Abstract
Nonnegative Tucker decomposition (NTD) is a robust method used for nonnegative multilinear feature extraction from nonnegative multi-way arrays. The standard version of NTD assumes that all of the observed data are accessible for batch processing. However, the data in many real-world applications are not static or are represented by a large number of multi-way samples that cannot be processing in one batch. To tackle this problem, a dynamic approach to NTD can be explored. In this study, we extend the standard model of NTD to an incremental or online version, assuming volatility of observed multi-way data along one mode. We propose two computational approaches for updating the factors in the incremental model: one is based on the recursive update model, and the other uses the concept of the block Kaczmarz method that belongs to coordinate descent methods. The experimental results performed on various datasets and streaming data demonstrate high efficiently of both algorithmic approaches, with respect to the baseline NTD methods.
Highlights
Tensor decompositions are robust tools for multi-linear feature extraction and multimodal dimensionality reduction [1,2]
We proposed new computational algorithms for an incremental version of the Nonnegative Tucker decomposition (NTD) model
One of them is based on the concept of row-action projections with the block Kaczmarz method, and the other uses the recursive nonnegative least-squares updates
Summary
Tensor decompositions are robust tools for multi-linear feature extraction and multimodal dimensionality reduction [1,2]. The Tucker decomposition model assumes that an input multi-way array, which will be referred to as a tensor, is decomposed into a core tensor and a set of lower-rank matrices, capturing the multilinear features associated with all the modes of the input tensor. R. Tucker [9] in 1966 as a multi-linear extension to principal component analysis (PCA). Many versions of this model are available across multiple applications in various areas of science and technology, among others, facial image representation [20,21,22,23,24], hand-written digit recognition [25], data clustering and segmentation [26,27,28,29], communication [28,30], hyperspectral image compression [31], muscle activity analysis [32]. A survey of its applications can be found in [10,33,34]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
