GTT: Guiding the Tensor Train Decomposition

• Published in: Lecture notes in computer science Vol. 12440; pp. 187 - 202
• Main Authors: Li, Mao-Lin, Candan, K. Selçuk, Sapino, Maria Luisa
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2020; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Low-rank embedding; Tensor train decomposition
• ISBN: 3030609359; 9783030609351
• ISSN: 0302-9743; 1611-3349; 1611-3349
• DOI: 10.1007/978-3-030-60936-8_15

The demand for searching, querying multimedia data such as image, video and audio is omnipresent, how to effectively access data for various applications is a critical task. Nevertheless, these data usually are encoded as multi-dimensional arrays, or Tensor, and traditional data mining techniques might be limited due to the curse of dimensionality. Tensor decomposition is proposed to alleviate this issue, commonly used tensor decomposition algorithms include CP-decomposition (which seeks a diagonal core) and Tucker-decomposition (which seeks a dense core). Naturally, Tucker maintains more information, but due to the denseness of the core, it also is subject to exponential memory growth with the number of tensor modes. Tensor train (TT) decomposition addresses this problem by seeking a sequence of three-mode cores: but unfortunately, currently, there are no guidelines to select the decomposition sequence. In this paper, we propose a GTT method for guiding the tensor train in selecting the decomposition sequence. GTT leverages the data characteristics (including number of modes, length of the individual modes, density, distribution of mutual information, and distribution of entropy) as well as the target decomposition rank to pick a decomposition order that will preserve information. Experiments with various data sets demonstrate that GTT effectively guides the TT-decomposition process towards decomposition sequences that better preserve accuracy.