ClusPath: a temporal-driven clustering to infer typical evolution paths

© 2015, The Author(s). We propose ClusPath, a novel algorithm for detecting general evolution tendencies in a population of entities. We show how abstract notions, such as the Swedish socio-economical model (in a political dataset) or the companies fiscal optimization (in an economical dataset) can be inferred from low-level descriptive features. Such high-level regularities in the evolution of entities are detected by combining spatial and temporal features into a spatio-temporal dissimilarity measure and using semi-supervised clustering techniques. The relations between the evolution phases are modeled using a graph structure, inferred simultaneously with the partition, by using a “slow changing world” assumption. The idea is to ensure a smooth passage for entities along their evolution paths, which catches the long-term trends in the dataset. Additionally, we also provide a method, based on an evolutionary algorithm, to tune the parameters of ClusPath to new, unseen datasets. This method assesses the fitness of a solution using four opposed quality measures and proposes a balanced compromise

Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes; sophisticated enhanced sampling methods have been proposed to generate these macromolecular transition paths. As such paths are curves in a high-dimensional space, they have been difficult to compare quantitatively, a prerequisite to, for instance, assess the quality of different sampling algorithms. The Path Similarity Analysis (PSA) approach alleviates these difficulties by utilizing the full information in 3N-dimensional trajectories in configuration space. PSA employs the Hausdorff or Fr\'echet path metrics---adopted from computational geometry---enabling us to quantify path (dis)similarity, while the new concept of a Hausdorff-pair map permits the extraction of atomic-scale determinants responsible for path differences. Combined with clustering techniques, PSA facilitates the comparison of many paths, including collections of transition ensembles. We use the closed-to-open transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for the assessment enhanced sampling algorithms---to examine multiple microsecond equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free form alongside transition ensembles from the MD-based dynamic importance sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for instance, that differences in DIMS-MD and FRODA paths were mediated by a set of conserved salt bridges whose charge-charge interactions are fully modeled in DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis methods relying on pre-defined collective variables, such as native contacts or geometric quantities, can be used synergistically with PSA, as well as the application of PSA to more complex systems such as membrane transporter proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also available from journal site

Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Drawing and Proximity Analysis

In the past decade there has been a resurgence of interest in nonlinear dimension reduction. Among new proposals are “Local Linear Embedding,” “Isomap,” and Kernel Principal Components Analysis which all construct global low-dimensional embeddings from local affine or metric information. We introduce a competing method called “Local Multidimensional Scaling” (LMDS). Like LLE, Isomap, and KPCA, LMDS constructs its global embedding from local information, but it uses instead a combination of MDS and “force-directed” graph drawing. We apply the force paradigm to create localized versions of MDS stress functions with a tuning parameter to adjust the strength of nonlocal repulsive forces. We solve the problem of tuning parameter selection with a meta-criterion that measures how well the sets of K-nearest neighbors agree between the data and the embedding. Tuned LMDS seems to be able to outperform MDS, PCA, LLE, Isomap, and KPCA, as illustrated with two well-known image datasets. The meta-criterion can also be used in a pointwise version as a diagnostic tool for measuring the local adequacy of embeddings and thereby detect local problems in dimension reductions

Parameter-free agglomerative hierarchical clustering to model learners' activity in online discussion forums

