1,883 research outputs found
Learning Discriminative Stein Kernel for SPD Matrices and Its Applications
Stein kernel has recently shown promising performance on classifying images
represented by symmetric positive definite (SPD) matrices. It evaluates the
similarity between two SPD matrices through their eigenvalues. In this paper,
we argue that directly using the original eigenvalues may be problematic
because: i) Eigenvalue estimation becomes biased when the number of samples is
inadequate, which may lead to unreliable kernel evaluation; ii) More
importantly, eigenvalues only reflect the property of an individual SPD matrix.
They are not necessarily optimal for computing Stein kernel when the goal is to
discriminate different sets of SPD matrices. To address the two issues in one
shot, we propose a discriminative Stein kernel, in which an extra parameter
vector is defined to adjust the eigenvalues of the input SPD matrices. The
optimal parameter values are sought by optimizing a proxy of classification
performance. To show the generality of the proposed method, three different
kernel learning criteria that are commonly used in the literature are employed
respectively as a proxy. A comprehensive experimental study is conducted on a
variety of image classification tasks to compare our proposed discriminative
Stein kernel with the original Stein kernel and other commonly used methods for
evaluating the similarity between SPD matrices. The experimental results
demonstrate that, the discriminative Stein kernel can attain greater
discrimination and better align with classification tasks by altering the
eigenvalues. This makes it produce higher classification performance than the
original Stein kernel and other commonly used methods.Comment: 13 page
Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction
It is difficult to find the optimal sparse solution of a manifold learning
based dimensionality reduction algorithm. The lasso or the elastic net
penalized manifold learning based dimensionality reduction is not directly a
lasso penalized least square problem and thus the least angle regression (LARS)
(Efron et al. \cite{LARS}), one of the most popular algorithms in sparse
learning, cannot be applied. Therefore, most current approaches take indirect
ways or have strict settings, which can be inconvenient for applications. In
this paper, we proposed the manifold elastic net or MEN for short. MEN
incorporates the merits of both the manifold learning based dimensionality
reduction and the sparse learning based dimensionality reduction. By using a
series of equivalent transformations, we show MEN is equivalent to the lasso
penalized least square problem and thus LARS is adopted to obtain the optimal
sparse solution of MEN. In particular, MEN has the following advantages for
subsequent classification: 1) the local geometry of samples is well preserved
for low dimensional data representation, 2) both the margin maximization and
the classification error minimization are considered for sparse projection
calculation, 3) the projection matrix of MEN improves the parsimony in
computation, 4) the elastic net penalty reduces the over-fitting problem, and
5) the projection matrix of MEN can be interpreted psychologically and
physiologically. Experimental evidence on face recognition over various popular
datasets suggests that MEN is superior to top level dimensionality reduction
algorithms.Comment: 33 pages, 12 figure
Quadratic Projection Based Feature Extraction with Its Application to Biometric Recognition
This paper presents a novel quadratic projection based feature extraction
framework, where a set of quadratic matrices is learned to distinguish each
class from all other classes. We formulate quadratic matrix learning (QML) as a
standard semidefinite programming (SDP) problem. However, the con- ventional
interior-point SDP solvers do not scale well to the problem of QML for
high-dimensional data. To solve the scalability of QML, we develop an efficient
algorithm, termed DualQML, based on the Lagrange duality theory, to extract
nonlinear features. To evaluate the feasibility and effectiveness of the
proposed framework, we conduct extensive experiments on biometric recognition.
Experimental results on three representative biometric recogni- tion tasks,
including face, palmprint, and ear recognition, demonstrate the superiority of
the DualQML-based feature extraction algorithm compared to the current
state-of-the-art algorithm
On Multi-Relational Link Prediction with Bilinear Models
We study bilinear embedding models for the task of multi-relational link
prediction and knowledge graph completion. Bilinear models belong to the most
basic models for this task, they are comparably efficient to train and use, and
they can provide good prediction performance. The main goal of this paper is to
explore the expressiveness of and the connections between various bilinear
models proposed in the literature. In particular, a substantial number of
models can be represented as bilinear models with certain additional
constraints enforced on the embeddings. We explore whether or not these
constraints lead to universal models, which can in principle represent every
set of relations, and whether or not there are subsumption relationships
between various models. We report results of an independent experimental study
that evaluates recent bilinear models in a common experimental setup. Finally,
we provide evidence that relation-level ensembles of multiple bilinear models
can achieve state-of-the art prediction performance
Semi-supervised tensor-based graph embedding learning and its application to visual discriminant tracking
An appearance model adaptable to changes in object appearance is critical in visual object tracking. In
this paper, we treat an image patch as a 2-order tensor which preserves the original image structure. We design
two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the
background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of
the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the
transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding
space. In order to encode more discriminant information in the embedding space, we propose a transfer-learningbased
semi-supervised strategy to iteratively adjust the embedding space into which discriminative information
obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph
embedding learning algorithm to visual tracking. The new tracking algorithm captures an object’s appearance
characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results
on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm
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