1,089 research outputs found
An Efficient Dual Approach to Distance Metric Learning
Distance metric learning is of fundamental interest in machine learning
because the distance metric employed can significantly affect the performance
of many learning methods. Quadratic Mahalanobis metric learning is a popular
approach to the problem, but typically requires solving a semidefinite
programming (SDP) problem, which is computationally expensive. Standard
interior-point SDP solvers typically have a complexity of (with
the dimension of input data), and can thus only practically solve problems
exhibiting less than a few thousand variables. Since the number of variables is
, this implies a limit upon the size of problem that can
practically be solved of around a few hundred dimensions. The complexity of the
popular quadratic Mahalanobis metric learning approach thus limits the size of
problem to which metric learning can be applied. Here we propose a
significantly more efficient approach to the metric learning problem based on
the Lagrange dual formulation of the problem. The proposed formulation is much
simpler to implement, and therefore allows much larger Mahalanobis metric
learning problems to be solved. The time complexity of the proposed method is
, which is significantly lower than that of the SDP approach.
Experiments on a variety of datasets demonstrate that the proposed method
achieves an accuracy comparable to the state-of-the-art, but is applicable to
significantly larger problems. We also show that the proposed method can be
applied to solve more general Frobenius-norm regularized SDP problems
approximately
Scalable Nonlinear Embeddings for Semantic Category-based Image Retrieval
We propose a novel algorithm for the task of supervised discriminative
distance learning by nonlinearly embedding vectors into a low dimensional
Euclidean space. We work in the challenging setting where supervision is with
constraints on similar and dissimilar pairs while training. The proposed method
is derived by an approximate kernelization of a linear Mahalanobis-like
distance metric learning algorithm and can also be seen as a kernel neural
network. The number of model parameters and test time evaluation complexity of
the proposed method are O(dD) where D is the dimensionality of the input
features and d is the dimension of the projection space - this is in contrast
to the usual kernelization methods as, unlike them, the complexity does not
scale linearly with the number of training examples. We propose a stochastic
gradient based learning algorithm which makes the method scalable (w.r.t. the
number of training examples), while being nonlinear. We train the method with
up to half a million training pairs of 4096 dimensional CNN features. We give
empirical comparisons with relevant baselines on seven challenging datasets for
the task of low dimensional semantic category based image retrieval.Comment: ICCV 2015 preprin
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
Deep Adaptive Feature Embedding with Local Sample Distributions for Person Re-identification
Person re-identification (re-id) aims to match pedestrians observed by
disjoint camera views. It attracts increasing attention in computer vision due
to its importance to surveillance system. To combat the major challenge of
cross-view visual variations, deep embedding approaches are proposed by
learning a compact feature space from images such that the Euclidean distances
correspond to their cross-view similarity metric. However, the global Euclidean
distance cannot faithfully characterize the ideal similarity in a complex
visual feature space because features of pedestrian images exhibit unknown
distributions due to large variations in poses, illumination and occlusion.
Moreover, intra-personal training samples within a local range are robust to
guide deep embedding against uncontrolled variations, which however, cannot be
captured by a global Euclidean distance. In this paper, we study the problem of
person re-id by proposing a novel sampling to mine suitable \textit{positives}
(i.e. intra-class) within a local range to improve the deep embedding in the
context of large intra-class variations. Our method is capable of learning a
deep similarity metric adaptive to local sample structure by minimizing each
sample's local distances while propagating through the relationship between
samples to attain the whole intra-class minimization. To this end, a novel
objective function is proposed to jointly optimize similarity metric learning,
local positive mining and robust deep embedding. This yields local
discriminations by selecting local-ranged positive samples, and the learned
features are robust to dramatic intra-class variations. Experiments on
benchmarks show state-of-the-art results achieved by our method.Comment: Published on Pattern Recognitio
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