In the era of big data, there are increasing demands to forecast incomplete, sparse, and nonstationary data. The current research aims to solve these problems for multilinear time series through a combination of tensor autoregression and low-rank tensor factorization. We propose an expansion of TMF to second-order data: temporal tensor factorization (TTF). The current research aims to interpolate missing values via low-rank tensor factorization, which produces a latent time series. We perform forecasting in the latent space with a transform-based tensor autoregression ($\mathcal{L}$-TAR) process. We present experimental results of the proposed method with other state-of-the-art methods on the benchmark datasets which include video imaging, dynamic networks, and energy usage.

In the era of big data, there is massive demand for new techniques to forecast and analyze multi-dimensional data. One task that has seen great interest in the community is anomaly detection of streaming data. Toward this end, the current research develops a novel approach to anomaly detection of streaming 2-dimensional observations via multilinear time-series analysis and 3-dimensional tensor principal component analysis (3DTPCA). We approach this problem utilizing dimensionality reduction and probabilistic inference in a low-dimensional space. We first propose a natural extension to 2-dimensional tensor principal component analysis (2DTPCA) to perform data dimensionality reduction on 4-dimensional tensor objects, aptly named 3DTPCA. We then represent the sub-sequences of our time-series observations as a 4-dimensional tensor utilizing a sliding window. Finally, we use 3DTPCA to compute reconstruction errors for inferring anomalous instances within the multilinear data stream. Experimental validation is presented via MovingMNIST data. Results illustrate that the proposed approach has a significant speedup in training time compared with deep learning, while performing competitively in terms of accuracy.

In this paper we consider the problem of analyzing streaming documents, in particular streaming news stories. The system is designed to extract statistics from the document, incorporate these into a graph-based model, and discard the document to reduce storage requirements. The model is defined in terms of a changing lexicon and sub-lexicons at each node in the graph, with the nodes of the graph representing topics. An approximation to the TFIDF term weighting is introduced. We illustrate the methodology on a dataset of news articles, and discuss the dynamic nature of the model

We introduce a methodology for adaptive sequential sensing and processing in a classification setting. Our objective for sensor optimization is the back-end performance metric--in this case, misclassification rate. Our methodology, which we dub Integrated Sensing and Processing Decision Trees (ISPDT), optimizes adaptive sequential sensing for scenarios in which sensor and/or throughput constraints dictate that only a small subset of all measurable attributes can be measured at any one time. Our decision trees optimize misclassification rate by invoking a local dimensionality reduction-based partitioning metric in the early stages, focusing on classification only in the leaves of the tree. We present the ISPDT methodology and illustrative theoretical, simulation, and experimental results.

Details work in our group on the use of low-level features for the identification of man-made regions in unmanned aerial vehicle (UAV) imagery. The feature sets that we have examined include classical statistical features such as the coefficient of variation in a window about a pixel, locally computed fractal dimension, and fractal dimension computed in the presence of wavelet boundaries. We discuss these techniques of feature extraction along with our approach to the classification of the features. Our classification work has focused on the use of a semiparametric probability density estimation technique. In addition, we present classification results for region of interest identification based on a set of test images from an UAV test flight.

In many applications, spatial observations must be segmented into homogeneous regions and the number, positions, and shapes of the regions are unknown a priori. Information about the underlying probability distributions are often unknown. Furthermore, the anticipated regions of interest may be small with few observations from the individual regions. This paper presents a technique designed to address these difficulties. A simple segmentation procedure can be obtained as a clustering of the disjoint subregions obtained through an initial low-level partitioning procedure. Clustering of these subregions based upon a similarity matrix derived from estimates of their marginal probability density functions yields the resultant segmentation. It is shown that this segmentation is improved through the use of a "borrowed strength" density estimation procedure wherein potential similarities between the density functions for the subregions are exploited. The borrowed strength technique is described and the performance of segmentation based on these estimates is investigated through an example from statistical image analysis.

A fundamental problem of automating the detection and recognition of abnormalities in digital mammograms utilizing computational statistics is one of extracting the appropriate features for use in a classification system. Several feature sets have been proposed although none have been shown to be sufficient for the problem. Many of these features tend to be local in nature, which means their calculation requires a connected region of the image over which an average or other statistic is extracted. The implicit assumption is that the region is homogeneous, but this is rarely the case if a fixed window is used for the calculation. We consider a method of using boundaries to segment the window into more homogeneous regions for use in the feature extraction calculation. This approach is applied to the problem of discriminating between tumor and healthy tissue in digital mammography. A set of 21 images, each containing a biopsied mass, is described. The results of the boundary-gated feature...

This paper examines techniques for the efficient use of high dimensional feature sets in the detection of micro-calcifications in mammograms. The paper focuses on techniques for dimensionality reduction and discriminant analysis. The paper examines the use of principal components and Fisher's linear discriminant for dimensionality reduction along with parametric and nonparametric statistical techniques for discriminant analysis.>