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Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data analytics characterized by diverse variety, large volume, and high velocity. We characterize these advances from four perspectives: general tensor completion algorithms, tensor completion with auxiliary information (variety), scalable tensor completion algorithms (volume), and dynamic tensor completion algorithms (velocity). Further, we identify several tensor completion applications on real-world data-driven problems and present some common experimental frameworks popularized in the literature. Our goal is to summarize these popular methods and introduce them to researchers and practitioners for promoting future research and applications. We conclude with a discussion of key challenges and promising research directions in this community for future exploration.
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Delivering effective data analytics is of crucial importance to the interpretation of the multitude of biological datasets currently generated by an ever increasing number of high throughput techniques. Logic programming has much to offer in this area. Here, we detail advances that highlight two of the strengths of logical formalisms in developing data analytic solutions in biological settings: access to large relational databases and building analytical pipelines collecting graph information from multiple sources. We present significant advances on the bio_db package which serves biological databases as Prolog facts that can be served either by in-memory loading or via database backends. These advances include modularising the underlying architecture and the incorporation of datasets from a second organism (mouse). In addition, we introduce a number of data analytics tools that operate on these datasets and are bundled in the analysis package: bio_analytics. Emphasis in both packages is on ease of installation and use. We highlight the general architecture of our components based approach. An experimental graphical user interface via SWISH for local installation is also available. Finally, we advocate that biological data analytics is a fertile area which can drive further innovation in applied logic programming.
Big data benchmarking is particularly important and provides applicable yardsticks for evaluating booming big data systems. However, wide coverage and great complexity of big data computing impose big challenges on big data benchmarking. How can we construct a benchmark suite using a minimum set of units of computation to represent diversity of big data analytics workloads? Big data dwarfs are abstractions of extracting frequently appearing operations in big data computing. One dwarf represents one unit of computation, and big data workloads are decomposed into one or more dwarfs. Furthermore, dwarfs workloads rather than vast real workloads are more cost-efficient and representative to evaluate big data systems. In this paper, we extensively investigate six most important or emerging application domains i.e. search engine, social network, e-commerce, multimedia, bioinformatics and astronomy. After analyzing forty representative algorithms, we single out eight dwarfs workloads in big data analytics other than OLAP, which are linear algebra, sampling, logic operations, transform operations, set operations, graph operations, statistic operations and sort.
We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows that the number of samples required to approximately recover an order-$t$ tensor with at most $n$ entries per dimension is linear in $n$, under the assumption that the rank and order of the tensor are $O(1)$. As steps in our proof, we find a new expander mixing lemma for a $t$-partite, $t$-uniform regular hypergraph model, and prove several new properties about tensor max-quasinorm. To the best of our knowledge, this is the first deterministic analysis of tensor completion. We develop a practical algorithm that solves a relaxed version of the max-quasinorm minimization problem, and we demonstrate its efficacy with numerical experiments.
In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases where the columns are points on a low-dimensional nonlinear algebraic variety, a problem we call Low Algebraic Dimension Matrix Completion (LADMC). Matrices whose columns belong to a union of subspaces are an important special case. We propose a LADMC algorithm that leverages existing LRMC methods on a tensorized representation of the data. For example, a second-order tensorized representation is formed by taking the Kronecker product of each column with itself, and we consider higher order tensorizations as well. This approach will succeed in many cases where traditional LRMC is guaranteed to fail because the data are low-rank in the tensorized representation but not in the original representation. We provide a formal mathematical justification for the success of our method. In particular, we give bounds of the rank of these data in the tensorized representation, and we prove sampling requirements to guarantee uniqueness of the solution. We also provide experimental results showing that the new approach outperforms existing state-of-the-art methods for matrix completion under a union of subspaces model.
Next Generation Sequencing (NGS) technology has resulted in massive amounts of proteomics and genomics data. This data is of no use if it is not properly analyzed. ETL (Extraction, Transformation, Loading) is an important step in designing data analytics applications. ETL requires proper understanding of features of data. Data format plays a key role in understanding of data, representation of data, space required to store data, data I/O during processing of data, intermediate results of processing, in-memory analysis of data and overall time required to process data. Different data mining and machine learning algorithms require input data in specific types and formats. This paper explores the data formats used by different tools and algorithms and also presents modern data formats that are used on Big Data Platform. It will help researchers and developers in choosing appropriate data format to be used for a particular tool or algorithm.
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