Search

With the abundance of data, machine learning applications engaged increased attention in the last decade. An attractive approach to robustify the statistical analysis is to preprocess the data through clustering. This paper develops a low-complexity Riemannian optimization framework for solving optimization problems on the set of positive semidefinite stochastic matrices. The low-complexity feature of the proposed algorithms stems from the factorization of the optimization variable $\mathbf {X}=\mathbf {Y}\mathbf {Y}^{\mathrm{T}}$ X = Y Y T and deriving conditions on the number of columns of $\mathbf {Y}$ Y under which the factorization yields a satisfactory solution. The paper further investigates the embedded and quotient geometries of the resulting Riemannian manifolds. In particular, the paper explicitly derives the tangent space, Riemannian gradients and Hessians, and a retraction operator allowing the design of efficient first and second-order optimization methods for the graph-based clustering applications of interest. The numerical results reveal that the resulting algorithms present a clear complexity advantage as compared with state-of-the-art euclidean and Riemannian approaches for graph clustering applications. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms (EAs) have become the standards and paradigms for solving inverse problems. However, their two inherited operations, namely, the crossover and mutation operations, are complicated and difficult, both in theory and in numerical implementations. In this regard, increasing efforts have been devoted to EAs which are based on probabilistic models (EAPMs) to overcome the shortcomings of available EAs. The population-based incremental learning (PBIL) is an EAPM; moreover, it can bridge the gap between machine learning and the EAs, hence enjoying several merits compared with other EAs. However, lukewarm efforts have been devoted to PBILs, especially the real coded PBILs, in the study of inverse problems in electromagnetics. In this regard, a novel real coded PBIL is being proposed in this paper. In the proposed real coded PBIL, a probability matrix is proposed to randomly generate a population, and the updating formulas for this probability matrix using the so far searched best solution and the best solution of the current population are introduced to strike a balance between convergence performance and solution quality. The proposed real coded PBIL algorithm is numerically experimented on several case studies and promising results are reported in this paper. [ABSTRACT FROM PUBLISHER]

Sparse unmixing has become a popular tool for hyperspectral imagery interpretation. It refers to finding the optimal subset of a spectral library to reconstruct the image data and further estimate the proportions of different materials. Recently, multi-objective based sparse unmixing methods have presented promising performance because of their advantages in addressing combinatorial problems. A spectral and multi-objective based sparse unmixing (SMoSU) algorithm was proposed in our previous work, which solves the decision-making problem well. However, it does not show outstanding advantages in strong noise cases. To solve the problem, in this paper, SMoSU is improved based on the estimation of distribution algorithms (EDAs). The machine learning based EDAs have been a reliable approach in solving multi-objective problems. However, most of them are for special problems and relatively weak in theoretical foundations. Thus, it is unreliable to extend it directly to sparse unmixing. Here, we improve EDA on the basis of classification and propose a classification-based model for individual generating under the framework of SMoSU (CM-MoSU). In CM-MoSU, the whole population is divided to be positive and negative. Then, the macroinformation of positive individuals is used to guide the generation of new individuals. Therefore, the optimization task could pay more attention to the feasible space with high quality. Moreover, some theoretical analyses are presented to prove the reliability of CM-MoSU. In experiments, several state-of-the-art sparse unmixing algorithms are compared. Both synthetic and real-world experiments demonstrate the effectiveness of CM-MoSU. [ABSTRACT FROM AUTHOR]

Even though evolutionary algorithm (EA) has now become the standard and paradigm for solving multi-objective design problems, the complexity of its genetic operation is, however, limiting its popularity in engineering applications. Hitherto, there has been insufficient research that addresses the inadequacy of EAs in extracting the characteristic landscape features of an objective function. However, increasing attentions have now been devoted to EAs based on probabilistic models (EAPMs) in computational intelligence studies. A real coded scalar population-based incremental learning algorithm, an EAPM, is proposed for multi-objective optimizations of electromagnetic devices. Major improvements include the design of a generating mechanism for new intermediate solutions, the selection of elite solutions to update the probability matrix, matrix updating formulations, and refinement mechanism for intervals to precisely generate intermediate solution. Also, a methodology to consider quantitatively both the number of improved objectives and the amount of improvements in a specified objective of multi-objective design problems is introduced in fitness assignments. Numerical results on a high frequency and a low inverse problem are reported to showcase the merits of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A Bayesian dynamic model based on multitask learning (MTL) is developed for radar automatic target recognition (RATR) using high-resolution range profile (HRRP). The aspect-dependent HRRP sequence is modeled using a truncated stick-breaking hidden Markov model (TSB-HMM) with time-evolving transition probabilities, in which the spatial structure across range cells is described by the hidden Markov structure and the temporal dependence between HRRP samples is described by the time evolution of the transition probabilities. This framework imposes the belief that temporally proximate HRRPs are more likely to be drawn from similar HMMs, while also allowing for possible distant repetition or “innovation”. In addition, as formulated the stick-breaking prior and MTL mechanism are employed to infer the number of hidden states in an HMM and learn the target-dependent states collectively for all targets. The form of the proposed hierarchical model allows efficient variational Bayesian (VB) inference, of interest for large-scale problems. To validate the formulation, example results are presented for an illustrative synthesized dataset and our main application—RATR, for which we consider the measured HRRP data. For the latter, we also make comparisons to the model with the independent state-transition statistics and some other existing statistical models for radar HRRP data. [ABSTRACT FROM PUBLISHER]