Related papers: Angle Tree: Nearest Neighbor Search in High Dimens…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
We study the Approximate Nearest Neighbor problem for metric spaces where the query points are constrained to lie on a subspace of low doubling dimension, while the data is high-dimensional. We show that this problem can be solved…
Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…
This work addresses the problem of billion-scale nearest neighbor search. The state-of-the-art retrieval systems for billion-scale databases are currently based on the inverted multi-index, the recently proposed generalization of the…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
This paper is about searching the combinatorial space of contingency tables during the inner loop of a nonlinear statistical optimization. Examples of this operation in various data analytic communities include searching for nonlinear…
We present several modifications to the previously proposed MSPP algorithm that can speed-up its execution considerably. The MSPP algorithm leverages a multiscale representation of the environment in $n$ dimensions. The information of the…
We study the number of distance queries needed to identify certain properties of a hidden tree $T$ on $n$ vertices. A distance query consists of two vertices $x,y$, and the answer is the distance of $x$ and $y$ in $T$. We determine the…
Self-nested trees present a systematic form of redundancy in their subtrees and thus achieve optimal compression rates by DAG compression. A method for quantifying the degree of self-similarity of plants through self-nested trees has been…
Subspace clustering aims to find groups of similar objects (clusters) that exist in lower dimensional subspaces from a high dimensional dataset. It has a wide range of applications, such as analysing high dimensional sensor data or DNA…
Let R^d -> A be a query problem over R^d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q in R^d. Let D be a probability measure over R^d representing a distribution of queries. We…
Existing object proposal algorithms usually search for possible object regions over multiple locations and scales separately, which ignore the interdependency among different objects and deviate from the human perception procedure. To…
Rapidly-exploring Random Tree (RRT) algorithms have been applied successfully to challenging robot motion planning and under-actuated nonlinear control problems. However a fundamental limitation of the RRT approach is the slow convergence…
Range reporting is a classical problem in computational geometry. A (rectangular) reporting data structure stores a point set $P$, such that, given a (rectangular) query region $\Delta$, it returns all points in $P \cap \Delta$. A variety…
Nearest neighbor (NN) search is inherently computationally expensive in high-dimensional spaces due to the curse of dimensionality. As a well-known solution, locality-sensitive hashing (LSH) is able to answer c-approximate NN (c-ANN)…
We propose a novel distance to calculate distance between high dimensional vector pairs, utilizing vector quantization generated encodings. Vector quantization based methods are successful in handling large scale high dimensional data.…
Random dimensionality reduction is a versatile tool for speeding up algorithms for high-dimensional problems. We study its application to two clustering problems: the facility location problem, and the single-linkage hierarchical clustering…
Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…
Locality-sensitive hashing (LSH) is a well-known solution for approximate nearest neighbor (ANN) search with theoretical guarantees. Traditional LSH-based methods mainly focus on improving the efficiency and accuracy of query phase by…