Incremental eigenpair computation for graph Laplacian matrices: theory and applications

The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications, the number of clusters or communities (say, K) is generally unknown a priori. Consequently, the majority of the existing methods either choose K heuristically or they repeat the clustering method with different choices of K and accept the best clustering result. The first option, more often, yields suboptimal result, while the second option is computationally expensive. In this work, we propose an incremental method for constructing the eigenspectrum of the graph Laplacian matrix. This method leverages the eigenstructure of graph Laplacian matrix to obtain the Kth smallest eigenpair of the Laplacian matrix given a collection of all previously compute

Data mining: a tool for detecting cyclical disturbances in supply networks.

Disturbances in supply chains may be either exogenous or endogenous. The ability automatically to detect, diagnose, and distinguish between the causes of disturbances is of prime importance to decision makers in order to avoid uncertainty. The spectral principal component analysis (SPCA) technique has been utilized to distinguish between real and rogue disturbances in a steel supply network. The data set used was collected from four different business units in the network and consists of 43 variables; each is described by 72 data points. The present paper will utilize the same data set to test an alternative approach to SPCA in detecting the disturbances. The new approach employs statistical data pre-processing, clustering, and classification learning techniques to analyse the supply network data. In particular, the incremental k-means clustering and the RULES-6 classification rule-learning algorithms, developed by the present authors’ team, have been applied to identify important patterns in the data set. Results show that the proposed approach has the capability automatically to detect and characterize network-wide cyclical disturbances and generate hypotheses about their root cause

Graph Summarization

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is graph summarization. It denotes a series of application-specific algorithms designed to transform graphs into more compact representations while preserving structural patterns, query answers, or specific property distributions. As this problem is common to several areas studying graph topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily based on statistical and optimization methods. The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie

Online Unsupervised Multi-view Feature Selection

In the era of big data, it is becoming common to have data with multiple modalities or coming from multiple sources, known as "multi-view data". Multi-view data are usually unlabeled and come from high-dimensional spaces (such as language vocabularies), unsupervised multi-view feature selection is crucial to many applications. However, it is nontrivial due to the following challenges. First, there are too many instances or the feature dimensionality is too large. Thus, the data may not fit in memory. How to select useful features with limited memory space? Second, how to select features from streaming data and handles the concept drift? Third, how to leverage the consistent and complementary information from different views to improve the feature selection in the situation when the data are too big or come in as streams? To the best of our knowledge, none of the previous works can solve all the challenges simultaneously. In this paper, we propose an Online unsupervised Multi-View Feature Selection, OMVFS, which deals with large-scale/streaming multi-view data in an online fashion. OMVFS embeds unsupervised feature selection into a clustering algorithm via NMF with sparse learning. It further incorporates the graph regularization to preserve the local structure information and help select discriminative features. Instead of storing all the historical data, OMVFS processes the multi-view data chunk by chunk and aggregates all the necessary information into several small matrices. By using the buffering technique, the proposed OMVFS can reduce the computational and storage cost while taking advantage of the structure information. Furthermore, OMVFS can capture the concept drifts in the data streams. Extensive experiments on four real-world datasets show the effectiveness and efficiency of the proposed OMVFS method. More importantly, OMVFS is about 100 times faster than the off-line methods