Related papers: Coresets for Time Series Clustering

Given a collection of $n$ points in $\mathbb{R}^d$, the goal of the $(k,z)$-clustering problem is to find a subset of $k$ "centers" that minimizes the sum of the $z$-th powers of the Euclidean distance of each point to the closest center.…

Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…

Time series forecasting has gained lots of attention recently; this is because many real-world phenomena can be modeled as time series. The massive volume of data and recent advancements in the processing power of the computers enable…

We consider the problem of constructing small coresets for $k$-Median in Euclidean spaces. Given a large set of data points $P\subset \mathbb{R}^d$, a coreset is a much smaller set $S\subset \mathbb{R}^d$, so that the $k$-Median costs of…

Cluster analysis faces two problems in high dimensions: first, the `curse of dimensionality' that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large…

We present an algorithm for computing $\epsilon$-coresets for $(k, \ell)$-median clustering of polygonal curves in $\mathbb{R}^d$ under the Fr\'echet distance. This type of clustering is an adaption of Euclidean $k$-median clustering: we…

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…

Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data…

We present algorithms for the computation of $\varepsilon$-coresets for $k$-median clustering of point sequences in $\mathbb{R}^d$ under the $p$-dynamic time warping (DTW) distance. Coresets under DTW have not been investigated before, and…

Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…

The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…

Clustering is the task of partitioning a given set of geometric objects. This is thoroughly studied when the objects are points in the euclidean space. There are also several approaches for points in general metric spaces. In this thesis we…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…

Diversity maximization is a fundamental problem in web search and data mining. For a given dataset $S$ of $n$ elements, the problem requires to determine a subset of $S$ containing $k\ll n$ "representatives" which minimize some diversity…

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…