一种基于GMM和BYY后向结构的非监督图像分割

贝叶斯阴阳和谐学习系统(BYY和谐学习系统)被广泛地应用于聚类算法中.BYY和谐学习系统有两种基本结构:具有后向结构的BYY学习系统和具有双向结构的BYY学习系统.本文将先对具有后向结构的BYY学习系统做简单的介绍,然后进行数值试验验证其聚类的有效性,最后将其应用于图像分割中.

On essential topics of BYY harmony learning： Current status, challenging issues, and gene analysis applications

As a supplementary of [Xu L. Front. Electr. Electron. Eng. China, 2010, 5（3）： 281-328], this paper outlines current status of efforts made on Bayesian Ying- Yang （BYY） harmony learning, plus gene analysis appli- cations. At the beginning, a bird＇s-eye view is provided via Gaussian mixture in comparison with typical learn- ing algorithms and model selection criteria. Particularly, semi-supervised learning is covered simply via choosing a scalar parameter. Then, essential topics and demand- ing issues about BYY system design and BYY harmony learning are systematically outlined, with a modern per- spective on Yin-Yang viewpoint discussed, another Yang factorization addressed, and coordinations across and within Ying-Yang summarized. The BYY system acts as a unified framework to accommodate unsupervised, su- pervised, and semi-supervised learning all in one formu- lation, while the best harmony learning provides novelty and strength to automatic model selection. Also, mathe- matical formulation of harmony functional has been ad- dressed as a unified scheme for measuring the proximity to be considered in a BYY system, and used as the best choice among others. Moreover, efforts are made on a number of learning tasks, including a mode-switching factor analysis proposed as a semi-blind learning frame- work for several types of independent factor analysis, a hidden Markov model （HMM） gated temporal fac- tor analysis suggested for modeling piecewise stationary temporal dependence, and a two-level hierarchical Gaus- sian mixture extended to cover semi-supervised learning, as well as a manifold learning modified to facilitate au- tomatic model selection. Finally, studies are applied to the problems of gene analysis, such as genome-wide asso- ciation, exome sequencing analysis, and gene transcrip- tional regulation.

Radar HRRP statistical recognition with temporal factor analysis by automatic Bayesian Ying-Yang harmony learning

Radar high-resolution range profiles(HRRPs)are typical high-dimensional and interdimension dependently distributed data,the statistical modeling of which is a challenging task for HRRP-based target recognition.Supposing that HRRP samples are independent and jointly Gaussian distributed,a recent work[Du L,Liu H W,Bao Z.IEEE Transactions on Signal Processing,2008,56(5):1931–1944]applied factor analysis(FA)to model HRRP data with a two-phase approach for model selection,which achieved satisfactory recognition performance.The theoretical analysis and experimental results reveal that there exists high temporal correlation among adjacent HRRPs.This paper is thus motivated to model the spatial and temporal structure of HRRP data simultaneously by employing temporal factor analysis(TFA)model.For a limited size of high-dimensional HRRP data,the two-phase approach for parameter learning and model selection suffers from intensive computation burden and deteriorated evaluation.To tackle these problems,this work adopts the Bayesian Ying-Yang(BYY)harmony learning that has automatic model selection ability during parameter learning.Experimental results show stepwise improved recognition and rejection performances from the twophase learning based FA,to the two-phase learning based TFA and to the BYY harmony learning based TFA with automatic model selection.In addition,adding many extra free parameters to the classic FA model and thus becoming even worse in identifiability,the model of a general linear dynamical system is even inferior to the classic FA model.

Optimization of fuzzy CMAC using evolutionary Bayesian Ying-Yang learning

Cerebellar model articulation controller(CMAC)is a popular associative memory neural network that imitates human’s cerebellum,which allows it to learn fast and carry out local generalization efficiently.This research aims to integrate evolutionary computation into fuzzy CMAC Bayesian Ying-Yang(FCMACBYY)learning,which is referred to as FCMAC-EBYY,to achieve a synergetic development in the search for optimal fuzzy sets and connection weights.Traditional evolutionary approaches are limited to small populations of short binary string length and as such are not suitable for neural network training,which involves a large searching space due to complex connections as well as real values.The methodology employed by FCMACEBYY is coevolution,in which a complex solution is decomposed into some pieces to be optimized in different populations/species and then assembled.The developed FCMAC-EBYY is compared with various neuro-fuzzy systems using a real application of traffic flow prediction.

Codimensional matrix pairing perspective of BYY harmony learning:hierarchy of bilinear systems,joint decomposition of data-covariance,and applications of network biology

One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang(BYY)harmony learning from a perspective of problem solving,parameter learning,and model selection.In a complementary role,the paper provides further insights from another perspective that a co-dimensional matrix pair(shortly co-dim matrix pair)forms a building unit and a hierarchy of such building units sets up the BYY system.The BYY harmony learning is re-examined via exploring the nature of a co-dim matrix pair,which leads to improved learning performance with refined model selection criteria and a modified mechanism that coordinates automatic model selection and sparse learning.Besides updating typical algorithms of factor analysis(FA),binary FA(BFA),binary matrix factorization(BMF),and nonnegative matrix factorization(NMF)to share such a mechanism,we are also led to(a)a new parametrization that embeds a de-noise nature to Gaussian mixture and local FA(LFA);(b)an alternative formulation of graph Laplacian based linear manifold learning;(c)a codecomposition of data and covariance for learning regularization and data integration;and(d)a co-dim matrix pair based generalization of temporal FA and state space model.Moreover,with help of a co-dim matrix pair in Hadamard product,we are led to a semi-supervised formation for regression analysis and a semi-blind learning formation for temporal FA and state space model.Furthermore,we address that these advances provide with new tools for network biology studies,including learning transcriptional regulatory,Protein-Protein Interaction network alignment,and network integration.

