When and Where: Predicting Human Movements Based on Social Spatial-Temporal Events

Predicting both the time and the location of human movements is valuable but challenging for a variety of applications. To address this problem, we propose an approach considering both the periodicity and the sociality of human movements. We first define a new concept, Social Spatial-Temporal Event (SSTE), to represent social interactions among people. For the time prediction, we characterise the temporal dynamics of SSTEs with an ARMA (AutoRegressive Moving Average) model. To dynamically capture the SSTE kinetics, we propose a Kalman Filter based learning algorithm to learn and incrementally update the ARMA model as a new observation becomes available. For the location prediction, we propose a ranking model where the periodicity and the sociality of human movements are simultaneously taken into consideration for improving the prediction accuracy. Extensive experiments conducted on real data sets validate our proposed approach

Online Spectral Clustering on Network Streams

Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirements certainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the parallelization of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be predetermined. The third challenge is the very limited existing work. In addition, there exists multiple limitations in the existing method, such as computational inefficiency on large similarity changes, the lack of sound theoretical basis, and the lack of effective way to handle accumulated approximate errors and large data variations over time. In this thesis, we proposed a new online spectral graph clustering approach with a family of three novel spectrum approximation algorithms. Our algorithms incrementally update the eigenpairs in an online manner to improve the computational performance. Our approaches outperformed the existing method in computational efficiency and scalability while retaining competitive or even better clustering accuracy. We derived our spectrum approximation techniques GEPT and EEPT through formal theoretical analysis. The well established matrix perturbation theory forms a solid theoretic foundation for our online clustering method. We facilitated our clustering method with a new metric to track accumulated approximation errors and measure the short-term temporal variation. The metric not only provides a balance between computational efficiency and clustering accuracy, but also offers a useful tool to adapt the online algorithm to the condition of unexpected drastic noise. In addition, we discussed our preliminary work on approximate graph mining with evolutionary process, non-stationary Bayesian Network structure learning from non-stationary time series data, and Bayesian Network structure learning with text priors imposed by non-parametric hierarchical topic modeling

Prediction of Emerging Technologies Based on Analysis of the U.S. Patent Citation Network

The network of patents connected by citations is an evolving graph, which provides a representation of the innovation process. A patent citing another implies that the cited patent reflects a piece of previously existing knowledge that the citing patent builds upon. A methodology presented here (i) identifies actual clusters of patents: i.e. technological branches, and (ii) gives predictions about the temporal changes of the structure of the clusters. A predictor, called the {citation vector}, is defined for characterizing technological development to show how a patent cited by other patents belongs to various industrial fields. The clustering technique adopted is able to detect the new emerging recombinations, and predicts emerging new technology clusters. The predictive ability of our new method is illustrated on the example of USPTO subcategory 11, Agriculture, Food, Textiles. A cluster of patents is determined based on citation data up to 1991, which shows significant overlap of the class 442 formed at the beginning of 1997. These new tools of predictive analytics could support policy decision making processes in science and technology, and help formulate recommendations for action

Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization