496 research outputs found
Sparse Coding on Symmetric Positive Definite Manifolds using Bregman Divergences
This paper introduces sparse coding and dictionary learning for Symmetric
Positive Definite (SPD) matrices, which are often used in machine learning,
computer vision and related areas. Unlike traditional sparse coding schemes
that work in vector spaces, in this paper we discuss how SPD matrices can be
described by sparse combination of dictionary atoms, where the atoms are also
SPD matrices. We propose to seek sparse coding by embedding the space of SPD
matrices into Hilbert spaces through two types of Bregman matrix divergences.
This not only leads to an efficient way of performing sparse coding, but also
an online and iterative scheme for dictionary learning. We apply the proposed
methods to several computer vision tasks where images are represented by region
covariance matrices. Our proposed algorithms outperform state-of-the-art
methods on a wide range of classification tasks, including face recognition,
action recognition, material classification and texture categorization
Compact Bilinear Pooling
Bilinear models has been shown to achieve impressive performance on a wide
range of visual tasks, such as semantic segmentation, fine grained recognition
and face recognition. However, bilinear features are high dimensional,
typically on the order of hundreds of thousands to a few million, which makes
them impractical for subsequent analysis. We propose two compact bilinear
representations with the same discriminative power as the full bilinear
representation but with only a few thousand dimensions. Our compact
representations allow back-propagation of classification errors enabling an
end-to-end optimization of the visual recognition system. The compact bilinear
representations are derived through a novel kernelized analysis of bilinear
pooling which provide insights into the discriminative power of bilinear
pooling, and a platform for further research in compact pooling methods.
Experimentation illustrate the utility of the proposed representations for
image classification and few-shot learning across several datasets.Comment: Camera ready version for CVP
LASS: a simple assignment model with Laplacian smoothing
We consider the problem of learning soft assignments of items to
categories given two sources of information: an item-category similarity
matrix, which encourages items to be assigned to categories they are similar to
(and to not be assigned to categories they are dissimilar to), and an item-item
similarity matrix, which encourages similar items to have similar assignments.
We propose a simple quadratic programming model that captures this intuition.
We give necessary conditions for its solution to be unique, define an
out-of-sample mapping, and derive a simple, effective training algorithm based
on the alternating direction method of multipliers. The model predicts
reasonable assignments from even a few similarity values, and can be seen as a
generalization of semisupervised learning. It is particularly useful when items
naturally belong to multiple categories, as for example when annotating
documents with keywords or pictures with tags, with partially tagged items, or
when the categories have complex interrelations (e.g. hierarchical) that are
unknown.Comment: 20 pages, 4 figures. A shorter version appears in AAAI 201
- …