1,896 research outputs found
Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models
Nonnegative matrix factorization (NMF) is a powerful class of feature
extraction techniques that has been successfully applied in many fields, namely
in signal and image processing. Current NMF techniques have been limited to a
single-objective problem in either its linear or nonlinear kernel-based
formulation. In this paper, we propose to revisit the NMF as a multi-objective
problem, in particular a bi-objective one, where the objective functions
defined in both input and feature spaces are taken into account. By taking the
advantage of the sum-weighted method from the literature of multi-objective
optimization, the proposed bi-objective NMF determines a set of nondominated,
Pareto optimal, solutions instead of a single optimal decomposition. Moreover,
the corresponding Pareto front is studied and approximated. Experimental
results on unmixing real hyperspectral images confirm the efficiency of the
proposed bi-objective NMF compared with the state-of-the-art methods
Feature and Region Selection for Visual Learning
Visual learning problems such as object classification and action recognition
are typically approached using extensions of the popular bag-of-words (BoW)
model. Despite its great success, it is unclear what visual features the BoW
model is learning: Which regions in the image or video are used to discriminate
among classes? Which are the most discriminative visual words? Answering these
questions is fundamental for understanding existing BoW models and inspiring
better models for visual recognition.
To answer these questions, this paper presents a method for feature selection
and region selection in the visual BoW model. This allows for an intermediate
visualization of the features and regions that are important for visual
learning. The main idea is to assign latent weights to the features or regions,
and jointly optimize these latent variables with the parameters of a classifier
(e.g., support vector machine). There are four main benefits of our approach:
(1) Our approach accommodates non-linear additive kernels such as the popular
and intersection kernel; (2) our approach is able to handle both
regions in images and spatio-temporal regions in videos in a unified way; (3)
the feature selection problem is convex, and both problems can be solved using
a scalable reduced gradient method; (4) we point out strong connections with
multiple kernel learning and multiple instance learning approaches.
Experimental results in the PASCAL VOC 2007, MSR Action Dataset II and YouTube
illustrate the benefits of our approach
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