Hierarchical clustering | EPFL Graph Search

In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories:

Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.
Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.

In general, the merges and splits are determined in a greedy manner. The results of hierarchical clustering are usually presented in a dendrogram. Hierarchical clustering has the distinct advantage that any valid measure of distance can be used. In fact, the observations themselves are not required: all that is used is a matrix of distances. On the other hand, except for the special case of single-linkage distance, none of th

RG-Flow: a hierarchical and explainable flow model based on renormalization group and sparse prior

Dian Wu

Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, RG-Flow, which can separate information at different scales of images and extract disentangled representations at each scale. We demonstrate our method on synthetic multi-scale image datasets and the CelebA dataset, showing that the disentangled representations enable semantic manipulation and style mixing of the images at different scales. To visualize the latent representations, we introduce receptive fields for flow-based models and show that the receptive fields of RG-Flow are similar to those of convolutional neural networks. In addition, we replace the widely adopted isotropic Gaussian prior distribution by the sparse Laplacian distribution to further enhance the disentanglement of representations. From a theoretical perspective, our proposed method has O(log L) complexity for inpainting of an image with edge length L, compared to previous generative models with O(L-2) complexity.

IOP Publishing Ltd2022

Parallel retrieval of correlated patterns: From Hopfield networks to Boltzmann machines

Andrea De Antoni

In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a modification of the Hebbian prescription, which induces a coupling between consecutive patterns and this effect is tuned by a parameter a. In the latter case, dilution is introduced in pattern entries, in such a way that a fraction d of them is blank. Then, we merge these two extensions to obtain a system able to retrieve several patterns in parallel and the quality of retrieval, encoded by the set of Mattis magnetizations {m(mu)}, is reminiscent of the correlation among patterns. By tuning the parameters d and a, qualitatively different outputs emerge, ranging from highly hierarchical to symmetric. The investigations are accomplished by means of both numerical simulations and statistical mechanics analysis, properly adapting a novel technique originally developed for spin glasses, i.e. the Hamilton-Jacobi interpolation, with excellent agreement. Finally, we show the thermodynamical equivalence of this associative network with a (restricted) Boltzmann machine and study its stochastic dynamics to obtain even a dynamical picture, perfectly consistent with the static scenario earlier discussed. (c) 2012 Elsevier Ltd. All rights reserved.

Elsevier2013

Predictable enriched environment prevents development of hyper-emotionality in the VPA rat model of autism

Dimitri Marco Christodoulou, Melissa Cochrane, Mônica Regina Favre, Deborah La Mendola, Henry Markram, Kamila Markram, Julie Meystre

Understanding the effects of environmental stimulation in autism can improve therapeutic interventions against debilitating sensory overload, social withdrawal, fear and anxiety. Here, we evaluate the role of environmental predictability on behavior and protein expression, and inter-individual differences, in the valproic acid (VPA) model of autism. Male rats embryonically exposed (E11.5) either to VPA, a known autism risk factor in humans, or to saline, were housed from weaning into adulthood in a standard laboratory environment, an unpredictably enriched environment, or a predictably enriched environment. Animals were tested for sociability, nociception, stereotypy, fear conditioning and anxiety, and for tissue content of glutamate signaling proteins in the primary somatosensory cortex, hippocampus and amygdala, and of corticosterone in plasma, amygdala and hippocampus. Standard group analyses on separate measures were complemented with a composite emotionality score, using Cronbach's Alpha analysis, and with multivariate profiling of individual animals, using Hierarchical Cluster Analysis. We found that predictable environmental enrichment prevented the development of hyper-emotionality in the VPA-exposed group, while unpredictable enrichment did not. Individual variation in the severity of the autistic-like symptoms (fear, anxiety, social withdrawal and sensory abnormalities) correlated with neurochemical profiles, and predicted their responsiveness to predictability in the environment. In controls, the association between socio-affective behaviors, neurochemical profiles and environmental predictability was negligible. This study suggests that rearing in a predictable environment prevents the development of hyper-emotional features in animals exposed to an autism risk factor, and demonstrates that unpredictable environments can lead to negative outcomes, even in the presence of environmental enrichment.

Frontiers Research Foundation2015

Predictable enriched environment prevents development of hyper-emotionality in the VPA rat model of autism

Dimitri Marco Christodoulou, Melissa Cochrane, Mônica Regina Favre, Deborah La Mendola, Henry Markram, Kamila Markram, Julie Meystre

Frontiers Research Foundation2015