Related papers: Matrix Factorization at Scale: a Comparison of Sci…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
Tomographic imaging has benefited from advances in X-ray sources, detectors and optics to enable novel observations in science, engineering and medicine. These advances have come with a dramatic increase of input data in the form of faster…
Big data analytics requires high programmer productivity and high performance simultaneously on large-scale clusters. However, current big data analytics frameworks (e.g. Apache Spark) have prohibitive runtime overheads since they are…
Distributed dataflow systems like Spark and Flink enable data-parallel processing of large datasets on clusters. Yet, selecting appropriate computational resources for dataflow jobs is often challenging. For efficient execution, individual…
In the big data era, the key feature that each algorithm needs to have is the possibility of efficiently running in parallel in a distributed environment. The popular Silhouette metric to evaluate the quality of a clustering, unfortunately,…
Distributed dataflow systems such as Apache Spark or Apache Flink enable parallel, in-memory data processing on large clusters of commodity hardware. Consequently, the appropriate amount of memory to allocate to the cluster is a crucial…
Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…
The current trend of multicore architectures on shared memory systems underscores the need of parallelism. While there are some programming model to express parallelism, thread programming model has become a standard to support these system…
Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…
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 $A \approx W H$. NMF is a useful tool for many applications in different domains…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be…
Non-negative matrix factorization (NMF) is widely used for dimensionality reduction and interpretable analysis, but standard formulations are unsupervised and cannot directly exploit class labels. Existing supervised or semi-supervised…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
With the explosive increase of big data in industry and academic fields, it is necessary to apply large-scale data processing systems to analysis Big Data. Arguably, Spark is state of the art in large-scale data computing systems nowadays,…
The well-known K-means clustering algorithm has been employed widely in different application domains ranging from data analytics to logistics applications. However, the K-means algorithm can be affected by factors such as the initial…
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable…
A QR factorization of a tall and skinny matrix with n columns can be represented as a reduction. The operation used along the reduction tree has in input two n-by-n upper triangular matrices and in output an n-by-n upper triangular matrix…
As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only…