Spectral unmixing based on nonnegative matrix factorization with local smoothness constraint

Spectral unmixing (SU) is an emerging problem in the remote sensing image processing. Since both the endmember signatures and their abundances have nonnegative values, it is a natural choice to employ the attractive nonnegative matrix factorization (NMF) methods to solve this problem. Motivated by that the abundances are sparse, the NMF with local smoothness constraint (NMF-LSC) is proposed in this paper. In the proposed method, the smoothness constraint is utilized to impose the sparseness, instead of the traditional L1-norm which is restricted by the underlying column-sum-to-one requirement of the to the abundance matrix. Simulations show the advantages of our algorithm over the compared methods.

Fast one-class support vector machine for novelty detection

Novelty detection arises as an important learning task in several applications. Kernel-based approach to novelty detection has been widely used due to its theoretical rigor and elegance of geometric interpretation. However, computational complexity is a major obstacle in this approach. In this paper, leveraging on the cutting-plane framework with the well-known One-Class Support Vector Machine, we present a new solution that can scale up seamlessly with data. The first solution is exact and linear when viewed through the cutting-plane; the second employed a sampling strategy that remarkably has a constant computational complexity defined relatively to the probability of approximation accuracy. Several datasets are benchmarked to demonstrate the credibility of our framework.

A matrix factorization framework for jointly analyzing multiple nonnegative data sources

Nonnegative matrix factorization based methods provide one of the simplest and most effective approaches to text mining. However, their applicability is mainly limited to analyzing a single data source. In this chapter, we propose a novel joint matrix factorization framework which can jointly analyze multiple data sources by exploiting their shared and individual structures. The proposed framework is flexible to handle any arbitrary sharing configurations encountered in real world data. We derive an efficient algorithm for learning the factorization and show that its convergence is theoretically guaranteed. We demonstrate the utility and effectiveness of the proposed framework in two real-world applications—improving social media retrieval using auxiliary sources and cross-social media retrieval. Representing each social media source using their textual tags, for both applications, we show that retrieval performance exceeds the existing state-of-the-art techniques. The proposed solution provides a generic framework and can be applicable to a wider context in data mining wherever one needs to exploit mutual and individual knowledge present across multiple data sources.

Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.