Dynamic L1-norm Tucker Tensor Decomposition

Abstract

<p>Tucker decomposition is a standard method for processing multi-way (tensor) measurements and finds many applications in machine learning and data mining, among other fields. When tensor measurements arrive in a streaming fashion or are too many to jointly decompose, incremental Tucker analysis is preferred. In addition, dynamic basis adaptation is desired when the nominal data subspaces change. At the same time, it has been documented that outliers in the data can significantly compromise the performance of existing methods for dynamic Tucker analysis. In this work, we present Dynamic L1-Tucker: an algorithm for dynamic and outlier-resistant Tucker analysis of tensor data. Our experimental studies on both real and synthetic datasets corroborate that the proposed method (i) attains high basis estimation performance, (ii) identifies/rejects outliers, and (iii) adapts to nominal subspace changes.</p>

Online Rank-Revealing Block-Term Tensor Decomposition

“…Future research can be directed towards extending the novel online BTD algorithm to incorporate constraints and side information [69] and perform completion [66] and DL [11] tasks. Modifications necessary for solving large-scale problems (using, for example, sampling/sketching) [54], [80] or being robust (to outliers) [12], [43] are also worth exploring. Coupled [81], [82] and Bayesian [83] versions should also be developed, greatly widening its applications spectrum.…”

“…Possible solution approaches include alternating optimization with alternating direction method of multipliers (AO-ADMM) [42]. Incorporating ℓ 1 -norm constraints in dynamic TD allows for rejecting outliers or detecting subspace changes [43]. [44] relies on the well-known in robust principal component analysis (PCA) [12], [45] low rank plus sparse representation model to come up with an online CPD scheme for (ADMM-based) outlier-resistant tracking and completion.…”