Related papers: Angle Tree: Nearest Neighbor Search in High Dimens…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
Answering range queries in the context of Local Differential Privacy (LDP) is a widely studied problem in Online Analytical Processing (OLAP). Existing LDP solutions all assume a uniform data distribution within each domain partition, which…
This paper presents the Cascaded Metric Tree (CMT) for efficient satisfaction of metric search queries over a dataset of N objects. It provides extra information that permits query algorithms to exploit all distance calculations performed…
We present a set of parallel algorithms for computing exact k-nearest neighbors in low dimensions. Many k-nearest neighbor algorithms use either a kd-tree or the Morton ordering of the point set; our algorithms combine these approaches…
We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent…
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to spaces in which the distance is measured with an arbitrary Bregman divergence. Perhaps surprisingly, this shows…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…
Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…
In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a…
The key challenge in neural architecture search (NAS) is designing how to explore wisely in the huge search space. We propose a new NAS method called TNAS (NAS with trees), which improves search efficiency by exploring only a small number…
In this paper, we propose a physically inspired graph-theoretical clustering method, which first makes the data points organized into an attractive graph, called In-Tree, via a physically inspired rule, called Nearest Descent (ND). In…
Meeting real-time constraints for high-performance Approximate Nearest Neighbor (ANN) search remains a critical challenge in remote sensing edge devices, which are essentially fusion systems like micro-satellites and UAVs, largely due to…
We introduce the concept of a k-spine of a tree. A k-spine is essentially a path in the tree whose removal leaves only "less-bushy" components of a smaller pathwidth. Using a k-spine as a central guide, we introduce an O(klog dist)…
Approximate nearest neighbour (ANN) search has become a central task in modern data-intensive applications, particularly when operating on large, heterogeneous, or high-dimensional datasets. However, many existing ANN methods struggle in…
Nearest neighbor search is known as a challenging issue that has been studied for several decades. Recently, this issue becomes more and more imminent in viewing that the big data problem arises from various fields. In this paper, a…
This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions,…
KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data…
An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…