A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary.

Area of Science:

• Computational Mathematics
• Machine Learning
• Data Analysis

Background:

• Nonnegative matrix factorization (NMF) is efficient under the separability assumption.
• Identifying conic basis columns typically involves nonnegative sparse regression and self-dictionaries.
• Existing methods require solving large-scale convex optimization problems.

Purpose of the Study:

• To propose a novel nonnegative sparse regression model with a self-dictionary.
• To develop an efficient optimization method for this model.
• To compare the proposed method against state-of-the-art algorithms.

Main Methods:

• Formulated a smooth optimization problem by enforcing sparsity through linear constraints.
• Developed an efficient Euclidean projection method for the defined polyhedron.
• Proposed a fast gradient method to solve the optimization problem.

Main Results:

• The proposed model yields a smooth optimization problem, unlike previous models.
• The Euclidean projection on the constraint polyhedron is efficiently computable.
• The fast gradient method effectively solves the proposed model, showing competitive performance against state-of-the-art methods on synthetic and real-world hyperspectral image data.

Conclusions:

• The novel nonnegative sparse regression model offers an efficient alternative for NMF under the separability assumption.
• The developed fast gradient method provides a computationally efficient solution.
• The approach demonstrates strong performance, particularly for hyperspectral image analysis.