The original RVM classification model uses the logistic link function to build the likelihood function making the model hard to be conducted since the posterior of the weight parameter has no closed-form solution. This paper proposes the probit link function approach instead of the logistic one for the likelihood function in the RVM classification model, namely PRVM (RVM with the probit link function). We show that the posterior of the weight parameter in PRVM follows the Multivariate Normal distribution and achieves a closed-form solution. A latent variable is needed in our algorithms to simplify the Bayesian computation greatly, and its conditional posterior follows a truncated Normal distribution. Compared with the original RVM classification model, our proposed one is a Fully Bayesian approach, and it has a more efficient computation process. For the prior structure, we first consider the Normal-Gamma independent prior to propose a Generic Bayesian PRVM algorithm. Furthermore, the Fully Bayesian PRVM algorithm with a hierarchical hyperprior structure is proposed, which improves the classification performance, especially in the imbalanced data problem.

As an essential data processing technology, cluster analysis has been widely used in various fields. In clustering, it is necessary to select appropriate measures to evaluate the similarity in the data. In this paper, firstly, a cluster center selection method based on the grey relational degree is proposed to solve the problem of sensitivity in initial cluster center selection. Secondly, combining the advantages of Euclidean distance, DTW distance, and SPDTW distance, a weighted distance measurement based on three kinds of reach is proposed. Then, it is applied to Fuzzy C-MeDOIDS and Fuzzy C-means hybrid clustering technology. Numerical experiments are carried out with the UCI datasets. The experimental results show that the accuracy of the clustering results is significantly improved by using the clustering method proposed in this paper. Besides, the method proposed in this paper is applied to the MUSIC INTO EMOTIONS and YEAST datasets. The clustering results show that the algorithm proposed in this paper can also achieve a better clustering effect when dealing with practical problems.

Relevance Vector Machine (RVM) is a supervised learning algorithm extended from Support Vector Machine based on the Bayesian sparsity model. Relevance Vector Machine classification suffers from theoretical limitations and computational inefficiency mainly because there is no closed-form solution for the posterior of the weight parameters. We propose two advanced Bayesian approaches for RVM classification, namely the Enhanced RVM and the Reinforced RVM, to perfect the theoretic framework of RVM and extend the algorithm to the imbalanced data problem, which has an arresting skew in data size between classes. First, the Enhanced RVM conducts a strict Bayesian sampling process instead of the approximation method in the original one to remedy its theoretic limitations, especially the nonconvergence of the iterations. Secondly, we conjecture that the hierarchical prior makes the Reinforced RVM achieve consistent estimations of the quantities of interest compared with the non-consistent estimations of the original RVM. Consistency is necessary for RVM classification since it makes the model more stable and localises the relevant vectors more accurately in the imbalanced data problem. The two-level prior also renders the Reinforced one competitive in the imbalanced data problem by building the inner connection of parameter dimensions and alloting a more vital relevance to the small class data weight parameter. The theoretic proofs and several numeric studies demonstrate the merits of our two proposed algorithms.