Interactive Segmentation in Multimodal Medical Imagery Using a Bayesian Transductive Learning Approach

Labeled training data in the medical domain is rare and expensive to obtain. The lack of labeled multimodal medical image data is a major obstacle for devising learning-based interactive segmentation tools. Transductive learning (TL) or semi-supervised learning (SSL) offers a workaround by leveraging unlabeled and labeled data to infer labels for the test set given a small portion of label information. In this paper we propose a novel algorithm for interactive segmentation using transductive learning and inference in conditional mixture nave Bayes models (T-CMNB) with spatial regularization constraints. T-CMNB is an extension of the transductive nave Bayes algorithm [1, 20]. The multimodal Gaussian mixture assumption on the class-conditional likelihood and spatial regularization constraints allow us to explain more complex distributions required for spatial classification in multimodal imagery. To simplify the estimation we reduce the parameter space by assuming nave conditional independence between the feature space and the class label. The nave conditional independence assumption allows efficient inference of marginal and conditional distributions for large scale learning and inference [19]. We evaluate the proposed algorithm on multimodal MRI brain imagery using ROC statistics and provide preliminary results. The algorithm shows promising segmentation performance with a sensitivity and specificity of 90.37% and 99.74% respectively and compares competitively to alternative interactive segmentation schemes

Bayesian inference for transductive learning of kernel matrix using the Tanner-Wong data augmentation algorithm

In kernel methods, an interesting recent development seeks to learn a good kernel from empirical data automatically. In this paper, by regarding the transductive learning of the kernel matrix as a missing data problem, we propose a Bayesian hierarchical model for the problem and devise the Tanner-Wong data augmentation algorithm for making inference on the model. The Tanner-Wong algorithm is closely related to Gibbs sampling, and it also bears a strong resemblance to the expectation-maximization (EM) algorithm. For an e#cient implementation, we propose a simplified Bayesian hierarchical model and the corresponding TannerWong algorithm. We express the relationship between the kernel on the input space and the kernel on the output space as a symmetric-definite generalized eigenproblem