Convex Formulation for Kernel PCA and Its Use in Semisupervised Learning.

In this brief, kernel principal component analysis (KPCA) is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is indeed a solution, and not a mere saddle point. Although these insights do not imply any algorithmic improvement, they can be used to further understand the method, formulate possible extensions, and properly address them. As an example, a new convex optimization problem for semisupervised classification is proposed, which seems particularly well suited whenever the number of known labels is small. Our formulation resembles a least squares support vector machine problem with a regularization parameter multiplied by a negative sign, combined with a variational principle for KPCA. Our primal optimization principle for semisupervised learning is solved in terms of the Lagrange multipliers. Numerical experiments in several classification tasks illustrate the performance of the proposed model in problems with only a few labeled data.

Magnetic eigenmaps for community detection in directed networks.

Communities in directed networks have often been characterized as regions with a high density of links, or as sets of nodes with certain patterns of connection. Our approach for community detection combines the optimization of a quality function and a spectral clustering of a deformation of the combinatorial Laplacian, the so-called magnetic Laplacian. The eigenfunctions of the magnetic Laplacian, which we call magnetic eigenmaps, incorporate structural information. Hence, using the magnetic eigenmaps, dense communities including directed cycles can be revealed as well as "role" communities in networks with a running flow, usually discovered thanks to mixture models. Furthermore, in the spirit of the Markov stability method, an approach for studying communities at different energy levels in the network is put forward, based on a quantum mechanical system at finite temperature.

Cell-based fuzzy metrics enhance high-content screening (HCS) assay robustness.

High-content screening (HCS) allows the exploration of complex cellular phenotypes by automated microscopy and is increasingly being adopted for small interfering RNA genomic screening and phenotypic drug discovery. We introduce a series of cell-based evaluation metrics that have been implemented and validated in a mono-parametric HCS for regulators of the membrane trafficking protein caveolin 1 (CAV1) and have also proved useful for the development of a multiparametric phenotypic HCS for regulators of cytoskeletal reorganization. Imaging metrics evaluate imaging quality such as staining and focus, whereas cell biology metrics are fuzzy logic-based evaluators describing complex biological parameters such as sparseness, confluency, and spreading. The evaluation metrics were implemented in a data-mining pipeline, which first filters out cells that do not pass a quality criterion based on imaging metrics and then uses cell biology metrics to stratify cell samples to allow further analysis of homogeneous cell populations. Use of these metrics significantly improved the robustness of the monoparametric assay tested, as revealed by an increase in Z' factor, Kolmogorov-Smirnov distance, and strict standard mean difference. Cell biology evaluation metrics were also implemented in a novel supervised learning classification method that combines them with phenotypic features in a statistical model that exceeded conventional classification methods, thus improving multiparametric phenotypic assay sensitivity.