Related papers: On Efficient Low Distortion Ultrametric Embedding

We prove that there is a randomized polynomial-time algorithm that given an edge-weighted graph $G$ excluding a fixed-minor $Q$ on $n$ vertices and an accuracy parameter $\varepsilon>0$, constructs an edge-weighted graph~$H$ and an…

Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is…

Performance of distributed optimization and learning systems is bottlenecked by "straggler" nodes and slow communication links, which significantly delay computation. We propose a distributed optimization framework where the dataset is…

Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…

Ensembling word embeddings to improve distributed word representations has shown good success for natural language processing tasks in recent years. These approaches either carry out straightforward mathematical operations over a set of…

Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked…

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…

We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally…

The paper presents an optimal synthesis of overconstrained linkages, based on the factorization of rational curves (representing one parametric motions) contained in Study's quadric. The group of Euclidean displacements is embedded in a…

In low distortion metric embeddings, the goal is to embed a host "hard" metric space into a "simpler" target space while approximately preserving pairwise distances. A highly desirable target space is that of a tree metric. Unfortunately,…

In network design problems, such as compact routing, the goal is to route packets between nodes using the (approximated) shortest paths. A desirable property of these routes is a small number of hops, which makes them more reliable, and…

Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…

Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here…

We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…