An overview of kernel based nonnegative matrix factorization

Duong, Viet Hang; Hsieh, Wan-Hsin; Wang, Jia Ching

doi:10.1109/icot.2014.6956641

Cited by 4 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Buciu et al ( 2008 ) introduced a polynomial NMF with the help of the non-linear polynomial kernel mapping contributing to the correlation of the high-order of basis image features. The kernel-based NMF can improve representations produced by NMF with the kernel mapping (Duong et al, 2014 ). Those methods fit the non-linear relation between data by kernels.…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

A Deep Non-negative Matrix Factorization Model for Big Data Representation Learning

et al. 2021

View full text Add to dashboard Cite

Nowadays, deep representations have been attracting much attention owing to the great performance in various tasks. However, the interpretability of deep representations poses a vast challenge on real-world applications. To alleviate the challenge, a deep matrix factorization method with non-negative constraints is proposed to learn deep part-based representations of interpretability for big data in this paper. Specifically, a deep architecture with a supervisor network suppressing noise in data and a student network learning deep representations of interpretability is designed, which is an end-to-end framework for pattern mining. Furthermore, to train the deep matrix factorization architecture, an interpretability loss is defined, including a symmetric loss, an apposition loss, and a non-negative constraint loss, which can ensure the knowledge transfer from the supervisor network to the student network, enhancing the robustness of deep representations. Finally, extensive experimental results on two benchmark datasets demonstrate the superiority of the deep matrix factorization method.

show abstract

Section: Preliminaries and Related Workmentioning

confidence: 99%

A Deep Non-negative Matrix Factorization Model for Big Data Representation Learning

et al. 2021

View full text Add to dashboard Cite

show abstract

“…To minimize the overall loss function (13) with matrices and fixed, we need the derivatives of the function with respect to . The derivatives with respect to each parameter in are,…”

Section: Proposed Methodsmentioning

confidence: 99%

“…Based on the non-linear transformation , the adapted loss function for PNMF (6) is defined as, (12) We take a weighted combination of the transformed PNMF error function and the cross-entropy function to form our overall loss function for the network, (13) Once the network has been trained layerwise to learn a suitable mapping based on minimizing only the reconstruction error, we fine-tune the overall network and update the matrices and to minimize the overall loss function (13) and get the desired factorization.…”

Section: Proposed Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Deep Probabilistic NMF Using Denoising Autoencoders

Bhattamishra¹

2018

IJMLC

View full text Add to dashboard Cite

Abstract-Non Negative Matrix Factorization (NMF) has received considerable attention due to its application in pattern recognition and computer vision. However, the algorithm is sensitive to noise and assumes that the signals in the data can be linearly reconstructed. In this paper, we propose a robust non-linear probabilistic model and develop its optimization algorithm. The proposed model reduces the data to a lower dimensional manifold to get a more meaningful representation and takes into account the noisy nature of the data to improve the clustering performance of NMF. Additionally, our empirical study validates the effectiveness of the proposed method on some benchmark datasets.

show abstract

“…Despite the versatility and wide range of applications of these methods, both NMF and jNMF are linear models, where the data observed are decomposed in linear combinations of columns of W and rows of H. However, in many cases, it is expected that the relations between basis vectors are non-linear given the nature of the data [9], [10]. A possible approach to find these relations is to map the observations (x i ) into a higher dimensional space where more meaningful associations may be found.…”

Section: Introductionmentioning

confidence: 99%

Kernel Joint Non-Negative Matrix Factorization for Genomic Data

et al. 2021

View full text Add to dashboard Cite

The multi-modal or multi-view integration of data has generated a wide range of applicability in pattern extraction, clustering, and data interpretation. Recently, variants of the Non-negative Matrix Factorization (NMF) such as joint NMF (jNMF) have allowed not only to integrate data from different sources but also have facilitated the incorporation of prior knowledge such as the interactions between variables from different sources. However, in both NMF and jNMF the factorization is carried out as a linear system, which does not identify non-linear patterns that are present in most real-world data. Therefore, we propose a new variant of jNMF called Kernel jNMF. This new method incorporates the factorization of the original matrices into a high-dimensional space. Applying our method on synthetic data and biological cancer data, we found that the method performed better in clustering and interpretation compared to the jNMF methods.INDEX TERMS Data integration, kernel, joint matrix factorization, cancer.

show abstract

An overview of kernel based nonnegative matrix factorization

Cited by 4 publications

References 16 publications

A Deep Non-negative Matrix Factorization Model for Big Data Representation Learning

A Deep Non-negative Matrix Factorization Model for Big Data Representation Learning

Deep Probabilistic NMF Using Denoising Autoencoders

Kernel Joint Non-Negative Matrix Factorization for Genomic Data

Contact Info

Product

Resources

About