Mark Eisen

Authorship Attribution Through Function Word Adjacency Networks

A method for authorship attribution based on function word adjacency networks (WANs) is introduced. Function words are parts of speech that express grammatical relationships between other words but do not carry lexical meaning on their own. In the WANs in this paper, nodes are function words and directed edges from a source function word to a target function word stand in for the likelihood of finding the latter in the ordered vicinity of the former. WANs of different authors can be interpreted as transition probabilities of a Markov chain and are therefore compared in terms of their relative entropies. Optimal selection of WAN parameters is studied and attribution accuracy is benchmarked across a diverse pool of authors and varying text lengths. This analysis shows that, since function words are independent of content, their use tends to be specific to an author and that the relational data captured by function WANs is a good summary of stylometric fingerprints. Attribution accuracy is observed to exceed the one achieved by methods that rely on word frequencies alone. Further combining WANs with methods that rely on word frequencies, results in larger attribution accuracy, indicating that both sources of information encode different aspects of authorial styles.

Decentralized Quasi-Newton Methods

We introduce the decentralized Broyden–Fletcher–Goldfarb–Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. Decentralized quasi-Newton methods are of interest in problems that are not well conditioned, making first-order decentralized methods ineffective, and in which second-order information is not readily available, making second-order decentralized methods impossible. D-BFGS is a fully distributed algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant condition. We additionally provide a formulation of the algorithm in asynchronous settings. Convergence of D-BFGS is established formally in both the synchronous and asynchronous settings and strong performance advantages relative to existing methods are shown numerically.

Authorship attribution using function words adjacency networks

We present an authorship attribution method based on relational data between function words. These are content independent words that help define grammatical relationships. As relational structures we use normalized word adjacency networks. We interpret these networks as Markov chains and compare them using entropy measures. We illustrate the accuracy of the method developed through a series of numerical experiments including comparisons with frequency based methods. We show that accuracy increases when combining relational and frequency based data, indicating that both sources of information encode different aspects of authorial styles.

Attributing the Authorship of the Henry VI Plays by Word Adjacency

The project was a collaboration between the Centre for Textual Studies at De Montfort University and the Department of Electrical & Systems Engineering at the University of Pennsylvania.

An incremental quasi-Newton method with a local superlinear convergence rate

We present an incremental Broyden-Fletcher-Goldfarb-Shanno (BFGS) method as a quasi-Newton algorithm with a cyclically iterative update scheme for solving large-scale optimization problems. The proposed incremental quasi-Newton (IQN) algorithm reduces computational cost relative to traditional quasi-Newton methods by restricting the update to a single function per iteration and relative to incremental second-order methods by removing the need to compute the inverse of the Hessian. A local superlinear convergence rate is established and a strong improvement is shown over first order methods numerically for a set of common large-scale optimization problems.

A decentralized quasi-Newton method for dual formulations of consensus optimization

This paper considers consensus optimization problems where each node of a network has access to a different summand of an aggregate cost function. Nodes try to maximize the aggregate cost function, while they exchange information only with their neighbors. We modify the dual decomposition method to incorporate a curvature correction inspired by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method. The resulting dual D-BFGS method is a fully decentralized algorithm in which nodes approximate curvature information of themselves and neighbors through the satisfaction of a secant condition. Dual D-BFGS is of interest in consensus problems that are not well conditioned, making first order decentralized methods ineffective, and in which second order information is not readily available, making decentralized second order methods infeasible. Asynchronous implementation is discussed and convergence of D-BFGS is established formally for synchronous and asynchronous implementations. Performance advantages relative to alternative decentralized algorithms are shown numerically.

Stylometric analysis of Early Modern period English plays

Function word adjacency networks (WANs) are used to study the authorship of plays from the Early Modern English period. In these networks, nodes are function words and directed edges between two nodes represent the relative frequency of directed co-appearance of the two words. For every analyzed play, a WAN is constructed and these are aggregated to generate author profile networks. We first study the similarity of writing styles between Early English playwrights by comparing the profile WANs. The accuracy of using WANs for authorship attribution is then demonstrated by attributing known plays among six popular playwrights. Moreover, the WAN method is shown to outperform other frequency-based methods on attributing Early English plays. In addition, WANs are shown to be reliable classifiers even when attributing collaborative plays. For several plays of disputed co-authorship, a deeper analysis is performed by attributing every act and scene separately, in which we both corroborate existing breakdowns and provide evidence of new assignments.

An asynchronous Quasi-Newton method for consensus optimization

We introduce the distributed Broyden-Fletcher-Goldfarb-Shanno (D-BFGS) method as an asynchronous decentralized variation of the BFGS quasi-Newton method for solving consensus optimization problems on a penalty function in the primal domain. The D-BFGS method is of interest in problems that are not well conditioned and in which second order information is not readily available, making decentralized first or second order methods ineffective. Convergence of asynchronous D-BFGS is established formally and strong performance advantages relative to other methods are shown numerically.