scholarly journals Label Distribution Learning with Label Correlations via Low-Rank Approximation

2019 ◽  
Author(s):  
Tingting Ren ◽  
Xiuyi Jia ◽  
Weiwei Li ◽  
Shu Zhao
Keyword(s):  
Correlation Matrix ◽  
Learning Algorithm ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Real World Data ◽  
Label Correlations ◽  
Rank Approximation ◽  
Label Distribution Learning ◽  
Label Distribution ◽  
Label Correlation

Label distribution learning (LDL) can be viewed as the generalization of multi-label learning. This novel paradigm focuses on the relative importance of different labels to a particular instance. Most previous LDL methods either ignore the correlation among labels, or only exploit the label correlations in a global way. In this paper, we utilize both the global and local relevance among labels to provide more information for training model and propose a novel label distribution learning algorithm. In particular, a label correlation matrix based on low-rank approximation is applied to capture the global label correlations. In addition, the label correlation among local samples are adopted to modify the label correlation matrix. The experimental results on real-world data sets show that the proposed algorithm outperforms state-of-the-art LDL methods.

scholarly journals A Scalable Kernel-Based Semisupervised Metric Learning Algorithm with Out-of-Sample Generalization Ability

2008 ◽  
Vol 20 (11) ◽  
pp. 2839-2861 ◽  
Author(s):  
Dit-Yan Yeung ◽  
Hong Chang ◽  
Guang Dai
Keyword(s):  
Learning Algorithm ◽  
Metric Learning ◽  
Low Rank ◽  
Data Sets ◽  
Low Rank Approximation ◽  
Real World Data ◽  
Data Set ◽  
Out Of Sample ◽  
Rank Approximation ◽  
Kernel Approach

In recent years, metric learning in the semisupervised setting has aroused a lot of research interest. One type of semisupervised metric learning utilizes supervisory information in the form of pairwise similarity or dissimilarity constraints. However, most methods proposed so far are either limited to linear metric learning or unable to scale well with the data set size. In this letter, we propose a nonlinear metric learning method based on the kernel approach. By applying low-rank approximation to the kernel matrix, our method can handle significantly larger data sets. Moreover, our low-rank approximation scheme can naturally lead to out-of-sample generalization. Experiments performed on both artificial and real-world data show very promising results.

PLANC

2021 ◽  
Vol 47 (3) ◽  
pp. 1-37
Author(s):  
Srinivas Eswar ◽  
Koby Hayashi ◽  
Grey Ballard ◽  
Ramakrishnan Kannan ◽  
Michael A. Matheson ◽  
...  
Keyword(s):  
Sparse Matrices ◽  
Computation Time ◽  
Low Rank ◽  
Data Sets ◽  
Low Rank Approximation ◽  
Real World Data ◽  
Alternating Direction ◽  
Nonnegativity Constraints ◽  
Rank Approximation ◽  
Tensor Data

We consider the problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlenecks in both computation time and available memory. We propose a distributed-memory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes, and performing efficient and scalable parallel algorithms to compute the low-rank approximation. We present a software package called Parallel Low-rank Approximation with Nonnegativity Constraints, which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work). We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and real-world data sets.

scholarly journals Thresholding Approach for Low-Rank Correlation Matrix based on MM algorithm

2021 ◽  
Author(s):  
Kensuke Tanioka ◽  
Yuki Furotani ◽  
Satoru Hiwa
Keyword(s):  
Correlation Matrix ◽  
Rank Correlation ◽  
Low Rank ◽  
Threshold Values ◽  
Low Rank Approximation ◽  
Microarray Gene Expression ◽  
Sparse Estimation ◽  
Mm Algorithm ◽  
Novel Approach ◽  
Rank Approximation

Background: Low-rank approximation is a very useful approach for interpreting the features of a correlation matrix; however, a low-rank approximation may result in estimation far from zero even if the corresponding original value was far from zero. In this case, the results lead to misinterpretation. Methods: To overcome these problems, we propose a new approach to estimate a sparse low-rank correlation matrix based on threshold values combined with cross-validation. In the proposed approach, the MM algorithm was used to estimate the sparse low-rank correlation matrix, and a grid search was performed to select the threshold values related to sparse estimation. Results: Through numerical simulation, we found that the FPR and average relative error of the proposed method were superior to those of the tandem approach. For the application of microarray gene expression, the FPRs of the proposed approach with d=2,3, and 5 were 0.128, 0.139, and 0.197, respectively, while FPR of the tandem approach was 0.285. Conclusions: We propose a novel approach to estimate sparse low-rank correlation matrix. The advantage of the proposed method is that it provides results that are easy to interpret and avoid misunderstandings. We demonstrated the superiority of the proposed method through both numerical simulations and real examples.

scholarly journals Downlink channel estimation for millimeter wave communication combining low-rank and sparse structure characteristics

2020 ◽  
Author(s):  
Jin Zhou
Keyword(s):  
Channel Estimation ◽  
Millimeter Wave ◽  
Dictionary Learning ◽  
Mimo Systems ◽  
Learning Algorithm ◽  
Nuclear Norm ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Norm Theory ◽  
Rank Approximation

