Abstract. Non-negative Matrix Factorization (NMF) has been widely exploited to learn latent features from data. However, previous NMF models often assume a fixed number of features, say p features, where p is simply searched by experiments. Moreover, it is even difficult to learn binary features, since binary matrix involves more challenging optimization problems. In this paper, we propose a new Bayesian model called infinite non-negative binary matrix tri-factorizations model (iNBMT), capable of learning automatically the latent binary features as well as feature number based on Indian Buffet Process (IBP). Moreover, iNBMT engages a tri-factorization process that decomposes a nonnegative matrix into the product of three components including two binary matrices and a non-negative real matrix. Compared with traditional bi-factorization, the tri-factorization can better reveal the latent structures among items (samples) and attributes (features). Specifically, we impose an IBP prior on the two infinite binary matrices while a truncated Gaussian distribution is assumed on the weight matrix. To optimize the model, we develop an efficient modified maximization-expectation algorithm (MEalgorithm), with the iteration complexity one order lower than another recently-proposed Maximization-Expectation-IBP model [9]. We present the model definition, detail the optimization, and finally conduct a series of experiments. Experimental results demonstrate that our proposed iNBMT model significantly outperforms the other comparison algorithms in both synthetic and real data.

We consider the problem of volumetric (3D) unsupervised domain adaptation (UDA) in cross-modality medical image segmentation, aiming to perform segmentation on the unannotated target domain (e.g. MRI) with the help of labeled source domain (e.g. CT). Previous UDA methods in medical image analysis usually suffer from two challenges: 1) they focus on processing and analyzing data at 2D level only, thus missing semantic information from the depth level; 2) one-to-one mapping is adopted during the style-transfer process, leading to insufficient alignment in the target domain. Different from the existing methods, in our work, we conduct a first of its kind investigation on multi-style image translation for complete image alignment to alleviate the domain shift problem, and also introduce 3D segmentation in domain adaptation tasks to maintain semantic consistency at the depth level. In particular, we develop an unsupervised domain adaptation framework incorporating a novel quartet self-attention module to efficiently enhance relationships between widely separated features in spatial regions on a higher dimension, leading to a substantial improvement in segmentation accuracy in the unlabeled target domain. In two challenging crossmodality tasks, specifically brain structures and multiorgan abdominal segmentation, our model is shown to outperform current state-of-the-art methods by a significant margin, demonstrating its potential as a benchmark resource for the biomedical and health informatics research community. 1

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