Related papers: Parzen Window Approximation on Riemannian Manifold

We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined by an ambient Gaussian kernel matrix. We show that the…

Recent advances in semi-supervised learning methods rely on estimating the categories of unlabeled data using a model trained on the labeled data (pseudo-labeling) and using the unlabeled data for various consistency-based regularization.…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…

We argue that existing training-free segmentation methods rely on an implicit and limiting assumption, that segmentation is a spectral graph partitioning problem over diffusion-derived affinities. Such approaches, based on global graph…

We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal…

Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive…

This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph,…

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…

Learning fair graph representations for downstream applications is becoming increasingly important, but existing work has mostly focused on improving fairness at the global level by either modifying the graph structure or objective function…

A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…

The deficiency of segmentation labels is one of the main obstacles to semantic segmentation in the wild. To alleviate this issue, we present a novel framework that generates segmentation labels of images given their image-level class…

Graph-based methods have been quite successful in solving unsupervised and semi-supervised learning problems, as they provide a means to capture the underlying geometry of the dataset. It is often desirable for the constructed graph to…

Domain adaptation manages to transfer the knowledge of well-labeled source data to unlabeled target data. Many recent efforts focus on improving the prediction accuracy of target pseudo-labels to reduce conditional distribution shift. In…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Unregularized deep neural networks (DNNs) can be easily overfit with a limited sample size. We argue that this is mostly due to the disriminative nature of DNNs which directly model the conditional probability (or score) of labels given the…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…