Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC as unknown parameters from measurements. Specifically, we focus on single linkage hierarchical clustering (SLHC) and study its geometry. We prove that under fairly reasonable conditions on the probability distribution governing measurements, SLHC is equivalent to maximum partial profile likelihood estimation (MPPLE) with some of the information contained in the data ignored. At the same time, we show that direct evaluation of SLHC on maximum likelihood estimation (MLE) of pairwise distances yields a consistent estimator. Consequently, a full MLE is expected to perform better than SLHC in getting the correct HC results for the ground truth metric.

As the election season rampages on, we categorize voters into broad demographics -- soccer moms, NASCAR dads, blacks, whites, ALICEs, yuppies -- in an attempt to understand and discuss this complex, churning electorate. In doing so we're tapping into something fundamental about how we perceive the world: not as a sequence of singular individuals, but rather as a massive set of overlapping taxonomies that, taken together, comprise an impressively structured human experience. With fewer than 20 yes/no queries on category membership we can often identify a single object amidst a staggering breadth of possibilities. We've grouped everything that we know to exist and the groupings themselves are the primary subject of our thoughts. We can go the other direction as well -- taking an object and placing it in its many groups.

This paper introduces a novel technique to track structures in time varying graphs. The method uses a maximum a posteriori approach for adjusting a three-dimensional co-clustering of the source vertices, the destination vertices and the time, to the data under study, in a way that does not require any hyper-parameter tuning. The three dimensions are simultaneously segmented in order to build clusters of source vertices, destination vertices and time segments where the edge distributions across clusters of vertices follow the same evolution over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make any a priori quantization. Experiments conducted on artificial data illustrate the good behavior of the technique, and a study of a real-life data set shows the potential of the proposed approach for exploratory data analysis.

Machine and statistical learning wizards are becoming more eager to perform analysis with Spark ML library if this is only possible. It's trendy, posh, spicy and gives the feeling of doing state of the art machine learning and being up to date with the newest computational trends. It is even more sexy and powerful when computations can be performed on the extraordinarily enormous computation cluster - let's say 100 machines on YARN hadoop cluster makes you the real data cruncher! In this post I present sparklyr package (by RStudio), the connector that will transform you from a regular R user, to the supa! Moreover, I present how I have extended the interface to K-means procedure, so that now it is also possible to compute cost for that model, which might be beneficial in determining the number of clusters in segmentation problems.

Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to deal with imbalanced cluster sizes. Our approach parameterizes a family of graphs by adaptively modulating node degrees on a fixed node set, yielding a set of parameter dependent cuts reflecting varying levels of imbalance. The solution to our problem is then obtained by optimizing over these parameters. We present rigorous limit cut analysis results to justify our approach and demonstrate the superiority of our method through experiments on synthetic and real datasets for data clustering, semi-supervised learning and community detection.

We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and then cluster the vertices into communities. We next employ nonparametric graph inference techniques to identify structural similarity among these communities. These two steps are then applied recursively on the communities, allowing us to detect more fine-grained structure. We describe a hierarchical stochastic blockmodel---namely, a stochastic blockmodel with a natural hierarchical structure---and establish conditions under which our algorithm yields consistent estimates of model parameters and motifs, which we define to be stochastically similar groups of subgraphs. Finally, we demonstrate the effectiveness of our algorithm in both simulated and real data. Specifically, we address the problem of locating similar subcommunities in a partially reconstructed Drosophila connectome and in the social network Friendster.

Multi-view data clustering refers to categorizing a data set by making good use of related information from multiple representations of the data. It becomes important nowadays because more and more data can be collected in a variety of ways, in different settings and from different sources, so each data set can be represented by different sets of features to form different views of it. Many approaches have been proposed to improve clustering performance by exploring and integrating heterogeneous information underlying different views. In this paper, we propose a new multi-view fuzzy clustering approach called MinimaxFCM by using minimax optimization based on well-known Fuzzy c means. In MinimaxFCM the consensus clustering results are generated based on minimax optimization in which the maximum disagreements of different weighted views are minimized. Moreover, the weight of each view can be learned automatically in the clustering process. In addition, there is only one parameter to be set besides the fuzzifier. The detailed problem formulation, updating rules derivation, and the in-depth analysis of the proposed MinimaxFCM are provided here. Experimental studies on nine multi-view data sets including real world image and document data sets have been conducted. We observed that MinimaxFCM outperforms related multi-view clustering approaches in terms of clustering accuracy, demonstrating the great potential of MinimaxFCM for multi-view data analysis.

Incremental clustering approaches have been proposed for handling large data when given data set is too large to be stored. The key idea of these approaches is to find representatives to represent each cluster in each data chunk and final data analysis is carried out based on those identified representatives from all the chunks. However, most of the incremental approaches are used for single view data. As large multi-view data generated from multiple sources becomes prevalent nowadays, there is a need for incremental clustering approaches to handle both large and multi-view data. In this paper we propose a new incremental clustering approach called incremental minimax optimization based fuzzy clustering (IminimaxFCM) to handle large multi-view data. In IminimaxFCM, representatives with multiple views are identified to represent each cluster by integrating multiple complementary views using minimax optimization. The detailed problem formulation, updating rules derivation, and the in-depth analysis of the proposed IminimaxFCM are provided. Experimental studies on several real world multi-view data sets have been conducted. We observed that IminimaxFCM outperforms related incremental fuzzy clustering in terms of clustering accuracy, demonstrating the great potential of IminimaxFCM for large multi-view data analysis.

When data becomes high-dimensional, the inherent relational structure between the variables can sometimes become unclear or indistinct. One, might want to find clusters for numerous amounts of reasons – me, I want to use it to better understand my childhood. To be more specific, I will be using clustering to highlight different groupings of pokemon. The results of this analysis can then retrospectively be applied to a younger me having to choose which pokemon I catch and keep, or perhaps which I must rather use in battle to gain experience points. The clusters should help me identify groupings of pokemons that assimilate with my style of play, be it catching pokemon who are specialist of their type, strong attackers, survivalist who have good defensive capabilities or pokemon who have the potential to become great as soon as they evolve.

Clustering is a class of Machine Learning Algorithms that looks to determine for clusters that represent similarity between groups of related data they each hold. While it is technically an Unsupervised type algorithm, in that it does not predict for a target variable, its application results in taking data that you might hypothesize has clusters that can categorize groups of related data, and forming clusters that represent data that have similarities. Thus, the effect of Clustering Algorithms could be viewed with the same effect as that of Classification Algorithms (a class type Supervised Algorithm). There are of course a number of type clustering algorithms, one being the K-Means Clustering Algorithm. The algorithm is shown as below.