对角型广义RBF神经网络与非线性时间序列预测

径向基函数(RBF)神经网络在非线性时间序列预测方面发挥着重要作用。本文提出了对角型广义RBF神经网络模型,并利用贝叶斯阴阳(BYY)和谐学习算法进行隐层单元个数的确定和参数初始值的选取,并且建立了同步LMS算法进行参数学习。进一步,将对角型广义RBF神经网络应用于非线性时间序列预测,得到了预测准确率高和速度快的效果。

广义RBF神经网络在煤矿冲击地压预测上的应用

本文将广义径向基函数(RBF)神经网络应用于华丰煤矿实测的煤矿中冲击地压数据的建模和短期预报。在网络设计上,本文采用了贝叶斯阴阳(BYY)和谐学习算法进行网络隐单元个数的确定和参数初始值的选取,而在参数学习上,本文则采用了同步LMS学习算法。实验结果表明,这种基于广义RBF神经网络的预测方法在精度和速度上有了显著的优势,能够满足在工程应用中的实际要求。

Information geometry in optimization,machine learning and statistical inference

The present article gives an introduction to information geometry and surveys its applications in the area of machine learning,optimization and statistical inference.Information geometry is explained intuitively by using divergence functions introduced in a manifold of probability distributions and other general manifolds.They give a Riemannian structure together with a pair of dual flatness criteria.Many manifolds are dually flat.When a manifold is dually flat,a generalized Pythagorean theorem and related projection theorem are introduced.They provide useful means for various approximation and optimization problems.We apply them to alternative minimization problems,Ying-Yang machines and belief propagation algorithm in machine learning.

Discriminative training of GMM-HMM acoustic model by RPCL learning

This paper presents a new discriminative approach for training Gaussian mixture models(GMMs)of hidden Markov models(HMMs)based acoustic model in a large vocabulary continuous speech recognition(LVCSR)system.This approach is featured by embedding a rival penalized competitive learning(RPCL)mechanism on the level of hidden Markov states.For every input,the correct identity state,called winner and obtained by the Viterbi force alignment,is enhanced to describe this input while its most competitive rival is penalized by de-learning,which makes GMMs-based states become more discriminative.Without the extensive computing burden required by typical discriminative learning methods for one-pass recognition of the training set,the new approach saves computing costs considerably.Experiments show that the proposed method has a good convergence with better performances than the classical maximum likelihood estimation(MLE)based method.Comparing with two conventional discriminative methods,the proposed method demonstrates improved generalization ability,especially when the test set is not well matched with the training set.

Learning Gaussian mixture with automatic model selection:A comparative study on three Bayesian related approaches

Three Bayesian related approaches,namely,variational Bayesian(VB),minimum message length(MML)and Bayesian Ying-Yang(BYY)harmony learning,have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model(GMM).This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conjugate Dirichlet-Normal-Wishart(DNW)prior on GMM.In addition to adopting the existing algorithms either directly or with some modifications,the algorithm for VB with Jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing gap.The performances of automatic model selection are evaluated through extensive experiments,with several empirical findings:1)Considering priors merely on the mixing weights,each of three approaches makes biased mistakes,while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance.2)As Jeffreys prior is replaced by the DNW prior,all the three approaches improve their performances.Moreover,Jeffreys prior makes MML slightly better than VB,while the DNW prior makes VB better than MML.3)As the hyperparameters of DNW prior are further optimized by each of its own learning principle,BYY improves its performances while VB and MML deteriorate their performances when there are too many free hyper-parameters.Actually,VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior.4)BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are optimized.Being different from VB and MML that rely on appropriate priors to perform model selection,BYY does not highly depend on the type of priors.It has model selection ability even without priors and performs already very well with Jeffreys prior,and incrementally improves as Jeffreys prior is replaced by the DNW prior.Finally,all algorithms are applied on the Berkeley segmentation database of real world images.Again,BYY considerably outperforms both VB and MML,especially in detecting the objects of interest from a confusing background.

Adaptive Electric Load Forecaster

In this paper, a methodology, Self-Developing and Self-Adaptive Fuzzy Neural Networks using Type-2 Fuzzy Bayesian Ying-Yang Learning （SDSA-FNN-T2FBYYL） algorithm and multi-objective optimization is proposed. The features of this methodology are as follows： （1） A Bayesian Ying-Yang Learning （BYYL） algorithm is used to construct a compact but high-performance system automatically. （2） A novel multi-objective T2FBYYL is presented that integrates the T2 fuzzy theory with BYYL to automatically construct its best structure and better tackle various data uncertainty problems simultaneously. （3） The weighted sum multi-objective optimization technique with combinations of different weightings is implemented to achieve the best trade-off among multiple objectives in the T2FBYYL. The proposed methods are applied to electric load forecast using a real operational dataset collected from Macao electric utility. The test results reveal that the proposed method is superior to other existing relevant techniques.