相关论文: Solving $k$-means on High-dimensional Big Data

Change-point analysis is thriving in this big data era to address problems arising in many fields where massive data sequences are collected to study complicated phenomena over time. It plays an important role in processing these data by…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

We design and implement two single-pass semi-streaming algorithms for the maximum weight $k$-disjoint matching ($k$-DM) problem. Given an integer $k$, the $k$-DM problem is to find $k$ pairwise edge-disjoint matchings such that the sum of…

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…

The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core…

Data clustering is a fundamental operation in data analysis. For handling large-scale data, the standard k-means clustering method is not only slow, but also memory-inefficient. We propose an efficient clustering method for billion-scale…

Computing the volume of a polytope in high dimensions is computationally challenging but has wide applications. Current state-of-the-art algorithms to compute such volumes rely on efficient sampling of a Gaussian distribution restricted to…

Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central…

$k$-means++ is an important algorithm for choosing initial cluster centers for the $k$-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with nearly optimal running time. Given $n$…

Distributed approaches based on the map-reduce programming paradigm have started to be proposed in the bioinformatics domain, due to the large amount of data produced by the next-generation sequencing techniques. However, the use of…

Iterative methods on irregular grids have been used widely in all areas of comptational science and engineering for solving partial differential equations with complex geometry. They provide the flexibility to express complex shapes with…

This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…

We present parameterized streaming algorithms for the graph matching problem in both the dynamic and the insert-only models. For the dynamic streaming model, we present a one-pass algorithm that, with high probability, computes a…

Several high-throughput distributed data-processing applications require multi-hop processing of streams of data. These applications include continual processing on data streams originating from a network of sensors, composing a multimedia…

We are in the era of data analytics and data science which is on full bloom. There is abundance of all kinds of data for example biometrics based data, satellite images data, chip-seq data, social network data, sensor based data etc. from a…

Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which…

The $k$-Maximum Inner Product Search ($k$MIPS) serves as a foundational component in recommender systems and various data mining tasks. However, while most existing $k$MIPS approaches prioritize the efficient retrieval of highly relevant…

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each…

In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…

K-means is one of the most widely used algorithms for clustering in Data Mining applications, which attempts to minimize the sum of the square of the Euclidean distance of the points in the clusters from the respective means of the…