Multi-Skill Collaborative Teams based on Densest Subgraphs

SDM 2012
Multi-Skill Collaborative Teams based on Densest Subgraphs
Atish Das Sarma, Amita Gajewar, Atish Das Sarma, Amita Gajewar

We consider the problem of identifying a team of skilled individuals for collaboration, in the presence of a social network, with the goal to maximize the collaborative compatibility of the team. Each node in the social network is associated with skills, and edge-weights specify affinity between respective nodes. We measure collaborative compatibility objective as the density of the induced subgraph on selected nodes.

This problem is NP-hard even when the team requires individuals of only one skill. We present a 3-approximation algorithm for the single-skill team formulation problem. We show the same approximation can be extended to a special case of multiple skills.

Our problem generalizes the formulation studied by Lappas et al. [KDD ’09] who measure team compatibility in terms of diameter or spanning tree. The experimental results show that the density-based algorithms outperform the diameter-based objective on several metrics.

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.