scholarly journals A Bi-level Formulation for Label Noise Learning with Spectral Cluster Discovery

2020 ◽  
Author(s):  
Yijing Luo ◽  
Bo Han ◽  
Chen Gong
Keyword(s):  
Ground Truth ◽  
Spectral Cluster ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Label Noise ◽  
Learning Stage ◽  
Cluster Membership ◽  
Rank Approximation ◽  
Real World Datasets ◽  
Classifier Learning

Practically, we often face the dilemma that some of the examples for training a classifier are incorrectly labeled due to various subjective and objective factors. Although intensive efforts have been put to design classifiers that are robust to label noise, most of the previous methods have not fully utilized data distribution information. To address this issue, this paper introduces a bi-level learning paradigm termed “Spectral Cluster Discovery'' (SCD) for combating with noisy labels. Namely, we simultaneously learn a robust classifier (Learning stage) by discovering the low-rank approximation to the ground-truth label matrix and learn an ideal affinity graph (Clustering stage). Specifically, we use the learned classifier to assign the examples with similar label to a mutual cluster. Based on the cluster membership, we utilize the learned affinity graph to explore the noisy examples based on the cluster membership. Both stages will reinforce each other iteratively. Experimental results on typical benchmark and real-world datasets verify the superiority of SCD to other label noise learning methods.

scholarly journals Incremental Matrix Factorization: A Linear Feature Transformation Perspective

2017 ◽  
Author(s):  
Xunpeng Huang ◽  
Le Wu ◽  
Enhong Chen ◽  
Hengshu Zhu ◽  
Qi Liu ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Low Rank ◽  
Feature Transformation ◽  
Low Rank Approximation ◽  
Linear Feature ◽  
Special Cases ◽  
Rank Approximation ◽  
Training Error ◽  
Real World Datasets ◽  
And Storage

Matrix Factorization (MF) is among the most widely used techniques for collaborative filtering based recommendation. Along this line, a critical demand is to incrementally refine the MF models when new ratings come in an online scenario. However, most of existing incremental MF algorithms are limited by specific MF models or strict use restrictions. In this paper, we propose a general incremental MF framework by designing a linear transformation of user and item latent vectors over time. This framework shows a relatively high accuracy with a computation and space efficient training process in an online scenario. Meanwhile, we explain the framework with a low-rank approximation perspective, and give an upper bound on the training error when this framework is used for incremental learning in some special cases. Finally, extensive experimental results on two real-world datasets clearly validate the effectiveness, efficiency and storage performance of the proposed framework.

scholarly journals Improving One-Class Collaborative Filtering via Ranking-Based Implicit Regularizer

2019 ◽  
Vol 33 ◽  
pp. 37-44 ◽  
Author(s):  
Jin Chen ◽  
Defu Lian ◽  
Kai Zheng
Keyword(s):  
Collaborative Filtering ◽  
State Of The Art ◽  
Ground Truth ◽  
The State ◽  
Low Rank ◽  
Model Parameters ◽  
Music Recommendation ◽  
Low Rank Approximation ◽  
The Arts ◽  
Rank Approximation

One-class collaborative filtering (OCCF) problems are vital in many applications of recommender systems, such as news and music recommendation, but suffers from sparsity issues and lacks negative examples. To address this problem, the state-of-the-arts assigned smaller weights to unobserved samples and performed low-rank approximation. However, the ground-truth ratings of unobserved samples are usually set to zero but ill-defined. In this paper, we propose a ranking-based implicit regularizer and provide a new general framework for OCCF, to avert the ground-truth ratings of unobserved samples. We then exploit it to regularize a ranking-based loss function and design efficient optimization algorithms to learn model parameters. Finally, we evaluate them on three realworld datasets. The results show that the proposed regularizer significantly improves ranking-based algorithms and that the proposed framework outperforms the state-of-the-art OCCF algorithms.

scholarly journals Pseudoinverse graph convolutional networks

2021 ◽  
Author(s):  
Dominik Alfke ◽  
Martin Stoll
Keyword(s):  
Real World ◽  
Point Clouds ◽  
Graph Laplacian ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Convolutional Networks ◽  
3D Point Clouds ◽  
Non Local ◽  
Rank Approximation ◽  
Real World Datasets

AbstractGraph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Our examples include graphs generated from 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data of real-world problems. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our method overcomes these issues by utilizing the pseudoinverse of the Laplacian. Another key ingredient is a low-rank approximation of the convolutional matrix, ensuring computational efficiency and increasing accuracy at the same time. We outline how the necessary eigeninformation can be computed efficiently in each applications and discuss the appropriate choice of the only metaparameter, the approximation rank. We finally showcase our method’s performance regarding runtime and accuracy in various experiments with real-world datasets.

Improved MR image denoising via low- rank approximation and Laplacian-of-Gaussian edge detector

2020 ◽  
Vol 14 (12) ◽  
pp. 2791-2798
Author(s):  
Xiaoqun Qiu ◽  
Zhen Chen ◽  
Saifullah Adnan ◽  
Hongwei He
Keyword(s):  
Image Denoising ◽  
Low Rank ◽  
Edge Detector ◽  
Low Rank Approximation ◽  
Mr Image ◽  
Rank Approximation

scholarly journals Fast Joint Multiband Reconstruction From Wideband Images Based on Low-Rank Approximation

2020 ◽  
Vol 6 ◽  
pp. 922-933
Author(s):  
M. Amine Hadj-Youcef ◽  
Francois Orieux ◽  
Alain Abergel ◽  
Aurelia Fraysse
Keyword(s):  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation

scholarly journals Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product

2021 ◽  
Vol 11 (10) ◽  
pp. 4582
Author(s):  
Kensuke Tanioka ◽  
Satoru Hiwa
Keyword(s):  
Dimensional Reduction ◽  
Low Rank ◽  
Inner Product ◽  
Low Rank Approximation ◽  
Correlation Matrices ◽  
Rank Matrix ◽  
Clustering Approach ◽  
Rank Approximation ◽  
The Difference ◽  
Low Rank Matrix

In the domain of functional magnetic resonance imaging (fMRI) data analysis, given two correlation matrices between regions of interest (ROIs) for the same subject, it is important to reveal relatively large differences to ensure accurate interpretation. However, clustering results based only on differences tend to be unsatisfactory and interpreting the features tends to be difficult because the differences likely suffer from noise. Therefore, to overcome these problems, we propose a new approach for dimensional reduction clustering. Methods: Our proposed dimensional reduction clustering approach consists of low-rank approximation and a clustering algorithm. The low-rank matrix, which reflects the difference, is estimated from the inner product of the difference matrix, not only from the difference. In addition, the low-rank matrix is calculated based on the majorize–minimization (MM) algorithm such that the difference is bounded within the range −1 to 1. For the clustering process, ordinal k-means is applied to the estimated low-rank matrix, which emphasizes the clustering structure. Results: Numerical simulations show that, compared with other approaches that are based only on differences, the proposed method provides superior performance in recovering the true clustering structure. Moreover, as demonstrated through a real-data example of brain activity measured via fMRI during the performance of a working memory task, the proposed method can visually provide interpretable community structures consisting of well-known brain functional networks, which can be associated with the human working memory system. Conclusions: The proposed dimensional reduction clustering approach is a very useful tool for revealing and interpreting the differences between correlation matrices, even when the true differences tend to be relatively small.

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