Finding the limit of diverging components in three-way Candecomp/Parafac: A demonstration of its practical merits

Three-way Candecomp/Parafac (CP) is a three-way generalization of principal component analysis (PCA) for matrices. Contrary to PCA, a CP decomposition is rotationally unique under mild conditions. However, a CP analysis may be hampered by the non-existence of a best-fitting CP decomposition with R≤2 components. In this case, fitting CP to a three-way data array results in diverging CP components. Recently, it has been shown that this can be solved by fitting a decomposition with several interaction terms, using initial values obtained from the diverging CP decomposition. The new decomposition is called CPlimit, since it is the limit of the diverging CP decomposition. The practical merits of this procedure are demonstrated for a well-known three-way dataset of TV-ratings. CPlimit finds main components with the same interpretation as Tucker models or when imposing orthogonality in CP. However, CPlimit has higher joint fit of the main components than Tucker models, contains only one small interaction term, and does not impose the unnatural constraint of orthogonality. The uniqueness properties of the CP limit decomposition are discussed in detail

Cortical resting state circuits: connectivity and oscillations

Ongoing spontaneous brain activity patterns raise ever-growing interest in the neuroscience community. Complex spatiotemporal patterns that emerge from a structural core and interactions of functional dynamics have been found to be far from arbitrary in empirical studies. They are thought to compose the network structure underlying human cognitive architecture. In this thesis, we use a biophysically realistic computer model to study key factors in producing complex spatiotemporal activation patterns. For the first time, we present a model of decreased physiological signal complexity in aging and demonstrate that delays shape functional connectivity in an oscillatory spiking-neuron network model for MEG resting-state data. Our results show that the inclusion of realistic delays maximizes model performance. Furthermore, we propose embracing a datadriven, comparative stance on decomposing the system into subnetworks.Últimamente, el interés de la comunidad científica sobre los patrones de la continua actividad espontanea del cerebro ha ido en aumento. Complejos patrones espacio-temporales emergen a partir de interacciones de un núcleo estructural con dinámicas funcionales. Se ha encontrado que estos patrones no son aleatorios y que componen la red estructural en la que la arquitectura cognitiva humana se basa. En esta tesis usamos un modelo computacional detallado para estudiar los factores clave en producir los patrones emergentes. Por primera vez, presentamos un modelo simplificado de la actividad cerebral en envejecimiento. También demostramos que la inclusión del desfase de transmisión en un modelo para grabaciones magnetoencefalográficas del estado en reposo maximiza el rendimiento del modelo. Para ello, aplicamos un modelo con una red de neuronas pulsantes (’spiking-neurons’) y con dinámicas oscilatorias. Además, proponemos adoptar una posición comparativa basada en los datos para descomponer el sistema en subredes