Related papers: Statistical Analysis and Parameter Selection for M…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…
The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…
Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
The choices of hyperparameters have critical effects on the performance of machine learning models. In this paper, we present a general framework that is able to construct an adaptive optimizer, which automatically adjust the appropriate…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…
Accuracy is the most important parameter among few others which defines the effectiveness of a machine learning algorithm. Higher accuracy is always desirable. Now, there is a vast number of well established learning algorithms already…
Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…
Carlsson, Singh and Memoli's TDA mapper takes a point cloud dataset and outputs a graph that depends on several parameter choices. Dey, Memoli, and Wang developed Multiscale Mapper for abstract topological spaces so that parameter choices…
We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods such as the adjacency and Laplacian spectral embedding, the proposed one-step procedure…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
Estimating the shape of an elliptical distribution is a fundamental problem in statistics. One estimator for the shape matrix, Tyler's M-estimator, has been shown to have many appealing asymptotic properties. It performs well in numerical…
Recently manifold learning algorithm for dimensionality reduction attracts more and more interests, and various linear and nonlinear, global and local algorithms are proposed. The key step of manifold learning algorithm is the neighboring…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical…