2 research outputs found
Semi-supervised Dictionary Learning Based on Hilbert-Schmidt Independence Criterion
In this paper, a novel semi-supervised dictionary learning and sparse
representation (SS-DLSR) is proposed. The proposed method benefits from the
supervisory information by learning the dictionary in a space where the
dependency between the data and class labels is maximized. This maximization is
performed using Hilbert-Schmidt independence criterion (HSIC). On the other
hand, the global distribution of the underlying manifolds were learned from the
unlabeled data by minimizing the distances between the unlabeled data and the
corresponding nearest labeled data in the space of the dictionary learned. The
proposed SS-DLSR algorithm has closed-form solutions for both the dictionary
and sparse coefficients, and therefore does not have to learn the two
iteratively and alternately as is common in the literature of the DLSR. This
makes the solution for the proposed algorithm very fast. The experiments
confirm the improvement in classification performance on benchmark datasets by
including the information from both labeled and unlabeled data, particularly
when there are many unlabeled data.Comment: Accepted at International conference on Image analysis and
Recognition (ICIAR) 201
Spectral Non-Convex Optimization for Dimension Reduction with Hilbert-Schmidt Independence Criterion
The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence
measure that has applications in various aspects of machine learning.
Conveniently, the objectives of different dimensionality reduction applications
using HSIC often reduce to the same optimization problem. However, the
nonconvexity of the objective function arising from non-linear kernels poses a
serious challenge to optimization efficiency and limits the potential of
HSIC-based formulations. As a result, only linear kernels have been
computationally tractable in practice. This paper proposes a spectral-based
optimization algorithm that extends beyond the linear kernel. The algorithm
identifies a family of suitable kernels and provides the first and second-order
local guarantees when a fixed point is reached. Furthermore, we propose a
principled initialization strategy, thereby removing the need to repeat the
algorithm at random initialization points. Compared to state-of-the-art
optimization algorithms, our empirical results on real data show a run-time
improvement by as much as a factor of while consistently achieving lower
cost and classification/clustering errors. The implementation source code is
publicly available on https://github.com/endsley.Comment: arXiv admin note: substantial text overlap with arXiv:1909.0309