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Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…
Clustering attempts to partition data instances into several distinctive groups, while the similarities among data belonging to the common partition can be principally reserved. Furthermore, incomplete data frequently occurs in many…
Cluster analysis is a popular unsupervised learning tool used in many disciplines to identify heterogeneous sub-populations within a sample. However, validating cluster analysis results and determining the number of clusters in a data set…
Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…
Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability…
We define the notion of a well-clusterable data set combining the point of view of the objective of $k$-means clustering algorithm (minimising the centric spread of data elements) and common sense (clusters shall be separated by gaps). We…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…
Though mostly used as a clustering algorithm, k-means are originally designed as a quantization algorithm. Namely, it aims at providing a compression of a probability distribution with k points. Building upon [21, 33], we try to investigate…
The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…
While traditional research on text clustering has largely focused on grouping documents by topic, it is conceivable that a user may want to cluster documents along other dimensions, such as the authors mood, gender, age, or sentiment.…
Multiple datasets containing different types of features may be available for a given task. For instance, users' profiles can be used to group users for recommendation systems. In addition, a model can also use users' historical behaviors…
Cluster analysis is an unsupervised learning strategy that can be employed to identify subgroups of observations in data sets of unknown structure. This strategy is particularly useful for analyzing high-dimensional data such as microarray…
$k$-means and $k$-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependences on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, Dasgupta,…
The avalanche quantity of the information developed by mankind has led to concept of automation of knowledge extraction - Data Mining ([1]). This direction is connected with a wide spectrum of problems - from recognition of the fuzzy set to…
Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g. electoral districts) whose benefit can only be attained by groups…
This paper introduces a new framework for clustering in a distributed network called Distributed Clustering based on Distributional Kernel (K) or KDC that produces the final clusters based on the similarity with respect to the distributions…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
Clustering is a data analysis method for extracting knowledge by discovering groups of data called clusters. Among these methods, state-of-the-art density-based clustering methods have proven to be effective for arbitrary-shaped clusters.…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…