20,438 research outputs found
Non-Redundant Spectral Dimensionality Reduction
Spectral dimensionality reduction algorithms are widely used in numerous
domains, including for recognition, segmentation, tracking and visualization.
However, despite their popularity, these algorithms suffer from a major
limitation known as the "repeated Eigen-directions" phenomenon. That is, many
of the embedding coordinates they produce typically capture the same direction
along the data manifold. This leads to redundant and inefficient
representations that do not reveal the true intrinsic dimensionality of the
data. In this paper, we propose a general method for avoiding redundancy in
spectral algorithms. Our approach relies on replacing the orthogonality
constraints underlying those methods by unpredictability constraints.
Specifically, we require that each embedding coordinate be unpredictable (in
the statistical sense) from all previous ones. We prove that these constraints
necessarily prevent redundancy, and provide a simple technique to incorporate
them into existing methods. As we illustrate on challenging high-dimensional
scenarios, our approach produces significantly more informative and compact
representations, which improve visualization and classification tasks
Linguistic Geometries for Unsupervised Dimensionality Reduction
Text documents are complex high dimensional objects. To effectively visualize
such data it is important to reduce its dimensionality and visualize the low
dimensional embedding as a 2-D or 3-D scatter plot. In this paper we explore
dimensionality reduction methods that draw upon domain knowledge in order to
achieve a better low dimensional embedding and visualization of documents. We
consider the use of geometries specified manually by an expert, geometries
derived automatically from corpus statistics, and geometries computed from
linguistic resources.Comment: 13 pages, 15 figure
Joint & Progressive Learning from High-Dimensional Data for Multi-Label Classification
Despite the fact that nonlinear subspace learning techniques (e.g. manifold
learning) have successfully applied to data representation, there is still room
for improvement in explainability (explicit mapping), generalization
(out-of-samples), and cost-effectiveness (linearization). To this end, a novel
linearized subspace learning technique is developed in a joint and progressive
way, called \textbf{j}oint and \textbf{p}rogressive \textbf{l}earning
str\textbf{a}teg\textbf{y} (J-Play), with its application to multi-label
classification. The J-Play learns high-level and semantically meaningful
feature representation from high-dimensional data by 1) jointly performing
multiple subspace learning and classification to find a latent subspace where
samples are expected to be better classified; 2) progressively learning
multi-coupled projections to linearly approach the optimal mapping bridging the
original space with the most discriminative subspace; 3) locally embedding
manifold structure in each learnable latent subspace. Extensive experiments are
performed to demonstrate the superiority and effectiveness of the proposed
method in comparison with previous state-of-the-art methods.Comment: accepted in ECCV 201
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