L'anàlisi de l'activitat dels estudiants en els fòrums de discussió online implica un problema de modelització altament depenent del context, el qual pot ser plantejat des d'aproximacions tant teòriques com empíriques. Quan aquest problema és abordat des de l'àmbit de la mineria de dades, l'enfocament més comunament adoptat és el de la classificació no supervisada (o clustering), donant lloc, d'aquesta manera, a un escenari de clustering en el qual el nombre real de clústers és a priori desconegut. Per tant, aquesta aproximació revela una qüestió subjacent, la qual no és sinó un dels problemes més coneguts del paradigma del clustering: l'estimació del nombre de clústers, habitualment seleccionat per l'usuari concorde a algun tipus de criteri subjectiu que pot comportar fàcilment l'aparició de biaixos indesitjats en els models obtinguts. Amb l'objectiu d'evitar qualsevol intervenció de l'usuari en l'etapa de clustering, dos nous criteris d'unió entre clústers són proposats en la present tesi, els quals, al seu torn, permeten la implementació d'un nou algorisme de clustering jeràrquic aglomeratiu lliure de paràmetres. Un complet conjunt d'experiments indica que el nou algorisme de clustering és capaç de proporcionar solucions de clustering òptimes enfront d'una gran varietat d'escenaris de clustering, sent capaç de bregar amb diferents classes de dades, així com de millorar el rendiment ofert pels algorismes de clustering més àmpliament emprats en la pràctica. Finalment, una estratègia d'anàlisi de dues etapes basada en el paradigma del clustering subespaial és proposada a fi d'abordar adequadament el problema de la modelització de la participació dels estudiants en les discussions asíncrones. Combinada amb el nou algorisme clustering, l'estratègia proposada demostra ser capaç de limitar la intervenció subjectiva de l'usuari a les etapes d'interpretació del procés d'anàlisi i de donar lloc a una completa modelització de l'activitat duta a terme pels estudiants en els fòrums de discussió online.El análisis de la actividad de los estudiantes en los foros de discusión online acarrea un problema de modelización altamente dependiente del contexto, el cual puede ser planteado desde aproximaciones tanto teóricas como empíricas. Cuando este problema es abordado desde el ámbito de la minería de datos, el enfoque más comúnmente adoptado es el de la clasificación no supervisada (o clustering), dando lugar, de este modo, a un escenario de clustering en el que el número real de clusters es a priori desconocido. Por tanto, esta aproximación revela una cuestión subyacente, la cual no es sino uno de los problemas más conocidos del paradigma del clustering: la estimación del número de clusters, habitualmente seleccionado por el usuario acorde a algún tipo de criterio subjetivo que puede conllevar fácilmente la aparición de sesgos indeseados en los modelos obtenidos. Con el objetivo de evitar cualquier intervención del usuario en la etapa de clustering, dos nuevos criterios de unión entre clusters son propuestos en la presente tesis, los cuales, a su vez, permiten la implementación de un nuevo algoritmo de clustering jerárquico aglomerativo libre de parámetros. Un completo conjunto de experimentos indica que el nuevo algoritmo de clustering es capaz de proporcionar soluciones de clustering óptimas frente a una gran variedad de escenarios de clustering, siendo capaz de lidiar con diferentes clases de datos, así como de mejorar el rendimiento ofrecido por los algoritmos de clustering más ampliamente utilizados en la práctica. Finalmente, una estrategia de análisis de dos etapas basada en el paradigma del clustering subespacial es propuesta a fin de abordar adecuadamente el problema de la modelización de la participación de los estudiantes en las discusiones asíncronas. Combinada con el nuevo algoritmo clustering, la estrategia propuesta demuestra ser capaz de limitar la intervención subjetiva del usuario a las etapas de interpretación del proceso de análisis y de dar lugar a una completa modelización de la actividad llevada a cabo por los estudiantes en los foros de discusión online.The analysis of learners' activity in online discussion forums leads to a highly context-dependent modelling problem, which can be posed from both theoretical and empirical approaches. When this problem is tackled from the data mining field, a clustering-based perspective is usually adopted, thus giving rise to a clustering scenario where the real number of clusters is a priori unknown. Hence, this approach reveals an underlying problem, which is one of the best-known issues of the clustering paradigm: the estimation of the number of clusters, habitually selected by user according to some kind of subjective criterion that may easily lead to the appearance of undesired biases in the obtained models. With the aim of avoiding any user intervention in the cluster analysis stage, two new cluster merging criteria are proposed in the present thesis, which allow to implement a novel parameter-free agglomerative hierarchical algorithm. A complete set of experiments indicate that the new clustering algorithm is able to provide optimal clustering solutions in the face of a great variety of clustering scenarios, both having the ability to deal with different kinds of data and outperforming clustering algorithms most widely used in practice. Finally, a two-stage analysis strategy based on the subspace clustering paradigm is proposed to properly tackle the issue of modelling learners' participation in the asynchronous discussions. In combination with the new clustering algorithm, the proposed strategy proves to be able to limit user's subjective intervention to the interpretation stages of the analysis process and to lead to a complete modelling of the activity performed by learners in online discussion forums

Discovering underlying dynamics in time series of networks

Understanding dramatic changes in the evolution of networks is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We consider a joint network model in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the time-varying evolution of the constellation of latent vectors exhibits low-dimensional manifold structure under a suitable notion of distance. This distance can be approximated by a measure of separation between the observed networks themselves, and there exist consistent Euclidean representations for underlying network structure, as characterized by this distance, at any given time. These Euclidean representations permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. We illustrate our methodology with real and synthetic data, and identify change points corresponding to massive shifts in pandemic policies in a communication network of a large organization.Comment: 31 pages, 7 figure