eBay: an E-commerce Marketplace as a Complex Network

in Proceedings of the fourth ACM international conference on Web search and data mining (WSDM), 2011.
eBay: an E-commerce Marketplace as a Complex Network
Zeqian Shen, Neel Sundaresan, Zeqian Shen, Neel Sundaresan

Commerce networks involve buying and selling activities among individuals or organizations. As the growing of the Internet and e-commerce, it brings opportunities for obtaining real world online commerce networks, which are magnitude larger than before.

Getting a deeper understanding of e-commerce networks, such as the eBay marketplace, in terms of what structure they have, what kind of interactions they afford, what trust and reputation measures exist, and how they evolve has tremendous value in suggesting business opportunities and building effective user applications.

In this paper, we modeled the eBay network as a complex network. We analyzed the macroscopic shape of the network using degree distribution and the bow-tie model. Networks of different eBay categories are also compared.

The results suggest that the categories vary from collector networks to retail networks. We also studied the local structures of the networks using motif profiling. Finally, patterns of preferential connections are visually analyzed using Auroral diagrams.

Another publication from the same category: Machine Learning and Data Science

IEEE Computing Conference 2018, London, UK

Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.