Structured point process data harvested from various platforms poses new challenges to the machine learning community.

Algorithmic stability is a key characteristic of an algorithm regarding its sensitivity to perturbations of input samples. In this paper, we propose an innovative unsupervised feature selection algorithm attaining this stability with provable guarantees.

Cross-Domain Recommendation (CDR) has been popularly studied to utilize different domain knowledge to solve the cold-start problem in recommender systems.

The spectral clustering algorithm for directed networks that we consider in this paper is shown in Algorithm A.1. Theorem B.1 provides an upper bound to the error rate of spectral clustering on the weighted The effect of this term is negligible as T, so we ignore it. We now present an upper bound on the error rate for communities (analogous to Theorem B.1) estimated from the unweighted adjacency matrix The upper bounds on the error rates in Theorems B.1 and B.2 are not very informative in terms of In Section 4.1, we considered a simplified special case Similarly, we have the following result for spectral clustering using the unweighted adjacency matrix A . 3 Theorem B.3. Hence the unweighted adjacency matrix has a 1 in almost all entries, and the community structure cannot be detected from this matrix. The density of the aggregate adjacency matrix is governed by the parameters of the CHIP model.

We reformulate the Wasserstein Discriminant Analysis (WDA) as a ratio trace problem and present an eigensolver-based algorithm to compute the discriminative subspace of WDA. This new formulation, along with the proposed algorithm, can be served as an efficient and more stable alternative to the original trace ratio formulation and its gradient-based algorithm. We provide a rigorous convergence analysis for the proposed algorithm under the self-consistent field framework, which is crucial but missing in the literature. As an application, we combine WDA with low-dimensional clustering techniques, such as K-means, to perform subspace clustering. Numerical experiments on real datasets show promising results of the ratio trace formulation of WDA in both classification and clustering tasks.

The most popular heuristic for solving this problem is Lloyd's algorithm ( Lloyd,