相关论文: Diffusion Self-Organizing Map on the Hypersphere

Existing approaches for diffusion on graphs, e.g., for label propagation, are mainly focused on isotropic diffusion, which is induced by the commonly-used graph Laplacian regularizer. Inspired by the success of diffusivity tensors for…

There has been an increasing interest in semi-supervised learning in the recent years because of the great number of datasets with a large number of unlabeled data but only a few labeled samples. Semi-supervised learning algorithms can work…

The remarkable performance of deep neural networks depends on the availability of massive labeled data. To alleviate the load of data annotation, active deep learning aims to select a minimal set of training points to be labelled which…

In this paper it is shown how to map a data manifold into a simpler form by progressively discarding small degrees of freedom. This is the key to self-organising data fusion, where the raw data is embedded in a very high-dimensional space…

We introduce, test and discuss a method for classifying and clustering data modeled as directed graphs. The idea is to start diffusion processes from any subset of a data collection, generating corresponding distributions for reaching…

This paper introduces a diffusion-based framework for universal image segmentation, making agnostic segmentation possible without depending on mask-based frameworks and instead predicting the full segmentation in a holistic manner. We…

Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…

Self Organizing Map is trained using unsupervised learning to produce a two-dimensional discretized representation of input space of the training cases. Growing Hierarchical SOM is an architecture which grows both in a hierarchical way…

We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent…

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…

We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…

In this paper, we apply the ideas of the matrix column based diffusion approach to define a new eigenvector computation algorithm of a stationary probability of a Markov chain.

We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…

We propose two distributed set-based observers using strip-based and set-propagation approaches for linear discrete-time dynamical systems with bounded modeling and measurement uncertainties. Both algorithms utilize a set-based diffusion…

Diffusion models (DMs) have recently been introduced in image deblurring and exhibited promising performance, particularly in terms of details reconstruction. However, the diffusion model requires a large number of inference iterations to…

Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…

The diffusion maps embedding of data lying on a manifold has shown success in tasks such as dimensionality reduction, clustering, and data visualization. In this work, we consider embedding data sets that were sampled from a manifold which…

In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc. 2006, and…

We present a novel method to generate a synthetic distribution of objects (mock) on a spherical surface (i.e. a sky), by using a real distribution. The resulting surrogate map mimics the clustering features of the real data, including the…