Distributional (or distribution-valued) data are a new type of data arising from several sources and are considered as realizations of distributional variables. A new set of fuzzy c-means algorithms for data described by distributional variables is proposed. The algorithms use the $L2$ Wasserstein distance between distributions as dissimilarity measures. Beside the extension of the fuzzy c-means algorithm for distributional data, and considering a decomposition of the squared $L2$ Wasserstein distance, we propose a set of algorithms using different automatic way to compute the weights associated with the variables as well as with their components, globally or cluster-wise. The relevance weights are computed in the clustering process introducing product-to-one constraints. The relevance weights induce adaptive distances expressing the importance of each variable or of each component in the clustering process, acting also as a variable selection method in clustering. We have tested the proposed algorithms on artificial and real-world data. Results confirm that the proposed methods are able to better take into account the cluster structure of the data with respect to the standard fuzzy c-means, with non-adaptive distances.

Faced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learning problem, we show how we can strategically summarize the data (control space) in order to trade off risk and time when data is generated by a probabilistic model. Our summarization is based on coreset constructions from computational geometry. We also develop an algorithm, TRAM, to navigate the space/time/data/risk tradeoff in practice. In particular, we show that for a fixed risk (or data size), as the data size increases (resp. risk increases) the running time of TRAM decreases. Our extensive experiments on real data sets demonstrate the existence and practical utility of such tradeoffs, not only for k-means but also for Gaussian Mixture Models.

We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family of high dimensional latent variable models, including high dimensional Gaussian mixture and mixtures of sparse regressions. A thorough theoretical investigation is further conducted. In particular, we show that the final decomposition estimator is guaranteed to achieve a local statistical rate, and further strengthen it to the global statistical rate by introducing a proper initialization procedure. In high dimensional regimes, the obtained statistical rate significantly improves those shown in the existing non-sparse decomposition methods. The empirical advantages of TTP are confirmed in extensive simulated results and two real applications of click-through rate prediction and high-dimensional gene clustering.

The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data encoded as normalized vectors, so that their "direction" is more important than their magnitude. Specifically, we consider high-dimensional vectors that lie either on the surface of the unit hypersphere or on the real projective plane. For such data, we briefly review common mathematical models prevalent in machine learning, while also outlining some technical aspects, software, applications, and open mathematical challenges.

In this paper we present a method for learning a discriminative classifier from unlabeled or partially labeled data. Our approach is based on an objective function that trades-off mutual information between observed examples and their predicted categorical class distribution, against robustness of the classifier to an adversarial generative model. The resulting algorithm can either be interpreted as a natural generalization of the generative adversarial networks (GAN) framework or as an extension of the regularized information maximization (RIM) framework to robust classification against an optimal adversary. We empirically evaluate our method - which we dub categorical generative adversarial networks (or CatGAN) - on synthetic data as well as on challenging image classification tasks, demonstrating the robustness of the learned classifiers. We further qualitatively assess the fidelity of samples generated by the adversarial generator that is learned alongside the discriminative classifier, and identify links between the CatGAN objective and discriminative clustering algorithms (such as RIM).

Clustering is a standard technique for exploratory data analysis that finds applications across different disciplines such as computer science, biology, marketing, and social science. The goal of clustering is to group a set of unlabeled data points into several clusters based on some notion of dissimilarity. Inspired by the success of classifier ensembles, consensus clustering has emerged as a research topic [8, 23]. Consensus clustering first generates several partitions of the same dataset. Then it combines the sample partitions to a single consensus partition. The assumption is that a consensus partition better fits to the hidden structure in the data than individual partitions. One standard approach of consensus clustering combines the sample partitions to a mean partition [3, 4, 5, 6, 9, 17, 20, 21, 22].

This paper presents a neural network-based end-to-end clustering framework. We design a novel strategy to utilize the contrastive criteria for pushing data-forming clusters directly from raw data, in addition to learning a feature embedding suitable for such clustering. The network is trained with weak labels, specifically partial pairwise relationships between data instances. The cluster assignments and their probabilities are then obtained at the output layer by feed-forwarding the data. The framework has the interesting characteristic that no cluster centers need to be explicitly specified, thus the resulting cluster distribution is purely data-driven and no distance metrics need to be predefined. The experiments show that the proposed approach beats the conventional two-stage method (feature embedding with k-means) by a significant margin. It also compares favorably to the performance of the standard cross entropy loss for classification. Robustness analysis also shows that the method is largely insensitive to the number of clusters. Specifically, we show that the number of dominant clusters is close to the true number of clusters even when a large k is used for clustering.

Any author would like to know if his/her article will be successful or not. Here is an attempt to deal with this task. We crawled 5000 URLs and for each URL we downloaded the title, body of the article and parameters: number of likes (not including Facebook likes), number of comments, number of views, article creation date and date of the last comment. First, we got rid of empty (or deleted), very short (less than 100 characters long) and "not found" articles, thus getting 2000 articles with associated parameters. Then we removed articles with missing parameters and ended up with only 1207 articles. Second, for every article we conducted tokenization of words.

Abstract--Clustering explores meaningful patterns in the non-labeled data sets. Cluster Ensemble Selection (CES) is a new approach, which can combine individual clustering results for increasing the performance of the final results. Although CES can achieve better final results in comparison with individual clustering algorithms and cluster ensemble methods, its performance can be dramatically affected by its consensus diversity metric and thresholding procedure. There are two problems in CES: 1) most of the diversity metrics is based on heuristic Shannon's entropy and 2) estimating threshold values are really hard in practice. The main goal of this paper is proposing a robust approach for solving the above mentioned problems. Accordingly, this paper develops a novel framework for clustering problems, which is called Weighted Spectral Cluster Ensemble (WSCE), by exploiting some concepts from community detection arena and graph based clustering. Under this framework, a new version of spectral clustering, which is called Two Kernels Spectral Clustering, is used for generating graphs based individual clustering results. Further, by using modularity, which is a famous metric in the community detection, on the transformed graph representation of individual clustering results, our approach provides an effective diversity estimation for individual clustering results. Moreover, this paper introduces a new approach for combining the evaluated individual clustering results without the procedure of thresh-olding. Experimental study on varied data sets demonstrates that the prosed approach achieves superior performance to state-of-the-art methods. Clustering, the art of discovering meaningful patterns in the non-labeled data sets, is one of the main tasks in machine learning.

Google recently open-sourced its Artificial Intelligence/Numerical Computing library called TensorFlow. TensorFlow was developed by members of the Google Brain team, and has the flexibility to run on a variety of platforms – including GPUs and mobile devices. TensorFlow's methodology uses what they called data-flow graphs. As you probably understood, the graphical structure is a way of representing a computational expression in the form of a Tree. Every node is an operation (TensorFlow calls them ops, short for operations).