Customer-Base Analysis using Repeated Cross-Sectional Summary (RCSS) Data

We address a critical question that many firms are facing today: Can customer data be stored and analyzed in an easy-to-manage and scalable manner without significantly compromising the inferences that can be made about the customers’ transaction activity? We address this question in the context of customer-base analysis. A number of researchers have developed customer-base analysis models that perform very well given detailed individual-level data. We explore the possibility of estimating these models using aggregated data summaries alone, namely repeated cross-sectional summaries (RCSS) of the transaction data. Such summaries are easy to create, visualize, and distribute, irrespective of the size of the customer base. An added advantage of the RCSS data structure is that individual customers cannot be identified, which makes it desirable from a data privacy and security viewpoint as well. We focus on the widely used Pareto/NBD model and carry out a comprehensive simulation study covering a vast spectrum of market scenarios. We find that the RCSS format of four quarterly histograms serves as a suitable substitute for individual-level data. We confirm the results of the simulations on a real dataset of purchasing from an online fashion retailer

Customer-Base Analysis Using Repeated Cross-Sectional Summary (RCSS) Data

Abstract We address a critical question that many firms are facing today: Can customer data be stored and analyzed in an easy-to-manage and scalable manner without significantly compromising the inferences that can be made about the customers' transaction activity? We address this question in the context of customer-base analysis. A number of researchers have developed customerbase analysis models that perform very well given detailed individual-level data. We explore the possibility of estimating these models using aggregated data summaries alone, namely repeated cross-sectional summaries (RCSS) of the transaction data (e.g., four quarterly histograms). Such summaries are easy to create, visualize, and distribute, irrespective of the size of the customer base. An added advantage of the RCSS data structure is that individual customers cannot be identified, which makes it desirable from a privacy viewpoint as well. We focus on the widely used Pareto/NBD model and carry out a comprehensive simulation study covering a vast spectrum of market scenarios. We find that the RCSS format of four quarterly histograms * Corresponding author Email addresses: [email protected] (Kinshuk Jerath), [email protected] (Peter S. Fader), [email protected] (Bruce G.S. Hardie) URL: www.petefader.com (Peter S. Fader), http://www.brucehardie.com (Bruce G.S. Hardie) 1 The authors thank David Bell for providing the Bonobos data used in this paper. 2 The second author acknowledges the support of the Wharton Customer Analytics Initiative. serves as an suitable substitute for individual-level data. We confirm the results of the simulations on a real dataset of purchasing from an online fashion retailer

Centrality measures and analyzing dot-product graphs

In this thesis we investigate two topics in data mining on graphs; in the first part we investigate the notion of centrality in graphs, in the second part we look at reconstructing graphs from aggregate information. In many graph related problems the goal is to rank nodes based on an importance score. This score is in general referred to as node centrality. In Part I. we start by giving a novel and more efficient algorithm for computing betweenness centrality. In many applications not an individual node but rather a set of nodes is chosen to perform some task. We generalize the notion of centrality to groups of nodes. While group centrality was first formally defined by Everett and Borgatti (1999), we are the first to pose it as a combinatorial optimization problem; find a group of k nodes with largest centrality. We give an algorithm for solving this optimization problem for a general notion of centrality that subsumes various instantiations of centrality that find paths in the graph. We prove that this problem is NP-hard for specific centrality definitions and we provide a universal algorithm for this problem that can be modified to optimize the specific measures. We also investigate the problem of increasing node centrality by adding or deleting edges in the graph. We conclude this part by solving the optimization problem for two specific applications; one for minimizing redundancy in information propagation networks and one for optimizing the expected number of interceptions of a group in a random navigational network. In the second part of the thesis we investigate what we can infer about a bipartite graph if only some aggregate information -- the number of common neighbors among each pair of nodes -- is given. First, we observe that the given data is equivalent to the dot-product of the adjacency vectors of each node. Based on this knowledge we develop an algorithm that is based on SVD-decomposition, that is capable of almost perfectly reconstructing graphs from such neighborhood data. We investigate two versions of this problem, in the versions the dot-product of nodes with themselves, e.g. the node degrees, are either known or hidden