# A high-performance parallel algorithm for nonnegative matrix factorization

@article{Kannan2016AHP, title={A high-performance parallel algorithm for nonnegative matrix factorization}, author={Ramakrishnan Kannan and Grey Ballard and Haesun Park}, journal={Proceedings of the 21st ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming}, year={2016} }

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A ≈ WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We…

## 57 Citations

### Partitioning and Communication Strategies for Sparse Non-negative Matrix Factorization

- Computer ScienceICPP
- 2018

This paper focuses on scaling algorithms for NMF to very large sparse datasets and massively parallel machines by employing effective algorithms, communication patterns, and partitioning schemes that leverage the sparsity of the input matrix.

### An Efficient Algorithm for Non-Negative Matrix Factorization with Random Projections

- Computer ScienceArXiv
- 2017

This work applies a random compression scheme to drastically reduce the dimensionality of the problem, preserving well the pairwise distances between data points and inherently limiting the memory and communication load.

### DSANLS: Accelerating Distributed Nonnegative Matrix Factorization via Sketching

- Computer ScienceWSDM
- 2018

This paper proposes a distributed sketched alternating nonnegative least squares (DSANLS) framework for NMF, which utilizes a matrix sketching technique to reduce the size of non negative least squares subproblems in each iteration for U and V.

### PL-NMF: Parallel Locality-Optimized Non-negative Matrix Factorization

- Computer ScienceArXiv
- 2019

A parallel NMF algorithm based on the HALS (Hierarchical Alternating Least Squares) scheme that incorporates algorithmic transformations to enhance data locality is devised, demonstrating significant performance improvement over existing state-of-the-art parallelNMF algorithms.

### ALO-NMF: Accelerated Locality-Optimized Non-negative Matrix Factorization

- Computer ScienceKDD
- 2020

A novel optimization method for parallel NMF algorithm based on the HALS (Hierarchical Alternating Least Squares) scheme that incorporates algorithmic transformations to enhance data locality is presented, demonstrating a new Accelerated Locality-Optimized NMF (ALO-NMF).

### Parallel Hierarchical Clustering using Rank-Two Nonnegative Matrix Factorization

- Computer Science2020 IEEE 27th International Conference on High Performance Computing, Data, and Analytics (HiPC)
- 2020

A parallel algorithm for hierarchical clustering that uses a divide-and-conquer approach based on rank-two NMF to split a data set into two cohesive parts, finding more structure in the data than a flat NMF clustering.

### GPU-accelerated Large-Scale Non-negative Matrix Factorization Using Spark

- Computer ScienceCollaborateCom
- 2018

A parallel algorithm based on GPU for NMF in Spark platform is proposed, which makes full use of the advantages of in-memory computation mode and GPU Single-Instruction Multiple-data Streams mode and can effectively deal with the non-negative decomposition of higher-order matrices, which greatly improves the computational efficiency.

### Parallelization of the Hierarchical Alternating Least Squares Algorithm for Nonnegative Matrix Factorization

- Computer Science2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI)
- 2018

It is shown that a parallelization strategy similar to ANLS parallelizations exists and yields good speedups for up to 64 processes and satisfactory beyond and are competitive in comparison to previous solutions to the NMF problem.

### High Performance Parallel Algorithms for Tensor Decompositions

- Computer Science
- 2017

The main focus of this thesis is on efficient decomposition of high dimensional sparse tensors, with hundreds of millions to billions of nonzero entries, which arise in many emerging big data applications and introduces a tree-based computational scheme that carries out expensive operations faster by factoring out and storing common partial results and effectivelyre-using them.

### PLANC: Parallel Low Rank Approximation with Non-negativity Constraints

- Computer ScienceACM Trans. Math. Softw.
- 2021

This work proposes 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.

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