Towards unsupervised segmentation in high-resolution medical nano-imaging

Recent advances in cellular and subcellular microscopy demonstrated its potential towards unraveling the mechanisms of various diseases at the molecular level. From a computer vision perspective nano-imaging is an inherently complex environment as can for example be seen from Fig.1(a,c). For the image analysis of intracellular organisms in high-resolution microscopy, new techniques which are capable of handling high-throughput data in a single pass and real time are of special interest. The additional emphasis is put therein on automated solutions which can provide the objective quantitative information in a reasonable time frame. The state-of-the-art is dominated by manual data annotation[1]and the early attempts to automate the segmentation are based on statistical machine-learning techniques[4]

Eigenvalue-based Incremental Spectral Clustering

Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a method of incremental spectral clustering. The method consists of the following steps: (1) split the data into manageable subsets, (2) cluster each of the subsets, (3) merge clusters from different subsets based on the eigenvalue spectrum similarity to form clusters of the entire set. This method can be especially useful for clustering methods of complexity strongly increasing with the size of the data sample,like in case of typical spectral clustering. Experiments were performed showing that in fact the clustering and merging the subsets yields clusters close to clustering the entire dataset.Comment: 14 tables, 6 figure

Multilevel Hierarchical Kernel Spectral Clustering for Real-Life Large Scale Complex Networks

Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual level. The dual formulation allows to build a model on a representative subgraph of the large scale network in the training phase and the model parameters are estimated in the validation stage. The KSC model has a powerful out-of-sample extension property which allows cluster affiliation for the unseen nodes of the big data network. In this paper we exploit the structure of the projections in the eigenspace during the validation stage to automatically determine a set of increasing distance thresholds. We use these distance thresholds in the test phase to obtain multiple levels of hierarchy for the large scale network. The hierarchical structure in the network is determined in a bottom-up fashion. We empirically showcase that real-world networks have multilevel hierarchical organization which cannot be detected efficiently by several state-of-the-art large scale hierarchical community detection techniques like the Louvain, OSLOM and Infomap methods. We show a major advantage our proposed approach i.e. the ability to locate good quality clusters at both the coarser and finer levels of hierarchy using internal cluster quality metrics on 7 real-life networks.Comment: PLOS ONE, Vol 9, Issue 6, June 201

Análisis exploratorio del comportamiento de datos cambiantes en el tiempo usando tópicos avanzados de álgebra lineal

En la actualidad, el análisis de datos dinámicos o variantes en el tiempo es de altísimo interés en la ciencia y la tecnología, y es de gran utilidad en diversas aplicaciones, tales como: predicción, análisis de vídeo, segmentación automática de movimiento, entre otras. Particularmente, las técnicas de reconocimiento de patrones, en especial, aquellas basadas en análisis espectral y álgebra de matrices han mostrado ser una buena alternativa. Sin embargo, aún existe un amplio abanico de problemas sin resolver relacionados con la precisión y la interpretación de los segmentos de movimiento. Esta tesis de maestría presenta un estudio sobre el uso en análisis de datos cambiantes en el tiempo de una técnica de reconocimiento de patrones no supervisada, denominada agrupamiento espectral basado en kernels (kernel spectral clustering, en inglés). Específicamente, se estudia la posibilidad de construir un vector de seguimiento que se encarga de segmentar automáticamente movimientos en una secuencia de cuadros de un vídeo, el cual comprueba su utilidad en la identificación de inicio y fin de movimientos en objetos rotativos y curvas de nivel en movimiento. Con el desarrollo de este trabajo se comprueba también el beneficio de las propiedades, la optimización y el álgebra de funciones con matrices para el análisis de datos dinámico