Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this article, we aim to bridge this gap by proposing a new dynamic tensor clustering method, which takes into account both sparsity and fusion structures, and enjoys strong statistical guarantees as well as high computational efficiency. Our proposal is based upon a new structured tensor factorization that encourages both sparsity and smoothness in parameters along the specified tensor modes. Computationally, we develop a highly efficient optimization algorithm that benefits from substantial dimension reduction. In theory, we first establish a non-asymptotic error bound for the estimator from the structured tensor factorization. Built upon this error bound, we then derive the rate of convergence of the estimated cluster centers, and show that the estimated clusters recover the true cluster structures with a high probability. Moreover, our proposed method can be naturally extended to co-clustering of multiple modes of the tensor data. The efficacy of our approach is illustrated via simulations and a brain dynamic functional connectivity analysis from an Autism spectrum disorder study.

We present a new method of generating mixture models for data with categorical attributes. The keys to this approach are an entropy-based density metric in categorical space and annealing of high-entropy/low-density components from an initial state with many components. Pruning of low-density components using the entropy-based density allows GALILEO to consistently find high-quality clusters and the same optimal number of clusters. GALILEO has shown promising results on a range of test datasets commonly used for categorical clustering benchmarks. We demonstrate that the scaling of GALILEO is linear in the number of records in the dataset, making this method suitable for very large categorical datasets.

This paper considers applications of trajectory data in transportation, and makes two primary contributions. First, it provides a comprehensive literature review detailing ways in which trajectory data has been used for transportation systems analysis, distilling existing research into the following six areas: demand estimation, modeling human behavior, designing public transit, measuring and predicting traffic performance, quantifying environmental impact, and safety analysis. Additionally, it presents innovative applications of trajectory data for the state of Maryland, employing visualization and machine learning techniques to extract value from 20 million GPS traces. These visual analytics will be implemented in the Regional Integrated Transportation Information System (RITIS), which provides free data sharing and visual analytics tools to help transportation agencies attain situational awareness, evaluate performance, and share insights with the public.

The act of clustering, or spotting patterns in data, is not much different from spotting patterns in groups of people. Before jumping into action, we'll begin by taking an in-depth look at exactly what clustering entails. Clustering is an unsupervised machine learning task that automatically divides the data into clusters, or groups of similar items. It does this without having been told how the groups should look ahead of time. As we may not even know what we're looking for, clustering is used for knowledge discovery rather than prediction. It provides an insight into the natural groupings found within data.

Machine Learning (ML) has some hefty gravitational force in the Software development world at the moment. But what exactly is it? In this post I'll take a top-down approach attempting to make it crystal clear, what it is, and what it can be used for in the real world. Machine Learning is a branch of Artificial Intelligence. Fundamentally it is Software that works like our brain, learning from information (data), then applying it to make smart decisions. Machine Learning algorithms can improve software (a robot) and it's ability to solve problems through gaining experience.

Machine learning is perhaps the principal technology behind two emerging domains: data science and artificial intelligence. The rise of machine learning is coming about through the availability of data and computation, but machine learning methdologies are fundamentally dependent on models. The emergence of machine learning is closely tied to the emergence of widely available data. Large amounts of data and high interconnection bandwidth mean that we receive much of our information about the world around us through computers. Economists try to measure productivity, one of the ways we can become more productive is by becoming more efficient. For example, moving from gathering food to settled agriculture. In the modern era one approach to becoming more efficient is automation of processes like manufacturing production lines. The manufacturing process is decomposed into a series of mechanical or manual processes each of which is applied sequentially. Manufacturing processes consist of production lines and robotic automation. Logistics can also be decomposed into the supply chain processes. Whether it's manufacturing or logistics, efficiency can be improved by automating components of the processes to improve the flow of goods. An interesting challenge for modern society is the management of both the flow of goods and the flow of information. The flow of information is also highly automated. Processing of data is decomposed into stages in computer code. In these processing pipelines, manufacturing, logistics or data management, the overall pipeline normally also requires human intervention from an operator. These interventions can create bottlenecks and slow the process of automation. Machine learning is the key technology in automating these manual stages. The human interventions that were easy to replicate with technology have already been replaced. The components that still require human intervention are the knottier problems. Often they represent components that are difficult, or impossible, to decompose into stages which could then be further automated. In that sense these components are process-atoms. In manufacturing or logistics settings these atoms involve the sort of flexible manual skills that we cannot replicate with current robotic technology.

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is demonstrated to efficiently solve eigenvalue problems for graph Laplacians that appear in spectral clustering. For static graph partitioning, 10-20 iterations of LOBPCG without preconditioning result in ~10x error reduction, enough to achieve 100% correctness for all Challenge datasets with known truth partitions, e.g., for graphs with 5K/.1M (50K/1M) Vertices/Edges in 2 (7) seconds, compared to over 5,000 (30,000) seconds needed by the baseline Python code. Our Python code 100% correctly determines 98 (160) clusters from the Challenge static graphs with 0.5M (2M) vertices in 270 (1,700) seconds using 10GB (50GB) of memory. Our single-precision MATLAB code calculates the same clusters at half time and memory. For streaming graph partitioning, LOBPCG is initiated with approximate eigenvectors of the graph Laplacian already computed for the previous graph, in many cases reducing 2-3 times the number of required LOBPCG iterations, compared to the static case. Our spectral clustering is generic, i.e. assuming nothing specific of the block model or streaming, used to generate the graphs for the Challenge, in contrast to the base code. Nevertheless, in 10-stage streaming comparison with the base code for the 5K graph, the quality of our clusters is similar or better starting at stage 4 (7) for emerging edging (snowballing) streaming, while the computations are over 100-1000 faster.

These days we hear about machine learning and artificial intelligence (AI) in all aspects of life. We see machines that learn and imitate the human brain in order to automate human processes. There are autonomous cars that learn the road conditions to drive, personal assistants we can converse with and machines that can predict what stock markets will do. In some respects, it can appear as "magic." Behind machine learning there are some fundamental, well-studied and understood techniques.

We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the given order of the features is arbitrary and does not convey a notion of locality. Therefore, traditional transforms and metrics cannot be used for data organization and analysis. In this paper, our goal is to organize the data by defining an appropriate representation and metric such that they respect the smoothness and structure underlying the data. We also aim to generalize the joint clustering of observations and features in the case the data does not fall into clear disjoint groups. For this purpose, we propose multiscale data-driven transforms and metrics based on trees. Their construction is implemented in an iterative refinement procedure that exploits the co-dependencies between features and observations. Beyond the organization of a single dataset, our approach enables us to transfer the organization learned from one dataset to another and to integrate several datasets together. We present an application to breast cancer gene expression analysis: learning metrics on the genes to cluster the tumor samples into cancer sub-types and validating the joint organization of both the genes and the samples. We demonstrate that using our approach to combine information from multiple gene expression cohorts, acquired by different profiling technologies, improves the clustering of tumor samples.

In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a single clustering. The main advantage of these algorithms is that they bring down significantly the computational cost of traditional algorithms, including spectral clustering, semi-definite programs, modularity based methods, likelihood based methods etc., without losing on accuracy and even improving accuracy at times. These algorithms are also, by nature, parallelizable. Thus, exploiting the facts that most traditional algorithms are accurate and the corresponding optimization problems are much simpler in small problems, our divide-and-conquer methods provide an omnibus recipe for scaling traditional algorithms up to large networks. We prove consistency of these algorithms under various subgraph selection procedures and perform extensive simulations and real-data analysis to understand the advantages of the divide-and-conquer approach in various settings.