18,492 research outputs found
Distance Metric Learning with Eigenvalue Optimization
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2012 Yiming Ying and Peng Li.The main theme of this paper is to develop a novel eigenvalue optimization framework for learning a Mahalanobis metric. Within this context, we introduce a novel metric learning approach called DML-eig which is shown to be equivalent to a well-known eigenvalue optimization problem called minimizing the maximal eigenvalue of a symmetric matrix (Overton, 1988; Lewis and Overton, 1996). Moreover, we formulate LMNN (Weinberger et al., 2005), one of the state-of-the-art metric learning methods, as a similar eigenvalue optimization problem. This novel framework not only provides new insights into metric learning but also opens new avenues to the design of efficient metric learning algorithms. Indeed, first-order algorithms are developed for DML-eig and LMNN which only need the computation of the largest eigenvector of a matrix per iteration. Their convergence characteristics are rigorously established. Various experiments on benchmark data sets show the competitive performance of our new approaches. In addition, we report an encouraging result on a difficult and challenging face verification data set called Labeled Faces in the Wild (LFW)
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
A Survey on Metric Learning for Feature Vectors and Structured Data
The need for appropriate ways to measure the distance or similarity between
data is ubiquitous in machine learning, pattern recognition and data mining,
but handcrafting such good metrics for specific problems is generally
difficult. This has led to the emergence of metric learning, which aims at
automatically learning a metric from data and has attracted a lot of interest
in machine learning and related fields for the past ten years. This survey
paper proposes a systematic review of the metric learning literature,
highlighting the pros and cons of each approach. We pay particular attention to
Mahalanobis distance metric learning, a well-studied and successful framework,
but additionally present a wide range of methods that have recently emerged as
powerful alternatives, including nonlinear metric learning, similarity learning
and local metric learning. Recent trends and extensions, such as
semi-supervised metric learning, metric learning for histogram data and the
derivation of generalization guarantees, are also covered. Finally, this survey
addresses metric learning for structured data, in particular edit distance
learning, and attempts to give an overview of the remaining challenges in
metric learning for the years to come.Comment: Technical report, 59 pages. Changes in v2: fixed typos and improved
presentation. Changes in v3: fixed typos. Changes in v4: fixed typos and new
method
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