26,736 research outputs found
Parametric Local Metric Learning for Nearest Neighbor Classification
We study the problem of learning local metrics for nearest neighbor
classification. Most previous works on local metric learning learn a number of
local unrelated metrics. While this "independence" approach delivers an
increased flexibility its downside is the considerable risk of overfitting. We
present a new parametric local metric learning method in which we learn a
smooth metric matrix function over the data manifold. Using an approximation
error bound of the metric matrix function we learn local metrics as linear
combinations of basis metrics defined on anchor points over different regions
of the instance space. We constrain the metric matrix function by imposing on
the linear combinations manifold regularization which makes the learned metric
matrix function vary smoothly along the geodesics of the data manifold. Our
metric learning method has excellent performance both in terms of predictive
power and scalability. We experimented with several large-scale classification
problems, tens of thousands of instances, and compared it with several state of
the art metric learning methods, both global and local, as well as to SVM with
automatic kernel selection, all of which it outperforms in a significant
manner
A Smoothed Dual Approach for Variational Wasserstein Problems
Variational problems that involve Wasserstein distances have been recently
proposed to summarize and learn from probability measures. Despite being
conceptually simple, such problems are computationally challenging because they
involve minimizing over quantities (Wasserstein distances) that are themselves
hard to compute. We show that the dual formulation of Wasserstein variational
problems introduced recently by Carlier et al. (2014) can be regularized using
an entropic smoothing, which leads to smooth, differentiable, convex
optimization problems that are simpler to implement and numerically more
stable. We illustrate the versatility of this approach by applying it to the
computation of Wasserstein barycenters and gradient flows of spacial
regularization functionals
Multi-view constrained clustering with an incomplete mapping between views
Multi-view learning algorithms typically assume a complete bipartite mapping
between the different views in order to exchange information during the
learning process. However, many applications provide only a partial mapping
between the views, creating a challenge for current methods. To address this
problem, we propose a multi-view algorithm based on constrained clustering that
can operate with an incomplete mapping. Given a set of pairwise constraints in
each view, our approach propagates these constraints using a local similarity
measure to those instances that can be mapped to the other views, allowing the
propagated constraints to be transferred across views via the partial mapping.
It uses co-EM to iteratively estimate the propagation within each view based on
the current clustering model, transfer the constraints across views, and then
update the clustering model. By alternating the learning process between views,
this approach produces a unified clustering model that is consistent with all
views. We show that this approach significantly improves clustering performance
over several other methods for transferring constraints and allows multi-view
clustering to be reliably applied when given a limited mapping between the
views. Our evaluation reveals that the propagated constraints have high
precision with respect to the true clusters in the data, explaining their
benefit to clustering performance in both single- and multi-view learning
scenarios
Low-shot learning with large-scale diffusion
This paper considers the problem of inferring image labels from images when
only a few annotated examples are available at training time. This setup is
often referred to as low-shot learning, where a standard approach is to
re-train the last few layers of a convolutional neural network learned on
separate classes for which training examples are abundant. We consider a
semi-supervised setting based on a large collection of images to support label
propagation. This is possible by leveraging the recent advances on large-scale
similarity graph construction.
We show that despite its conceptual simplicity, scaling label propagation up
to hundred millions of images leads to state of the art accuracy in the
low-shot learning regime
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