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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 plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…

We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…

Consider unsupervised clustering of objects drawn from a discrete set, through the use of human intelligence available in crowdsourcing platforms. This paper defines and studies the problem of universal clustering using responses of crowd…

We present a new Compact Trip Representation (CTR) that allows us to manage users' trips (moving objects) over networks. These could be public transportation networks (buses, subway, trains, and so on) where nodes are stations or stops, or…

It is well understood that Dynamic Time Warping (DTW) is effective in revealing similarities between time series that do not align perfectly. In this paper, we illustrate this on spectroscopy time-series data. We show that DTW is effective…

In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that…

Dynamic time warping (DTW) is a robust similarity measure of time series. However, it does not satisfy triangular inequality and has high computational complexity, severely limiting its applications in similarity search on large-scale…

Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…

Multivariate time series forecasting is crucial for various applications, such as financial investment, energy management, weather forecasting, and traffic optimization. However, accurate forecasting is challenging due to two main factors.…

As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering…

Clustering algorithms have significantly improved along with Deep Neural Networks which provide effective representation of data. Existing methods are built upon deep autoencoder and self-training process that leverages the distribution of…

Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a…

In this work, we consider the problem of sequence-to-sequence alignment for signals containing outliers. Assuming the absence of outliers, the standard Dynamic Time Warping (DTW) algorithm efficiently computes the optimal alignment between…

In this paper, we study a new data mining problem of obstacle detection from trajectory data. Intuitively, given two kinds of trajectories, i.e., reference and query trajectories, the obstacle is a region such that most query trajectories…

This paper deals with clustering methods based on adaptive distances for histogram data using a dynamic clustering algorithm. Histogram data describes individuals in terms of empirical distributions. These kind of data can be considered as…

Objective: To provide an overview of clustering methods for categorical time series (CTS), a data structure commonly found in epidemiology, sociology, biology, and marketing, and to support method selection in regards to data…

Motif discovery is a fundamental step in data mining tasks for time-series data such as clustering, classification and anomaly detection. Even though many papers have addressed the problem of how to find motifs in time-series by proposing…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…