Multilinear Time Invariant System Theory

In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are not amenable to the standard system and controls framework which requires the state to be in the form of a vector. In order to address this limitation, recently a new class of multiway dynamical systems has been introduced in which the states, inputs and outputs are tensors. We propose a new form of multilinear time invariant (MLTI) systems based on the Einstein product and even-order paired tensors. We extend classical linear time invariant (LTI) system notions including stability, reachability and observability for the new MLTI system representation by leveraging recent advances in tensor algebra.Comment: 8 pages, SIAM Conference on Control and its Applications 2019, accepted to appea

Unsupervised Lesion Detection via Image Restoration with a Normative Prior

Unsupervised lesion detection is a challenging problem that requires accurately estimating normative distributions of healthy anatomy and detecting lesions as outliers without training examples. Recently, this problem has received increased attention from the research community following the advances in unsupervised learning with deep learning. Such advances allow the estimation of high-dimensional distributions, such as normative distributions, with higher accuracy than previous methods.The main approach of the recently proposed methods is to learn a latent-variable model parameterized with networks to approximate the normative distribution using example images showing healthy anatomy, perform prior-projection, i.e. reconstruct the image with lesions using the latent-variable model, and determine lesions based on the differences between the reconstructed and original images. While being promising, the prior-projection step often leads to a large number of false positives. In this work, we approach unsupervised lesion detection as an image restoration problem and propose a probabilistic model that uses a network-based prior as the normative distribution and detect lesions pixel-wise using MAP estimation. The probabilistic model punishes large deviations between restored and original images, reducing false positives in pixel-wise detections. Experiments with gliomas and stroke lesions in brain MRI using publicly available datasets show that the proposed approach outperforms the state-of-the-art unsupervised methods by a substantial margin, +0.13 (AUC), for both glioma and stroke detection. Extensive model analysis confirms the effectiveness of MAP-based image restoration.Comment: Extended version of 'Unsupervised Lesion Detection via Image Restoration with a Normative Prior' (MIDL2019

Latent Class Model with Application to Speaker Diarization

In this paper, we apply a latent class model (LCM) to the task of speaker diarization. LCM is similar to Patrick Kenny's variational Bayes (VB) method in that it uses soft information and avoids premature hard decisions in its iterations. In contrast to the VB method, which is based on a generative model, LCM provides a framework allowing both generative and discriminative models. The discriminative property is realized through the use of i-vector (Ivec), probabilistic linear discriminative analysis (PLDA), and a support vector machine (SVM) in this work. Systems denoted as LCM-Ivec-PLDA, LCM-Ivec-SVM, and LCM-Ivec-Hybrid are introduced. In addition, three further improvements are applied to enhance its performance. 1) Adding neighbor windows to extract more speaker information for each short segment. 2) Using a hidden Markov model to avoid frequent speaker change points. 3) Using an agglomerative hierarchical cluster to do initialization and present hard and soft priors, in order to overcome the problem of initial sensitivity. Experiments on the National Institute of Standards and Technology Rich Transcription 2009 speaker diarization database, under the condition of a single distant microphone, show that the diarization error rate (DER) of the proposed methods has substantial relative improvements compared with mainstream systems. Compared to the VB method, the relative improvements of LCM-Ivec-PLDA, LCM-Ivec-SVM, and LCM-Ivec-Hybrid systems are 23.5%, 27.1%, and 43.0%, respectively. Experiments on our collected database, CALLHOME97, CALLHOME00 and SRE08 short2-summed trial conditions also show that the proposed LCM-Ivec-Hybrid system has the best overall performance