|Dr. Andrzej Cichocki / Dr. Gene Cheung
|ポーランド科学アカデミー / ヨーク大学 （ポーランド / カナダ）
|◆講演者：Dr. Andrzej Cichocki （ポーランド、ポーランド科学アカデミー、教授）
◆タイトル：'Simplicity is the ultimate sophistication’ : Cross Tensor Approximation Methods and their Applications in Machine Learning and Signal / Image Processing
As modern big datasets are often represented in the form of huge tensors, tensor decompositions and tensor networks have become recently ubiquitous across science and engineering applications, including signal/image processing machine learning, communication, chemometrics, genetic engineering and so on. Tensor decompositions are widely used due to their compact and distributed representation of high-dimensional tensors, overcoming the curse of dimensionality.
Cross approximation called also CUR decomposition - originally developed for representing a low rank structured matrix factorization from a set of selected rows and columns - has been generalized as an efficient and simple method for constructing of various tensor decompositions of a data tensor from few of its entries : tubes and frames.
Cross Tensor Approximation (CTA) can be considered as a generalization of Cross/skeleton matrix or CUR matrix decomposition and is a suitable tool for fast low-rank tensor approximations. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as non-negativity, smoothness, or sparsity, can be preserved. We discuss state of-the-art deterministic and randomized algorithms for cross tensor approximation with intuitive graphical illustrations. We discuss several possible variants of CTA based on fiber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Tensor Ring (TR), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We illustrate the performance of the CTA algorithms by extensive computer simulations to reconstruct incomplete and noisy images and compare their performance.
In this talk we discuss in detail a general framework of cross tensor approximation mostly for the tensor completion tasks. The smooth variants of the developed CTA completion algorithms is proposed to improve the performance.
We experimentally show that the smooth algorithms tackle the problem of reconstructing data tensor with a large missing ratio. The proposed algorithms are relatively simple and easy to be implemented, only in a few lines of code. The efficiency and performance of the proposed algorithms are confirmed by extensive simulations on distorted, noisy and/or incomplete images/videos.
Moreover, we will show how the cross tensor approximation framework can combined with Hankelization / tensorization step as a pre-processing of raw data, which allows us to further improve the performance and extend applications, like global optimization, compression of deep neural networks and reinforcement learning.
◆講演者：Dr. Gene Cheung （カナダ、ヨーク大学、准教授）
◆タイトル：Efficient Signed Graph Sampling via Balancing & Gershgorin Disc Perfect Alignment
A basic premise in graph signal processing (GSP) is that a graph encoding pairwise (anti-)correlations of the targeted signal as edge weights is exploited for graph filtering. However, existing fast graph sampling schemes are designed and tested only for positive graphs describing positive correlations. In this talk, I show that for datasets with strong inherent anti-correlations, a suitable graph contains both positive and negative edge weights. In response, we propose a linear-time signed graph sampling method centered on the concept of balanced signed graphs. A balanced signed graph has no cycles of odd number of negative edges. We show that balanced signed graphs have a natural definition of graph frequencies, and are more amenable to efficient sampling than unbalanced graphs. Experimental results show that our signed graph sampling method outperformed existing fast sampling schemes noticeably on different datasets.
|グローバルイノベーション研究院 ライフサイエンス分野 田中雄一チーム
APSIPA Japan Chapter
|グローバルイノベーション研究院・工学研究院 田中 雄一
e-mail: ytnk（ここに@ を入れてください）cc.tuat.ac.jp