Two to Five Truths in Non-Negative Matrix Factorization

In this paper, we explore the role of matrix scaling on a matrix of counts when building a topic model using non-negative matrix factorization. We present a scaling inspired by the normalized Laplacian (NL) for graphs that can greatly improve the quality of a non-negative matrix factorization. The results parallel those in the spectral graph clustering work of \cite{Priebe:2019}, where the authors proved adjacency spectral embedding (ASE) spectral clustering was more likely to discover core-periphery partitions and Laplacian Spectral Embedding (LSE) was more likely to discover affinity partitions. In text analysis non-negative matrix factorization (NMF) is typically used on a matrix of co-occurrence ``contexts'' and ``terms" counts. The matrix scaling inspired by LSE gives significant improvement for text topic models in a variety of datasets. We illustrate the dramatic difference a matrix scalings in NMF can greatly improve the quality of a topic model on three datasets where human annotation is available. Using the adjusted Rand index (ARI), a measure cluster similarity we see an increase of 50\% for Twitter data and over 200\% for a newsgroup dataset versus using counts, which is the analogue of ASE. For clean data, such as those from the Document Understanding Conference, NL gives over 40\% improvement over ASE. We conclude with some analysis of this phenomenon and some connections of this scaling with other matrix scaling methods

Name Disambiguation from link data in a collaboration graph using temporal and topological features

In a social community, multiple persons may share the same name, phone number or some other identifying attributes. This, along with other phenomena, such as name abbreviation, name misspelling, and human error leads to erroneous aggregation of records of multiple persons under a single reference. Such mistakes affect the performance of document retrieval, web search, database integration, and more importantly, improper attribution of credit (or blame). The task of entity disambiguation partitions the records belonging to multiple persons with the objective that each decomposed partition is composed of records of a unique person. Existing solutions to this task use either biographical attributes, or auxiliary features that are collected from external sources, such as Wikipedia. However, for many scenarios, such auxiliary features are not available, or they are costly to obtain. Besides, the attempt of collecting biographical or external data sustains the risk of privacy violation. In this work, we propose a method for solving entity disambiguation task from link information obtained from a collaboration network. Our method is non-intrusive of privacy as it uses only the time-stamped graph topology of an anonymized network. Experimental results on two real-life academic collaboration networks show that the proposed method has satisfactory performance.Comment: The short version of this paper has been accepted to ASONAM 201

Communities in Networks

We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems. As a running theme, we emphasize the connections of community detection to problems in statistical physics and computational optimization.Comment: survey/review article on community structure in networks; published version is available at http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd

Edge-Parallel Graph Encoder Embedding

New algorithms for embedding graphs have reduced the asymptotic complexity of finding low-dimensional representations. One-Hot Graph Encoder Embedding (GEE) uses a single, linear pass over edges and produces an embedding that converges asymptotically to the spectral embedding. The scaling and performance benefits of this approach have been limited by a serial implementation in an interpreted language. We refactor GEE into a parallel program in the Ligra graph engine that maps functions over the edges of the graph and uses lock-free atomic instrutions to prevent data races. On a graph with 1.8B edges, this results in a 500 times speedup over the original implementation and a 17 times speedup over a just-in-time compiled version.Comment: 4 pages, 4 figure