Recently, deep clustering, which is able to perform feature learning that favors clustering tasks via deep neural networks, has achieved remarkable performance in image clustering applications. However, the existing deep clustering algorithms generally need the number of clusters in advance, which is usually unknown in real-world tasks. In addition, the initial cluster centers in the learned feature space are generated by $k$-means. This only works well on spherical clusters and probably leads to unstable clustering results. In this paper, we propose a two-stage deep density-based image clustering (DDC) framework to address these issues. The first stage is to train a deep convolutional autoencoder (CAE) to extract low-dimensional feature representations from high-dimensional image data, and then apply t-SNE to further reduce the data to a 2-dimensional space favoring density-based clustering algorithms. The second stage is to apply the developed density-based clustering technique on the 2-dimensional embedded data to automatically recognize an appropriate number of clusters with arbitrary shapes. Concretely, a number of local clusters are generated to capture the local structures of clusters, and then are merged via their density relationship to form the final clustering result. Experiments demonstrate that the proposed DDC achieves comparable or even better clustering performance than state-of-the-art deep clustering methods, even though the number of clusters is not given.

Traditional plane-based clustering methods measure the cost of within-cluster and between-cluster by quadratic, linear or some other unbounded functions, which may amplify the impact of cost. This letter introduces a ramp cost function into the plane-based clustering to propose a new clustering method, called ramp-based twin support vector clustering (RampTWSVC). RampTWSVC is more robust because of its boundness, and thus it is more easier to find the intrinsic clusters than other plane-based clustering methods. The non-convex programming problem in RampTWSVC is solved efficiently through an alternating iteration algorithm, and its local solution can be obtained in a finite number of iterations theoretically. In addition, the nonlinear manifold-based formation of RampTWSVC is also proposed by kernel trick. Experimental results on several benchmark datasets show the better performance of our RampTWSVC compared with other plane-based clustering methods.

Ruben A. Gevorgyan · Y enok B. Hakobyan Abstract Cluster analysis is one of the essential tasks in data mining and knowledge discovery. Each type of data poses unique challenges in achieving relatively efficient partitioning of the data into homogeneous groups. While the algorithms for numeric data are relatively well studied in the literature, there are still challenges to address in case of categorical data. The main issue is the unordered structure of categorical data, which makes the implementation of the standard concepts of clustering algorithms difficult. For instance, the assessment of distance between objects, the selection of representatives for categorical data is not as straightforward as for numeric data. Therefore, this paper presents a new framework for partitioning categorical data, which does not use the distance measure as a key concept. The Matching based clustering algorithm is designed based on the similarity matrix and a framework for updating the latter using the feature importance criteria. The experimental results show this algorithm can serve as an alternative to existing ones and can be an efficient knowledge discovery tool. Keywords categorical data · clustering algorithm · similarity matrix · feature importance Mathematics Subject Classification (2010) 62H30 · 62H17 · 62H20 Ruben A Gevorgyan Faculty of Economics and Management, Y erevan State University, Alex Manukyan 1, 0025 Y erevan, Republic of Armenia Email: rubengevorgyan@ysu.am Y enok B. Hakobyan Faculty of Economics and Management, Y erevan State University, Alex Manukyan 1, 0025 Y erevan, Republic of Armenia Email: e.hakobyan@ysu.am 1 Introduction Cluster analysis is one of the "super problems"s in data mining. Generally speaking, clustering is partitioning data points into intuitively similar groups (Saxena et al. 2017).

The article addresses balanced clustering problems with an additional requirement as a tree-like structure over the obtained balanced clusters. This kind of clustering problems can be useful in some applications (e.g., network design, management and routing). Various types of the initial elements are considered. Four basic greedy-like solving strategies (design framework) are considered: balancing-spanning strategy, spanning-balancing strategy, direct strategy, and design of layered structures with balancing. An extended description of the spanning-balancing strategy is presented including four solving schemes and an illustrative numerical example.

We present a novel method that can learn a graph representation from multivariate data. In our representation, each node represents a cluster of data points and each edge represents the subset-superset relationship between clusters, which can be mutually overlapped. The key to our method is to use formal concept analysis (FCA), which can extract hierarchical relationships between clusters based on the algebraic closedness property. We empirically show that our method can effectively extract hierarchical structures of clusters compared to the baseline method.

