9,075 research outputs found
Regularized Optimal Transport and the Rot Mover's Distance
This paper presents a unified framework for smooth convex regularization of
discrete optimal transport problems. In this context, the regularized optimal
transport turns out to be equivalent to a matrix nearness problem with respect
to Bregman divergences. Our framework thus naturally generalizes a previously
proposed regularization based on the Boltzmann-Shannon entropy related to the
Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We
call the regularized optimal transport distance the rot mover's distance in
reference to the classical earth mover's distance. We develop two generic
schemes that we respectively call the alternate scaling algorithm and the
non-negative alternate scaling algorithm, to compute efficiently the
regularized optimal plans depending on whether the domain of the regularizer
lies within the non-negative orthant or not. These schemes are based on
Dykstra's algorithm with alternate Bregman projections, and further exploit the
Newton-Raphson method when applied to separable divergences. We enhance the
separable case with a sparse extension to deal with high data dimensions. We
also instantiate our proposed framework and discuss the inherent specificities
for well-known regularizers and statistical divergences in the machine learning
and information geometry communities. Finally, we demonstrate the merits of our
methods with experiments using synthetic data to illustrate the effect of
different regularizers and penalties on the solutions, as well as real-world
data for a pattern recognition application to audio scene classification
Euclidean Distances, soft and spectral Clustering on Weighted Graphs
We define a class of Euclidean distances on weighted graphs, enabling to
perform thermodynamic soft graph clustering. The class can be constructed form
the "raw coordinates" encountered in spectral clustering, and can be extended
by means of higher-dimensional embeddings (Schoenberg transformations).
Geographical flow data, properly conditioned, illustrate the procedure as well
as visualization aspects.Comment: accepted for presentation (and further publication) at the ECML PKDD
2010 conferenc
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
Energy Confused Adversarial Metric Learning for Zero-Shot Image Retrieval and Clustering
Deep metric learning has been widely applied in many computer vision tasks,
and recently, it is more attractive in \emph{zero-shot image retrieval and
clustering}(ZSRC) where a good embedding is requested such that the unseen
classes can be distinguished well. Most existing works deem this 'good'
embedding just to be the discriminative one and thus race to devise powerful
metric objectives or hard-sample mining strategies for leaning discriminative
embedding. However, in this paper, we first emphasize that the generalization
ability is a core ingredient of this 'good' embedding as well and largely
affects the metric performance in zero-shot settings as a matter of fact. Then,
we propose the Energy Confused Adversarial Metric Learning(ECAML) framework to
explicitly optimize a robust metric. It is mainly achieved by introducing an
interesting Energy Confusion regularization term, which daringly breaks away
from the traditional metric learning idea of discriminative objective devising,
and seeks to 'confuse' the learned model so as to encourage its generalization
ability by reducing overfitting on the seen classes. We train this confusion
term together with the conventional metric objective in an adversarial manner.
Although it seems weird to 'confuse' the network, we show that our ECAML indeed
serves as an efficient regularization technique for metric learning and is
applicable to various conventional metric methods. This paper empirically and
experimentally demonstrates the importance of learning embedding with good
generalization, achieving state-of-the-art performances on the popular CUB,
CARS, Stanford Online Products and In-Shop datasets for ZSRC tasks.
\textcolor[rgb]{1, 0, 0}{Code available at http://www.bhchen.cn/}.Comment: AAAI 2019, Spotligh
- …