3,443 research outputs found
Learning Local Invariant Mahalanobis Distances
Abstract For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a local Mahalanobis metric per datum, and show how we can learn a local invariant metric to any transformation in order to improve performance
Regression on fixed-rank positive semidefinite matrices: a Riemannian approach
The paper addresses the problem of learning a regression model parameterized
by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear
nature of the search space and on scalability to high-dimensional problems. The
mathematical developments rely on the theory of gradient descent algorithms
adapted to the Riemannian geometry that underlies the set of fixed-rank
positive semidefinite matrices. In contrast with previous contributions in the
literature, no restrictions are imposed on the range space of the learned
matrix. The resulting algorithms maintain a linear complexity in the problem
size and enjoy important invariance properties. We apply the proposed
algorithms to the problem of learning a distance function parameterized by a
positive semidefinite matrix. Good performance is observed on classical
benchmarks
Positive Semidefinite Metric Learning Using Boosting-like Algorithms
The success of many machine learning and pattern recognition methods relies
heavily upon the identification of an appropriate distance metric on the input
data. It is often beneficial to learn such a metric from the input training
data, instead of using a default one such as the Euclidean distance. In this
work, we propose a boosting-based technique, termed BoostMetric, for learning a
quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance
metric requires enforcing the constraint that the matrix parameter to the
metric remains positive definite. Semidefinite programming is often used to
enforce this constraint, but does not scale well and easy to implement.
BoostMetric is instead based on the observation that any positive semidefinite
matrix can be decomposed into a linear combination of trace-one rank-one
matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak
learners within an efficient and scalable boosting-based learning process. The
resulting methods are easy to implement, efficient, and can accommodate various
types of constraints. We extend traditional boosting algorithms in that its
weak learner is a positive semidefinite matrix with trace and rank being one
rather than a classifier or regressor. Experiments on various datasets
demonstrate that the proposed algorithms compare favorably to those
state-of-the-art methods in terms of classification accuracy and running time.Comment: 30 pages, appearing in Journal of Machine Learning Researc
Positive Semidefinite Metric Learning with Boosting
The learning of appropriate distance metrics is a critical problem in image
classification and retrieval. In this work, we propose a boosting-based
technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One
of the primary difficulties in learning such a metric is to ensure that the
Mahalanobis matrix remains positive semidefinite. Semidefinite programming is
sometimes used to enforce this constraint, but does not scale well.
\BoostMetric is instead based on a key observation that any positive
semidefinite matrix can be decomposed into a linear positive combination of
trace-one rank-one matrices. \BoostMetric thus uses rank-one positive
semidefinite matrices as weak learners within an efficient and scalable
boosting-based learning process. The resulting method is easy to implement,
does not require tuning, and can accommodate various types of constraints.
Experiments on various datasets show that the proposed algorithm compares
favorably to those state-of-the-art methods in terms of classification accuracy
and running time.Comment: 11 pages, Twenty-Third Annual Conference on Neural Information
Processing Systems (NIPS 2009), Vancouver, Canad
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