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Over the past decades, there has been an increase of attention to adapting machine learning methods to fully exploit the higher order structure of tensorial data. One problem of great interest is tensor classification, and in particular the extension of linear discriminant analysis to the multilinear setting. We propose a novel method for multilinear discriminant analysis that is radically different from the ones considered so far, and it is the first extension to tensors of quadratic discriminant analysis. Our proposed approach uses invariant theory to extend the nearest Mahalanobis distance classifier to the higher-order setting, and to formulate a well-behaved optimization problem. We extensively test our method on a variety of synthetic data, outperforming previously proposed MDA techniques. We also show how to leverage multi-lead ECG data by constructing tensors via taut string, and use our method to classify healthy signals versus unhealthy ones; our method outperforms state-of-the-art MDA methods, especially after adding significant levels of noise to the signals. Our approach reached an AUC of 0.95(0.03) on clean signals—where the second best method reached 0.91(0.03)—and an AUC of 0.89(0.03) after adding noise to the signals (with a signal-to-noise-ratio of −30)—where the second best method reached 0.85(0.05). Our approach is fundamentally different than previous work in this direction, and proves to be faster, more stable, and more accurate on the tests we performed.

 

Abstract Predicting the interactions between drugs and targets plays an important role in the process of new drug discovery, drug repurposing (also known as drug repositioning). There is a need to develop novel and efficient prediction approaches in order to avoid the costly and laborious process of determining drug–target interactions (DTIs) based on experiments alone. These computational prediction approaches should be capable of identifying the potential DTIs in a timely manner. Matrix factorization methods have been proven to be the most reliable group of methods. Here, we first propose a matrix factorization-based method termed ‘Coupled Matrix–Matrix Completion’ (CMMC). Next, in order to utilize more comprehensive information provided in different databases and incorporate multiple types of scores for drug–drug similarities and target–target relationship, we then extend CMMC to ‘Coupled Tensor–Matrix Completion’ (CTMC) by considering drug–drug and target–target similarity/interaction tensors. Results: Evaluation on two benchmark datasets, DrugBank and TTD, shows that CTMC outperforms the matrix-factorization-based methods: GRMF, $L_{2,1}$-GRMF, NRLMF and NRLMF$\beta $. Based on the evaluation, CMMC and CTMC outperform the above three methods in term of area under the curve, F1 score, sensitivity and specificity in a considerably shorter run time.