Tensor methods are powerful data analytic tools from multilinear algebra which are widely used in machine learning and data science. Tensors can represent heterogeneous, multi-modal datasets which come from a wide variety of real-world applications, including social network analysis, computer vision, recommendation systems, and scientific applications. The main focus of the project was to develop and apply robust tensor methods, where the data that are being analyzed are corrupted, noisy, or incomplete, which is very frequently the case in real-world scenarios.  The research outcomes of this project fall into two thrusts: (1) Fundamental algorithm development for robust tensor methods, and (2) Real-world applications. 

The project advanced the state-of-the-art in robust tensor methods while also innovating in key high-impact applications where the power and generality of tensor methods in obtaining state-of-the-art results was demonstrated. As part of this project, graduate students were trained in the PI’s lab, and the results of the research were broadly disseminated at top scientific venues. Furthermore, as part of fostering a vibrant research community, the PI was actively involved in the organization of symposia and workshops in the area of tensor methods for data science and machine learning.

Highlights for research outcomes are outlined below.

Fundamental algorithm development for robust tensor methods:

The first main thrust of the project was the design and development of fundamental algorithms for tensor analysis, with specific emphasis on robustness. Within that framework, the following two threads were explored:

(a) Robust tensor decomposition and compression: Within this thread, the project developed novel formulations for computing tensor decompositions for data analysis and compression in a manner which is less sensitive to outliers and noise, thus offering higher-quality in terms of data representation, reconstruction, and compression. Furthermore, a compression-based streaming tensor decomposition was developed.

(b) Tensor model order selection and its interplay with compression: Model selection in tensor analysis refers to the selection of the number of hidden patterns in the data, and is of utmost importance, since it dictates the number of insights that can be extracted from the data. The selection of this number is an extremely hard problem. Different methods for model order selection were developed, with specific emphasis on doing so in compressed data, which allows for scalable computations.

Real-world Applications:

The second main thrust of the work was the adaptation and application of tensor methods to high-impact real-world problems, including social media and network analysis, recommendation systems, computer vision, and scientific data analysis.

(a) Social media and network analysis:

WIthin the umbrella of social media and network analysis, the project focused on a number of high-impact and timely problems, such as misinformation detection (studying different aspects of it, including analyzing article content, analyzing visual cues from website screenshots, and detecting DeepFake images), geolocation of social media posts from text and images, humor recognition especially in the cases where limited human annotations are present, and the development of methods for shielding graph neural networks against adversarial attacks, where corrupted network interactions are meant to mislead the classification of certain entities in the network.

(b) Recommendation systems:

One of the main tensor models studied in the first thrust (RESCAL) was successfully applied to the challenging problem of complementary item recommendation in online grocery shopping.

(c) Computer vision:

As part of shielding neural networks that specialize in image classification, the project focused on tensor compression for alleviating adversarially corrupted images, which are meant to fool the classifier while remaining imperceptible to humans. Furthermore, the project developed tensor-based methods for computing representations of hyperspectral images which rival neural network methods in pixel classification. 

(d) Scientific data analysis:

Scientific data are inherently multi-dimensional and multi-modal. In this project, specific emphasis was placed in the analysis of data from the Laser Interferometer Gravitational Wave Observatory (LIGO) with tensor methods towards the detection of so-called “glitches”, noise transients that appear similar to meaningful patterns in the data, thus corrupting the scientific data and impacting the accurate detection of gravitational waves.

Last Modified: 12/22/2021
Modified by: Evangelos Papalexakis