The City of Detroit maintains an active fleet of over 2500 vehicles, spending an annual average of over @math 7.7 million on maintaining this fleet. Understanding the existence of patterns and trends in this data could be useful to a variety of stakeholders, particularly as Detroit emerges from Chapter 9 bankruptcy, but the patterns in such data are often complex and multivariate and the city lacks dedicated resources for detailed analysis of this data. This work, a data collaboration between the Michigan Data Science Team (this http URL) and the City of Detroit's Operations and Infrastructure Group, seeks to address this unmet need by analyzing data from the City of Detroit's entire vehicle fleet from 2010-2017. We utilize tensor decomposition techniques to discover and visualize unique temporal patterns in vehicle maintenance; apply differential sequence mining to demonstrate the existence of common and statistically unique maintenance sequences by vehicle make and model; and, after showing these time-dependencies in the dataset, demonstrate an application of a predictive Long Short Term Memory (LSTM) neural network model to predict maintenance sequences. Our analysis shows both the complexities of municipal vehicle fleet data and useful techniques for mining and modeling such data.
For a more detailed overview of tensor decompositions, their mechanics, and their applications, we refer the interested reader to @cite_11 . We describe the decompositions that are relevant to our data analysis in .
@cite_11
1429947488 2528907418 2768445292 2962881496
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most existing approaches are not designed to meet the major challenges posed by big data analytics. This paper attempts to improve the scalability of tensor decompositions and provides two contributions: A flexible and fast algorithm for the CP decomposition (FFCP) of tensors based on their Tucker compression; A distributed randomized Tucker decomposition approach for arbitrarily big tensors but with relatively low multilinear rank. These two algorithms can deal with huge tensors, even if they are dense. Extensive simulations provide empirical evidence of the validity and efficiency of the proposed algorithms. Tensors and tensor decompositions are very powerful and versatile tools that can model a wide variety of heterogeneous, multiaspect data. As a result, tensor decompositions, which extract useful latent information out of multiaspect data tensors, have witnessed increasing popularity and adoption by the data mining community. In this survey, we present some of the most widely used tensor decompositions, providing the key insights behind them, and summarizing them from a practitioner’s point of view. We then provide an overview of a very broad spectrum of applications where tensors have been instrumental in achieving state-of-the-art performance, ranging from social network analysis to brain data analysis, and from web mining to healthcare. Subsequently, we present recent algorithmic advances in scaling tensor decompositions up to today’s big data, outlining the existing systems and summarizing the key ideas behind them. Finally, we conclude with a list of challenges and open problems that outline exciting future research directions. Abstract Tensor decomposition, the higher-order analogue to singular value decomposition, has emerged as a useful tool for finding relationships in large, sparse, multidimensional data. As this technique matures and is applied to increasingly larger data sets, the need for high performance implementations becomes critical. A better understanding of the performance characteristics of tensor decomposition on large and sparse tensors can help drive the development of such implementations. In this work, we perform an objective empirical evaluation of three state of the art parallel tools that implement the Canonical Decomposition Parallel Factorization tensor decomposition algorithm using alternating least squares fitting (CP-ALS): SPLATT, DFacTo, and ENSIGN. We conduct performance studies across a variety of data sets and evaluate the tools with respect to total memory required, processor stall cycles, execution time, data distribution, and communication patterns. Furthermore, we investigate the performance of the implementations on tensors with up to 6 dimensions and when executing high rank decompositions. We find that tensor data structure layout and distribution choices can result in differences as large as 14.6x with respect to memory usage and 39.17x with respect to execution time. We provide an outline of a distributed heterogeneous CP-ALS implementation that addresses the performance issues we observe. Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of statistical theory and of scalable algorithms. In this paper, we address the limitations. First, we introduce a convex relaxation of the TT decomposition problem and derive its error bound for the tensor completion task. Next, we develop a randomized optimization method, in which the time complexity is as efficient as the space complexity is. In experiments, we numerically confirm the derived bounds and empirically demonstrate the performance of our method with a real higher-order tensor.