Abstract The acquisition of channel state information (CSI) is essential in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. The mmWave channel exhibits sparse scattering characteristics and a meaningful low-rank structure, which can be simultaneously employed to reduce the complexity of channel estimation. Most existing works recover the low-rank structure of channels using nuclear norm theory. However, solving the nuclear norm-based convex problem often leads to a suboptimal solution of the rank minimization problem, thus degrading the accuracy of channel estimation. Previous contributions recover the channel using over-complete dictionary with the assumption that the mmWave channel can be sparsely represented under some dictionary. While over-complete dictionary may increase the computational complexity. To address these problems, we propose a channel estimation framework based on non-convex low-rank approximation and dictionary learning by exploring the joint low-rank and sparse representations of wireless channels. We surrogate the widely used nuclear norm theory with non-convex low-rank approximation method and design a dictionary learning algorithm based on channel feature classification employing deep neural network (DNN). Our simulation results reveal the proposed scheme outperform the conventional dictionary learning algorithm, Bayesian framework algorithm, and compressed sensing-based algorithms.

scholarly journals Label distribution learning with label-specific features

2019 ◽  
Author(s):  
Tingting Ren ◽  
Xiuyi Jia ◽  
Weiwei Li ◽  
Lei Chen ◽  
Zechao Li
Keyword(s):  
Feature Space ◽  
Data Representation ◽  
Data Sets ◽  
Real World Data ◽  
Feature Selection Problem ◽  
Label Correlations ◽  
The Common ◽  
Label Distribution Learning ◽  
Class Labels ◽  
Label Distribution

Label distribution learning (LDL) is a novel machine learning paradigm to deal with label ambiguity issues by placing more emphasis on how relevant each label is to a particular instance. Many LDL algorithms have been proposed and most of them concentrate on the learning models, while few of them focus on the feature selection problem. All existing LDL models are built on a simple feature space in which all features are shared by all the class labels. However, this kind of traditional data representation strategy tends to select features that are distinguishable for all labels, but ignores label-specific features that are pertinent and discriminative for each class label. In this paper, we propose a novel LDL algorithm by leveraging label-specific features. The common features for all labels and specific features for each label are simultaneously learned to enhance the LDL model. Moreover, we also exploit the label correlations in the proposed LDL model. The experimental results on several real-world data sets validate the effectiveness of our method.

scholarly journals Label Enhancement with Sample Correlations via Low-Rank Representation

2020 ◽  
Vol 34 (04) ◽  
pp. 5932-5939
Author(s):  
Haoyu Tang ◽  
Jihua Zhu ◽  
Qinghai Zheng ◽  
Jun Wang ◽  
Shanmin Pang ◽  
...  
Keyword(s):  
Real World ◽  
State Of The Art ◽  
Low Rank ◽  
Real World Applications ◽  
Enhancement Method ◽  
Low Rank Representation ◽  
Label Distribution Learning ◽  
Representation Method ◽  
Label Distribution ◽  
Label Correlation

Compared with single-label and multi-label annotations, label distribution describes the instance by multiple labels with different intensities and accommodates to more-general conditions. Nevertheless, label distribution learning is unavailable in many real-world applications because most existing datasets merely provide logical labels. To handle this problem, a novel label enhancement method, Label Enhancement with Sample Correlations via low-rank representation, is proposed in this paper. Unlike most existing methods, a low-rank representation method is employed so as to capture the global relationships of samples and predict implicit label correlation to achieve label enhancement. Extensive experiments on 14 datasets demonstrate that the algorithm accomplishes state-of-the-art results as compared to previous label enhancement baselines.

scholarly journals Detection of core–periphery structure in networks using spectral methods and geodesic paths

2016 ◽  
Vol 27 (6) ◽  
pp. 846-887 ◽  
Author(s):  
MIHAI CUCURINGU ◽  
PUCK ROMBACH ◽  
SANG HOON LEE ◽  
MASON A. PORTER
Keyword(s):  
Goodness Of Fit ◽  
Low Rank ◽  
Data Sets ◽  
Computationally Efficient ◽  
Low Rank Approximation ◽  
Real World Data ◽  
Mesoscale Structure ◽  
Product Matrix ◽  
Geodesic Paths ◽  
Rank Approximation

We introduce several novel and computationally efficient methods for detecting “core–periphery structure” in networks. Core–periphery structure is a type of mesoscale structure that consists of densely connected core vertices and sparsely connected peripheral vertices. Core vertices tend to be well-connected both among themselves and to peripheral vertices, which tend not to be well-connected to other vertices. Our first method, which is based on transportation in networks, aggregates information from many geodesic paths in a network and yields a score for each vertex that reflects the likelihood that that vertex is a core vertex. Our second method is based on a low-rank approximation of a network's adjacency matrix, which we express as a perturbation of a tensor-product matrix. Our third approach uses the bottom eigenvector of the random-walk Laplacian to infer a coreness score and a classification into core and peripheral vertices. We also design an objective function to (1) help classify vertices into core or peripheral vertices and (2) provide a goodness-of-fit criterion for classifications into core versus peripheral vertices. To examine the performance of our methods, we apply our algorithms to both synthetically generated networks and a variety of networks constructed from real-world data sets.

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