1-\epsilon)^(1/2)<= \sigma'_j/\sigma_j <= (1 + \epsilon)^(1/2) as compared
to the singular values \sigma_j of the original matrix X. Furthermore, the
right singular vectors v'_j of Y satisfy
||v_j-v_j'||_2 <= min(sqrt{2},
(\epsilon\sqrt{1+\epsilon})/(\sqrt{1-\epsilon}) max_{i\neq j}
(\sqrt{2}\sigma_i\sigma_j)/(min_{c\in[-1,1]}(|\sigma^2_i-\sigma^2_j(1+c\epsilon)|)))
as compared to the right singular vectors v_j of X. We apply this result to
obtain a streaming graph algorithm to approximate the eigenvalues and
eigenvectors of the graph Laplacian in the case where the graph has low rank
(many connected components)
Multi-View Surveillance Video Summarization via Joint Embedding and Sparse Optimization
Most traditional video summarization methods are designed to generate
effective summaries for single-view videos, and thus they cannot fully exploit
the complicated intra and inter-view correlations in summarizing multi-view
videos in a camera network. In this paper, with the aim of summarizing
multi-view videos, we introduce a novel unsupervised framework via joint
embedding and sparse representative selection. The objective function is
two-fold. The first is to capture the multi-view correlations via an embedding,
which helps in extracting a diverse set of representatives. The second is to
use a `2;1- norm to model the sparsity while selecting representative shots for
the summary. We propose to jointly optimize both of the objectives, such that
embedding can not only characterize the correlations, but also indicate the
requirements of sparse representative selection. We present an efficient
alternating algorithm based on half-quadratic minimization to solve the
proposed non-smooth and non-convex objective with convergence analysis. A key
advantage of the proposed approach with respect to the state-of-the-art is that
it can summarize multi-view videos without assuming any prior
correspondences/alignment between them, e.g., uncalibrated camera networks.
Rigorous experiments on several multi-view datasets demonstrate that our
approach clearly outperforms the state-of-the-art methods.Comment: IEEE Trans. on Multimedia, 2017 (In Press
Hypergraph p-Laplacian Regularization for Remote Sensing Image Recognition
It is of great importance to preserve locality and similarity information in
semi-supervised learning (SSL) based applications. Graph based SSL and manifold
regularization based SSL including Laplacian regularization (LapR) and
Hypergraph Laplacian regularization (HLapR) are representative SSL methods and
have achieved prominent performance by exploiting the relationship of sample
distribution. However, it is still a great challenge to exactly explore and
exploit the local structure of the data distribution. In this paper, we present
an effect and effective approximation algorithm of Hypergraph p-Laplacian and
then propose Hypergraph p-Laplacian regularization (HpLapR) to preserve the
geometry of the probability distribution. In particular, p-Laplacian is a
nonlinear generalization of the standard graph Laplacian and Hypergraph is a
generalization of a standard graph. Therefore, the proposed HpLapR provides
more potential to exploiting the local structure preserving. We apply HpLapR to
logistic regression and conduct the implementations for remote sensing image
recognition. We compare the proposed HpLapR to several popular manifold
regularization based SSL methods including LapR, HLapR and HpLapR on UC-Merced
dataset. The experimental results demonstrate the superiority of the proposed
HpLapR.Comment: 9 pages, 6 figure
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