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Mixtures of Hidden Markov Models (MHMM) are widely used for clustering of sequential data, by letting each cluster correspond to a Hidden Markov Model (HMM). Expectation Maximization (EM) is the standard approach for learning the parameters of an MHMM. However, due to the non-convexity of the objective function, EM can converge to poor local optima. To tackle this problem, we propose a novel method, the Orthogonal Mixture of Hidden Markov Models (oMHMM), which aims to direct the search away from candidate solutions that include very similar HMMs, since those do not fully exploit the power of the mixture model. The directed search is achieved by including a penalty in the objective function that favors higher orthogonality between the transition matrices of the HMMs. Experimental results on both simulated and real-world datasets show that the oMHMM consistently finds equally good or better local optima than the standard EM for an MHMM; for some datasets, the clustering performance is significantly improved by our novel oMHMM (up to 55 percentage points w.r.t. the v-measure). Moreover, the oMHMM may also decrease the computational cost substantially, reducing the number of iterations down to a fifth of those required by MHMM using standard EM., QC 20211203Conference ISBN 978-3-030-67658-2; 978-3-030-67657-5

The ability to accurately estimate risk of developing breast cancer would be invaluable for clinical decision-making. One promising new approach is to integrate image-based risk models based on deep neural networks. However, one must take care when using such models, as selection of training data influences the patterns the network will learn to identify. With this in mind, we trained networks using three different criteria to select the positive training data (i.e. images from patients that will develop cancer): an inherent risk model trained on images with no visible signs of cancer, a cancer signs model trained on images containing cancer or early signs of cancer, and a conflated model trained on all images from patients with a cancer diagnosis. We find that these three models learn distinctive features that focus on different patterns, which translates to contrasts in performance. Short-term risk is best estimated by the cancer signs model, whilst long-term risk is best estimated by the inherent risk model. Carelessly training with all images conflates inherent risk with early cancer signs, and yields sub-optimal estimates in both regimes. As a consequence, conflated models may lead physicians to recommend preventative action when early cancer signs are already visible., QC 20210323