Hierarchical clustering techniques can reveal nested structures within data by representing patterns in a tree-like form. However, when dealing with complex data, many traditional hierarchical methods produce cluttered and hard-to-interpret trees. To address this, we propose a novel hierarchical clustering method called Discovery of Multi-Density Hierarchical Cluster structures (DMDHC), which introduces a new type of cluster tree to represent hierarchical information more effectively. Our approach automatically generates hierarchical local cuts along the tree structure. In contrast to state-of-the-art methods like PEARCH, which typically apply only a single cut across the hierarchy, DMDHC takes advantage of density-based insights to perform multiple cuts at different levels. This results in a more compact and comprehensible representation of intricate hierarchical structures. Extensive experiments on real- world datasets demonstrate that DMDHC, along with its newly introduced tree structure, outperforms existing methods.

In contrast to global graph clustering, local graph clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local graph cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). They measure the homogeneity/unimodality of the graph structure and the subspace that is composed of the designated attributes, respectively. We call their linear combination Compactness. Further, we propose LOCLU to optimize the Compactness score in order to find a good local graph cluster. The local graph cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph, and exhibits a unimodal data distribution in the subspace of the designated attributes.

A major challenge in cluster analysis is the discovery of clusters with widely varying sizes, densities, and shapes. Most clustering algorithms lack the ability to detect heterogeneous clusters that differ greatly in all three properties simultaneously. In this work, we propose the Density Clustering for Highly varying Density algorithm (DBHD). DBHD uses a novel approach that considers local density information and introduces two new conditions to distinguish between different types of data points. Based on this and the adaptively computed density information, DBHD can detect the clusters described above and is robust to noise. Moreover, DBHD has intuitive and robust parameters. In extensive experiments, we show that our technique is considerably more effective in detecting clusters of different shapes, sizes, and densities than well-known (DBSCAN or OPTICS) and recently proposed algorithms such as DPC, SNN-DPC, or LSDBC.

High-dimensional datasets often contain multiple meaningful clusterings in different subspaces. For example, objects can be clustered either by color, weight, or size, revealing different interpretations of the given dataset. A variety of approaches are able to identify such non-redundant clusterings. However, most of these methods require the user to specify the expected number of subspaces and clusters for each subspace. Stating these values is a non-trivial problem and usually requires detailed knowledge of the input dataset. In this paper, we propose a framework that utilizes the Minimum Description Length Principle (MDL) to detect the number of subspaces and clusters per subspace automatically. We describe an efficient procedure that greedily searches the parameter space by splitting and merging subspaces and clusters within subspaces. Additionally, an encoding strategy is introduced that allows us to detect outliers in each subspace. Extensive experiments show that our approach is highly competitive to state-of-the-art methods.

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination asCompactness. Further, we propose LOCLU to optimize theCompactnessscore. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.

Abstract The idea of combining the high representational power of deep learning techniques with clustering methods has gained much attention in recent years. Optimizing a clustering objective and the dataset representation simultaneously has been shown to be advantageous over separately optimizing them. So far, however, all proposed methods have been using a flat clustering strategy, with the actual number of clusters known a priori. In this paper, we propose the Deep Embedded Cluster Tree (DeepECT), the first divisive hierarchical embedded clustering method. The cluster tree does not need to know the actual number of clusters during optimization. Instead, the level of detail to be analyzed can be chosen afterward and for each sub-tree separately. An optional data-augmentation-based extension allows DeepECT to ignore prior-known invariances of the dataset, such as affine transformations in image data. We evaluate and show the advantages of DeepECT in extensive experiments.

A huge object collection in high-dimensional space can often be clustered in more than one way, for instance, objects could be clustered by their shape or alternatively by their color. Each grouping represents a different view of the dataset. The new research field of non-redundant clustering addresses this class of problems. In this article, we follow the approach that different, non-redundant k -means-like clusterings may exist in different, arbitrarily oriented subspaces of the high-dimensional space. We assume that these subspaces (and optionally a further noise space without any cluster structure) are orthogonal to each other. This assumption enables a particularly rigorous mathematical treatment of the non-redundant clustering problem and thus a particularly efficient algorithm, which we call N r -K means (for non-redundant k -means). The superiority of our algorithm is demonstrated both theoretically, as well as in extensive experiments. Further, we propose an extension of N r -K means that harnesses Hartigan’s dip test to identify the number of clusters for each subspace automatically.

The idea of combining the high representational power of deep learning techniques with clustering methods has gained much interest in recent years. Optimizing representation and clustering simultaneously has been shown to have an advantage over optimizing them separately. However, so far all proposed methods have been using a flat clustering strategy, with the true number of clusters known a priori. In this paper, we propose the Deep Embedded Cluster Tree (DeepECT), the first divisive hierarchical embedded clustering method. The cluster tree does not need to know the true number of clusters during optimization. Instead, the level of detail to be analyzed can be chosen afterward and for each sub-tree separately. An optional data-augmentation-based extension allows DeepECT to ignore prior-known invariances of the dataset, such as affine transformations in image data. We evaluate and show the advantages of DeepECT in extensive experiments.

A huge object collection in high-dimensional space can often be clustered in more than one way, for instance, objects could be clustered by their shape or alternatively by their color. Each grouping represents a different view of the data set. The new research field of non-redundant clustering addresses this class of problems. In this paper, we follow the approach that different, non-redundant k-means-like clusterings may exist in different, arbitrarily oriented subspaces of the high-dimensional space. We assume that these subspaces (and optionally a further noise space without any cluster structure) are orthogonal to each other. This assumption enables a particularly rigorous mathematical treatment of the non-redundant clustering problem and thus a particularly efficient algorithm, which we call Nr-Kmeans (for non-redundant k-means). The superiority of our algorithm is demonstrated both theoretically, as well as in extensive experiments.

Is there an optimal dimensionality reduction for k-means, revealing the prominent cluster structure hidden in the data? We propose SUBKMEANS, which extends the classic k-means algorithm. The goal of this algorithm is twofold: find a sufficient k-means-style clustering partition and transform the clusters onto a common subspace, which is optimal for the cluster structure. Our solution is able to pursue these two goals simultaneously. The dimensionality of this subspace is found automatically and therefore the algorithm comes without the burden of additional parameters. At the same time this subspace helps to mitigate the curse of dimensionality. The SUBKMEANS optimization algorithm is intriguingly simple and efficient. It is easy to implement and can readily be adopted to the current situation. Furthermore, it is compatible to many existing extensions and improvements of k-means.

Networks such as social networks, citation networks, protein-protein interaction networks, etc., are prevalent in real world. However, only very few vertices have labels compared to large amounts of unlabeled vertices. For example, in social networks, not every user provides his/her profile information such as the personal interests which are relevant for targeted advertising. Can we leverage the limited user information and friendship network wisely to infer the labels of unlabeled users?