Revisiting Conventional Assumptions in Static and Dynamic Tensor Mining

Tensor methods have been used successfully in modeling multi-aspect data and finding useful latent factors in various applications. These applications range from finding meaningful communities in social networks, detecting fake news, brain data analysis (EEG) and countless other applications in various domains like Chemometrics, Psychometrics, and Signal Processing.Despite the success of tensor methods in a wide variety of problems, the application of tensor methods typically entails a number of assumptions which, even though they may pertain only to a limited set of applications or to certain algorithms, are so pervasive that they are considered conventional. However, those assumptions may not be generalizable and, in fact, may hurt performance of tensor methods broadly. The main motivation behind this thesis is to revisit some of those conventional assumptions, propose methods to tackle problems arising from relaxing those assumptions, and observing the subsequent advantages of doing so. Below is the list of works covered in this thesis. Firstly, we focus on a domain specific problem, in which we create a richer feature space for hyperspectral pixel classifications. The next three projects focus on time-evolving graphs, specifically how latent factors evolve over time in streaming tensor decomposition and adaptive granularity in multi-aspect temporal data.1. Feature Space Explosion: In this work, we used tensor factorization to generate a richer feature space for pixel classification in hyperspectral images. We propose a feature explosion technique which maps the input space to a higher dimensional space, which is contrary to the typical low-rank factorization to a low-dimensional space. We propose an algorithm called ORION, which exploits the multi-linear structure of the 3-D hyperspectral tensor using tensor decomposition and generates a space which is more expressive than the original input space. Effectiveness of our method was demonstrated against traditional