Youngser Park

Scan Statistics on Enron Graphs

We introduce a theory of scan statistics on graphs and apply the ideas to the problem of anomaly detection in a time series of Enron email graphs.

The complete connectome of a learning and memory centre in an insect brain

Associating stimuli with positive or negative reinforcement is essential for survival, but a complete wiring diagram of a higher-order circuit supporting associative memory has not been previously available. Here we reconstruct one such circuit at synaptic resolution, the Drosophila larval mushroom body. We find that most Kenyon cells integrate random combinations of inputs but that a subset receives stereotyped inputs from single projection neurons. This organization maximizes performance of a model output neuron on a stimulus discrimination task. We also report a novel canonical circuit in each mushroom body compartment with previously unidentified connections: reciprocal Kenyon cell to modulatory neuron connections, modulatory neuron to output neuron connections, and a surprisingly high number of recurrent connections between Kenyon cells. Stereotyped connections found between output neurons could enhance the selection of learned behaviours. The complete circuit map of the mushroom body should guide future functional studies of this learning and memory centre.

Locality Statistics for Anomaly Detection in Time Series of Graphs

The ability to detect change-points in a dynamic network or a time series of graphs is an increasingly important task in many applications of the emerging discipline of graph signal processing. This paper formulates change-point detection as a hypothesis testing problem in terms of a generative latent position model, focusing on the special case of the Stochastic Block Model time series. We analyze two classes of scan statistics, based on distinct underlying locality statistics presented in the literature. Our main contribution is the derivation of the limiting properties and power characteristics of the competing scan statistics. Performance is compared theoretically, on synthetic data, and empirically, on the Enron email corpus.

Collaborative Computational Anatomy: An MRI Morphometry Study of the Human Brain Via Diffeomorphic Metric Mapping

This article describes a large multi‐institutional analysis of the shape and structure of the human hippocampus in the aging brain as measured via MRI. The study was conducted on a population of 101 subjects including nondemented control subjects (n = 57) and subjects clinically diagnosed with Alzheimers Disease (AD, n = 38) or semantic dementia (n = 6) with imaging data collected at Washington University in St. Louis, hippocampal structure annotated at the Massachusetts General Hospital, and anatomical shapes embedded into a metric shape space using large deformation diffeomorphic metric mapping (LDDMM) at the Johns Hopkins University. A global classifier was constructed for discriminating cohorts of nondemented and demented subjects based on linear discriminant analysis of dimensions derived from metric distances between anatomical shapes, demonstrating class conditional structure differences measured via LDDMM metric shape (P < 0.01). Localized analysis of the control and AD subjects only on the coordinates of the population template demonstrates shape changes in the subiculum and the CA1 subfield in AD (P < 0.05). Such large scale collaborative analysis of anatomical shapes has the potential to enhance the understanding of neurodevelopmental and neuropsychiatric disorders. Hum Brain Mapp, 2009.

Anomaly Detection in Time Series of Graphs using Fusion of Graph Invariants

Given a time series of graphs <i>G</i>(<i>t</i>)=(<i>V</i>,<i>E</i>(<i>t</i>)) , <i>t</i>=1,2,... , where the fixed vertex set <i>V</i> represents “actors” and an edge between vertex <i>u</i> and vertex <i>v</i> at time <i>t</i>(<i>uv</i> ∈ <i>E</i>(<i>t</i>)) represents the existence of a communications event between actors <i>u</i> and <i>v</i> during the <i>t</i>^th time period, we wish to detect anomalies and/or change points. We consider a collection of graph features, or invariants, and demonstrate that adaptive fusion provides superior inferential efficacy compared to naive equal weighting for a certain class of anomaly detection problems. Simulation results using a latent process model for time series of graphs, as well as illustrative experimental results for a time series of graphs derived from the Enron email data, show that a fusion statistic can provide superior inference compared to individual invariants alone. These results also demonstrate that an adaptive weighting scheme for fusion of invariants performs better than naive equal weighting.

Spectral clustering for divide-and-conquer graph matching

We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic block model random graphs are correctly matched utilizing very few seeds through our divide-and-conquer procedure. We also demonstrate the effectiveness of our approach in matching very large graphs in simulated and real data examples, showing up to a factor of 8 improvement in runtime with minimal sacrifice in accuracy.

Iterative Denoising for Cross-Corpus Discovery

We consider the problem of statistical pattern recognition in a heterogeneous, high-dimensional setting. In particular, we consider the search for meaningful cross-category associations in a heterogeneous text document corpus. Our approach involves “iterative denoising ” — that is, iteratively extracting (corpus-dependent) features and partitioning the document collection into sub-corpora. We present an anecdote wherein this methodology discovers a meaningful cross-category association in a heterogeneous collection of scientific documents.

Statistical inference on attributed random graphs: Fusion of graph features and content: An experiment on time series of Enron graphs

Fusion of information from graph features and content can provide superior inference for an anomaly detection task, compared to the corresponding content-only or graph feature-only statistics. In this paper, we design and execute an experiment on a time series of attributed graphs extracted from the Enron email corpus which demonstrates the benefit of fusion. The experiment is based on injecting a controlled anomaly into the real data and measuring its detectability.

Community Detection and Classification in Hierarchical Stochastic Blockmodels

In disciplines as diverse as social network analysis and neuroscience, many large graphs are believed to be composed of loosely connected smaller graph primitives, whose structure is more amenable to analysis We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and then cluster the vertices into communities. We next employ nonparametric graph inference techniques to identify structural similarity among these communities. These two steps are then applied recursively on the communities, allowing us to detect more fine-grained structure. We describe a hierarchical stochastic blockmodel—namely, a stochastic blockmodel with a natural hierarchical structure—and establish conditions under which our algorithm yields consistent estimates of model parameters and motifs, which we define to be stochastically similar groups of subgraphs. Finally, we demonstrate the effectiveness of our algorithm in both simulated and real data. Specifically, we address the problem of locating similar sub-communities in a partially reconstructed Drosophila connectome and in the social network Friendster.

Attribute Fusion in a Latent Process Model for Time Series of Graphs

Hypothesis testing on time series of attributed graphs has applications in diverse areas, e.g., social network analysis (wherein vertices represent individual actors or organizations), connectome inference (wherein vertices are neurons or brain regions) and text processing (wherein vertices represent authors or documents). We consider the problem of anomaly/change point detection given the latent process model for time series of graphs with categorical attributes on the edges presented in [N. H. Lee and C. E. Priebe, “A latent process model for time series of attributed random graphs,” Statist. Inference Stoch. Process., vol. 14, pp. 231–253, 2011]. Various attributed graph invariants are considered, and their power for detection as a function of a linear fusion parameter is presented. Our main result is that inferential performance in mathematically tractable first-order and second-order approximation models does provide guidance for methodological choices applicable to the exact (realistic but intractable) model. Furthermore, to the extent that the exact model is realistic, we may tentatively conclude that approximation model investigations have some bearing on real data applications.