24,029 research outputs found
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
Bridge Simulation and Metric Estimation on Landmark Manifolds
We present an inference algorithm and connected Monte Carlo based estimation
procedures for metric estimation from landmark configurations distributed
according to the transition distribution of a Riemannian Brownian motion
arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric.
The distribution possesses properties similar to the regular Euclidean normal
distribution but its transition density is governed by a high-dimensional PDE
with no closed-form solution in the nonlinear case. We show how the density can
be numerically approximated by Monte Carlo sampling of conditioned Brownian
bridges, and we use this to estimate parameters of the LDDMM kernel and thus
the metric structure by maximum likelihood
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