Related papers: Neighborhood and Graph Constructions using Non-Neg…

The k-Nearest Neighbors (kNN) classifier is a fundamental non-parametric machine learning algorithm. However, it is well known that it suffers from the curse of dimensionality, which is why in practice one often applies a kNN classifier on…

Approximate nearest neighbor search (ANNS) constitutes an important operation in a multitude of applications, including recommendation systems, information retrieval, and pattern recognition. In the past decade, graph-based ANNS algorithms…

The recently proposed Graph Convolutional Networks (GCNs) have achieved significantly superior performance on various graph-related tasks, such as node classification and recommendation. However, currently researches on GCN models usually…

Graph Structure Learning (GSL) has demonstrated considerable potential in the analysis of graph-unknown non-Euclidean data across a wide range of domains. However, constructing an end-to-end graph structure learning model poses a challenge…

Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…

The exponential growth of data has intensified the gap between the availability of unlabeled data and the high cost of manual annotation. Graph Neural Networks (GNNs) have emerged as a promising solution, as they exploit relational…

We consider graph representation learning in a self-supervised manner. Graph neural networks (GNNs) use neighborhood aggregation as a core component that results in feature smoothing among nodes in proximity. While successful in various…

This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-$k$ nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into…

Graph-based algorithms have shown great empirical potential for the approximate nearest neighbor (ANN) search problem. Currently, graph-based ANN search algorithms are designed mainly using heuristics, whereas theoretical analysis of such…

Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…

Graph neural networks (GNNs) have drawn significant research attention recently, mostly under the setting of semi-supervised learning. When task-agnostic representations are preferred or supervision is simply unavailable, the auto-encoder…

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.…

Neighbor-based methods are a natural alternative to linear prediction for tabular data when relationships between inputs and targets exhibit complexity such as nonlinearity, periodicity, or heteroscedasticity. Yet in deep learning on…

Graph neural networks (GNNs) have been successfully applied in many structured data domains, with applications ranging from molecular property prediction to the analysis of social networks. Motivated by the broad applicability of GNNs, we…

We introduce a graphical presentation for the false nearest neighbors (FNN) method. In the original method only the percentage of false neighbors is computed without regard to the distribution of neighboring points in the time-delay…

The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks…

A Shared Nearest Neighbor (SNN) graph is a type of graph construction using shared nearest neighbor information, which is a secondary similarity measure based on the rankings induced by a primary $k$-nearest neighbor ($k$-NN) measure. SNN…

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…

Top-k Nearest Neighbors (kNN) problem on road network has numerous applications on location-based services. As direct search using the Dijkstra's algorithm results in a large search space, a plethora of complex-index-based approaches have…

Approximate K-Nearest Neighbor Search (AKNNS) has now become ubiquitous in modern applications, for example, as a fast search procedure with two tower deep learning models. Graph-based methods for AKNNS in particular have received great…