Book Chapter10.1007/978-3-030-74386-4_6
Robust Principal Tensor Component Analysis
Yipeng Liu,Jiani Liu,Zhen Long,Ce Zhu +3 more
- 01 Jan 2022
- pp 133-162
2
TL;DR: In this article, robust principal tensor component analysis (RPTCA) is proposed, which separates the low-rank and the sparse tensor from the whole tensor by exploring the multidimensional structure properties.
read more
Abstract: As a fundamental and popular tool for data analysis and dimensionality reduction, principal component analysis (PCA) plays an important role in a wide range of disciplines. Due to PCA’s sensitivity to sparse noise, robust PCA formulates a data matrix as the superposition of a low-rank component and a sparse component. When dealing with the ubiquitous multidimensional data, matrix transformation operation is inevitable, which will cause the loss of structure information. Therefore, robust principal tensor component analysis (RPTCA) is proposed, which separates the low-rank and the sparse tensor from the whole tensor by exploring the multidimensional structure properties.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The application of immersive multimedia information technology in the teaching of vocal music
Shanyu Guo
TL;DR: The results show that the subjects had the best emotional experience with an emotional immersion degree of 5.651 when the music of the calm category and the visual music motion picture of the Calm category constituted the visualMusic immersion based on the vocal music emotional regression model of “combining multimedia information technology” was significantly enhanced.
References
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography
TL;DR: New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.
•Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
Stephen Boyd,Neal Parikh,Eric Chu,Borja Peleato,Jonathan Eckstein +4 more
- 23 May 2011
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
LIII. On lines and planes of closest fit to systems of points in space
TL;DR: This paper is concerned with the construction of planes of closest fit to systems of points in space and the relationships between these planes and the planes themselves.
Robust principal component analysis
TL;DR: In this paper, the authors prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm.
A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics
David Martin,Charless C. Fowlkes,D. Tal,Jitendra Malik +3 more
- 07 Jul 2001
TL;DR: In this paper, the authors present a database containing ground truth segmentations produced by humans for images of a wide variety of natural scenes, and define an error measure which quantifies the consistency between segmentations of differing granularities.