MOTIVATION: Developing computational tools for integrative analysis across multiple types of omics data has been of immense importance in cancer molecular biology and precision medicine research. While recent advancements have yielded integrative prediction solutions for multi-omics data, these methods lack a comprehensive and cohesive understanding of the rationale behind their specific predictions. To shed light on personalized medicine and unravel previously unknown characteristics within integrative analysis of multi-omics data, we introduce a novel integrative neural network approach for cancer molecular subtype and biomedical classification applications, named Integrative Graph Convolutional Networks (IGCN). RESULTS: To demonstrate the superiority of IGCN, we compare its performance with other state-of-the-art approaches across different cancer subtype and biomedical classification tasks. Our experimental results show that our proposed model outperforms the state-of-the-art and baseline methods. IGCN identifies which types of omics data receive more emphasis for each patient when predicting a specific class. Additionally, IGCN has the capability to pinpoint significant biomarkers from a range of omics data types. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/bozdaglab/IGCN.

In the era of big data, there is massive demand for new techniques to forecast and analyze multi-dimensional data. One task that has seen great interest in the community is anomaly detection of streaming data. Toward this end, the current research develops a novel approach to anomaly detection of streaming 2-dimensional observations via multilinear time-series analysis and 3-dimensional tensor principal component analysis (3DTPCA). We approach this problem utilizing dimensionality reduction and probabilistic inference in a low-dimensional space. We first propose a natural extension to 2-dimensional tensor principal component analysis (2DTPCA) to perform data dimensionality reduction on 4-dimensional tensor objects, aptly named 3DTPCA. We then represent the sub-sequences of our time-series observations as a 4-dimensional tensor utilizing a sliding window. Finally, we use 3DTPCA to compute reconstruction errors for inferring anomalous instances within the multilinear data stream. Experimental validation is presented via MovingMNIST data. Results illustrate that the proposed approach has a significant speedup in training time compared with deep learning, while performing competitively in terms of accuracy.

Multilinear discriminantanalysis (MLDA), a novel approach based upon recent developments in tensor-tensor decomposition, has been proposed recently and showed better performance than traditional matrix linear discriminant analysis (LDA). The current paper presents a nonlinear generalization of MLDA (referred to as KMLDA) by extending the well known "kernel trick" to multilinear data. The approach proceeds by defining a new dot product based on new tensor operators for third-order tensors. Experimental results on the ORL, extended Yale B, and COIL-100 data sets demonstrate that performing MLDA in feature space provides more class separability. It is also shown that the proposed KMLDA approach performs better than the Tucker-based discriminant analysis methods in terms of image classification.

Two-directional two-dimensional principal component analysis ((2D$)^{2}$PCA) has shown promising results for it’s ability to both represent and recognize facial images. The current paper extends these results into a multilinear framework (referred to as two-directional Tensor PCA or 2DTPCA for short) using a recently defined tensor operator for 3rd-order tensors. The approach proceeds by first computing a low-dimensional projection tensor for the row-space of the image data (generally referred to as mode-l) and then subsequently computing a low-dimensional projection tensor for the column space of the image data (generally referred to as mode-3). Experimental results are presented on the ORL, extended Yale-B, COIL100, and MNIST data sets that show the proposed approach outperforms traditional “ tensor-based” PCA approaches with a much smaller subspace dimension in terms of recognition rates.

With the massive influx of 2-dimensional observational data, new methods for analyzing, modeling, and forecasting multidimensional data need to be developed. The current research aims to accomplish these goals through the intersection of time-series modeling and multi-linear algebraic systems. In particular, the current research, aptly named the $\mathcal{L}$-Transform Tensor Auto-Regressive ($\mathcal{L}$-TAR for short) model expands previous auto-regressive techniques to forecast data from multilinear observations as oppose to scalars or vectors. The approach is based on recent developments in tensor decompositions and multilinear tensor products. Transforming the multilinear data through invertible discrete linear transforms enables statistical Independence between observations. As such, can be reformulated to a collection of vector auto-regression problems for model learning. Experimental results are provided on benchmark datasets containing image collections, video sequences, sea surface temperature measurements, and stock closing prices.

The tensor singular value decomposition (t-SVD) based on an algebra of circulants is an effective multilinear sub- space learning technique for dimensionality reduction and data classification. Unfortunately, the computational cost associated with computing the t-SVD can become prohibitively expensive, particularly when dealing with very large data sets. In this paper, we present a computationally efficient approach for estimating the t-SVD by capitalizing on the correlations of the data in the temporal dimension. The approach proceeds by extending our prior work on fast eigenspace decompositions by transforming the tensor data from the spatial domain to the spectral domain in order to obtain reduced order harmonic tensor. The t-SVD can then be applied in the transform domain thereby significantly reducing the computational burden. Experimental results which are presented on the extended Yale-B, COIL-100, and MNIST data sets show the proposed method provides considerable computational savings with the approximated subspaces that are nearly the same as the true subspaces as computed via the t-SVD.