We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares criterion function and takes into consideration the full structure of the stochastic block model and is evaluated at each point in time. Hence, as an intermediate step, it requires estimating the community structure based on a clustering algorithm at every time point. The second method comprises of the following two steps: in the first one, a least squares function is used and evaluated at each time point, but ignores the community structures and just considers a random graph generating mechanism exhibiting a change point. Once the change point is identified, in the second step, all network data before and after it are used together with a clustering algorithm to obtain the corresponding community structures and subsequently estimate the generating stochastic block model parameters. A comparison between these two methods is illustrated. Further, for both methods under their respective identifiability and certain additional regularity conditions, we establish rates of convergence and derive the asymptotic distributions of the change point estimators. The results are illustrated on synthetic data.

Optimization is nothing but a mathematical technique which finds maxima or minima of any function of concern in some realistic region. Different optimization techniques are proposed which are competing for the best solution. Particle Swarm Optimization (PSO) is a new, advanced, and most powerful optimization methodology that performs empirically well on several optimization problems. It is the extensively used Swarm Intelligence (SI) inspired optimization algorithm used for finding the global optimal solution in a multifaceted search region. Data clustering is one of the challenging real world applications that invite the eminent research works in variety of fields. Applicability of different PSO variants to data clustering is studied in the literature, and the analyzed research work shows that, PSO variants give poor results for multidimensional data. This paper describes the different challenges associated with multidimensional data clustering and scope of research on optimizing the clustering problems using PSO. We also propose a strategy to use hybrid PSO variant for clustering multidimensional numerical, text and image data.

Large scale astronomical surveys continue to increase their depth and scale, providing new opportunities to observe large numbers of celestial objects with ever increasing precision. At the same time, the sheer scale of ongoing and future surveys pose formidable challenges to classify astronomical objects. Pioneering efforts on this front include the citizen science approach adopted by the Sloan Digital Sky Survey (SDSS). These SDSS datasets have been used recently to train neural network models to classify galaxies in the Dark Energy Survey (DES) that overlap the footprint of both surveys. While this represents a significant step to classify unlabeled images of astrophysical objects in DES, the key issue at heart still remains, i.e., the classification of unlabelled DES galaxies that have not been observed in previous surveys. To start addressing this timely and pressing matter, we demonstrate that knowledge from deep learning algorithms trained with real-object images can be transferred to classify elliptical and spiral galaxies that overlap both SDSS and DES surveys, achieving state-of-the-art accuracy 99.6%. More importantly, to initiate the characterization of unlabelled DES galaxies that have not been observed in previous surveys, we demonstrate that our neural network model can also be used for unsupervised clustering, grouping together unlabeled DES galaxies into spiral and elliptical types. We showcase the application of this novel approach by classifying over ten thousand unlabelled DES galaxies into spiral and elliptical classes. We conclude by showing that unsupervised clustering can be combined with recursive training to start creating large-scale DES galaxy catalogs in preparation for the Large Synoptic Survey Telescope era.

The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface nearby the intersection and result in incorrect clustering. The Isomap algorithm uses the shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper, we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighbourhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as an input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering.

Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and community detection, has led to increased interest on the problem leading to a number of recent advances. Much like PCA in the feature domain, node embedding is an inherently \emph{unsupervised} task; in lack of metadata used for validation, practical methods may require standardization and limiting the use of tunable hyperparameters. Finally, node embedding methods are faced with maintaining scalability in the face of large-scale real-world graphs of ever-increasing sizes. In the present work, we propose an adaptive node embedding framework that adjusts the embedding process to a given underlying graph, in a fully unsupervised manner. To achieve this, we adopt the notion of a tunable node similarity matrix that assigns weights on paths of different length. The design of the multilength similarities ensures that the resulting embeddings also inherit interpretable spectral properties. The proposed model is carefully studied, interpreted, and numerically evaluated using stochastic block models. Moreover, an algorithmic scheme is proposed for training the model parameters effieciently and in an unsupervised manner. We perform extensive node classification, link prediction, and clustering experiments on many real world graphs from various domains, and compare with state-of-the-art scalable and unsupervised node embedding alternatives. The proposed method enjoys superior performance in many cases, while also yielding interpretable information on the underlying structure of the graph.