We propose infinite mixture prototypes to adaptively represent both simple and complex data distributions for few-shot learning. Our infinite mixture prototypes represent each class by a set of clusters, unlike existing prototypical methods that represent each class by a single cluster. By inferring the number of clusters, infinite mixture prototypes interpolate between nearest neighbor and prototypical representations, which improves accuracy and robustness in the few-shot regime. We show the importance of adaptive capacity for capturing complex data distributions such as alphabets, with 25% absolute accuracy improvements over prototypical networks, while still maintaining or improving accuracy on the standard Omniglot and mini-ImageNet benchmarks. In clustering labeled and unlabeled data by the same clustering rule, infinite mixture prototypes achieves state-of-the-art semi-supervised accuracy. As a further capability, we show that infinite mixture prototypes can perform purely unsupervised clustering, unlike existing prototypical methods.

We describe in this paper the theory and practice behind a new modal clustering method for binary data. Our approach (BinNNMS) is based on the nearest neighbor median shift. The median shift is an extension of the well-known mean shift, which was designed for continuous data, to handle binary data. We demonstrate that BinNNMS can discover accurately the location of clusters in binary data with theoretical and experimental analyses.

In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering which computes arbitrarily shaped clusters as defined as the basins of attraction to the local modes created by the density gradient ascent paths. Despite its potential, the Mean Shift approach is a computationally expensive method for unsupervised learning. Thus, we introduce two contributions aiming to provide clustering algorithms with a linear time complexity, as opposed to the quadratic time complexity for the exact Mean Shift clustering. Firstly we propose a scalable procedure to approximate the density gradient ascent. Second, our proposed scalable cluster labeling technique is presented. Both propositions are based on Locality Sensitive Hashing (LSH) to approximate nearest neighbors. These two techniques may be used for moderate sized datasets. Furthermore, we show that using our proposed approximations of the density gradient ascent as a pre-processing step in other clustering methods can also improve dedicated classification metrics. For the latter, a distributed implementation, written for the Spark/Scala ecosystem is proposed. For all these considered clustering methods, we present experimental results illustrating their labeling accuracy and their potential to solve concrete problems.

The consensus information and complementary information of multi-view data ensure the success of multi-view clustering. Since statistic properties of different views are diverse, even incompatible, few approaches directly implement multi-view clustering based on concatenated features. This paper proposes a novel multi-view subspace clustering approach dubbed Feature Concatenation Multi-view Subspace Clustering (FCMSC), which utilizes the joint view representation of multi-view data so as to leverage both the consensus and complementary information for clustering. Specifically, multi-view data are firstly concatenated into one matrix, which is used to derive a special coefficient matrix enjoying the low-rank property. Then, $l_{2,1}$-norm is integrated into the objective function to deal with the sample-specific and cluster-specific corruptions of multiple views for benefiting the clustering performance. It is noteworthy that the obtained coefficient matrix is not derived by simply applying the Low-Rank Representation (LRR) to the joint view representation. What's more, a novel algorithm based on the Augmented Lagrangian Multiplier (ALM) is designed to optimize the object function. Finally, the spectral clustering algorithm is applied to an adjacency matrix calculated from the coefficient matrix. Comprehensive experiments on six real world datasets illustrate its superiority over several state-of-the-art approaches for multi-view clustering.

This paper documents the release of the ELKI data mining framework, version 0.7.5. ELKI is an open source (AGPLv3) data mining software written in Java. The focus of ELKI is research in algorithms, with an emphasis on unsupervised methods in cluster analysis and outlier detection. In order to achieve high performance and scalability, ELKI offers data index structures such as the R*-tree that can provide major performance gains. ELKI is designed to be easy to extend for researchers and students in this domain, and welcomes contributions of additional methods. ELKI aims at providing a large collection of highly parameterizable algorithms, in order to allow easy and fair evaluation and benchmarking of algorithms. We will first outline the motivation for this release, the plans for the future, and then give a brief overview over the new functionality in this version. We also include an appendix presenting an overview on the overall implemented functionality.

An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for unsupervised machine learning than those based on spectra alone. The regularized diffusion process is subsequently used to embed the high-dimensional HSI into a lower dimensional space through diffusion distances. Cluster modes are computed using density estimation and diffusion distances, and all other points are labeled according to these modes. The proposed method has low computational complexity and performs competitively against state-of-the-art HSI clustering algorithms on real data. In particular, the proposed spatial regularization confers an empirical advantage over non-regularized methods.

Deep image clustering is a recent research area, but with exciting published works [15]. The approaches use the most diverse architectures varying the structure of the deep networks, theclustering algorithms and the combination of both parts. Approachessuch as the Deep Clustering Network (DCN) [9] use a pretrained autoencoder combined with the k-means algorithm. Methods such as Joint Unsupervised Learning (JULE) [10] combines deep convolutional networks with hierarchical clustering. Deep Embbed Cluster (DEC) [11], also uses a pretrained autoencoder, then removes the decoder part and uses the encoder as a feature extractor to feed the clustering method. After that, the network is fine-tuned using the cluster assignment hardening loss. Meanwhile, the clusters are iteratively tuned by minimizing the KL-divergence between the distribution of soft labels and the auxiliary target distribution.

This paper introduces Bounded Fuzzy Possibilistic Method (BFPM) by addressing several issues that previous clustering/classification methods have not considered. In fuzzy clustering, object's membership values should sum to 1. Hence, any object may obtain full membership in at most one cluster. Possibilistic clustering methods remove this restriction. However, BFPM differs from previous fuzzy and possibilistic clustering approaches by allowing the membership function to take larger values with respect to all clusters. Furthermore, in BFPM, a data object can have full membership in multiple clusters or even in all clusters. BFPM relaxes the boundary conditions (restrictions) in membership assignment. The proposed methodology satisfies the necessity of obtaining full memberships and overcomes the issues with conventional methods on dealing with overlapping. Analysing the objects' movements from their own cluster to another (mutation) is also proposed in this paper. BFPM has been applied in different domains in geometry, set theory, anomaly detection, risk management, diagnosis diseases, and other disciplines. Validity and comparison indexes have been also used to evaluate the accuracy of BFPM. BFPM has been evaluated in terms of accuracy, fuzzification constant (different norms), objects' movement analysis, and covering diversity. The promising results prove the importance of considering the proposed methodology in learning methods to track the behaviour of data objects, in addition to obtain accurate results.

With the dawn of the Big Data era, data sets are growing rapidly. Data is streaming from everywhere - from cameras, mobile phones, cars, and other electronic devices. Clustering streaming data is a very challenging problem. Unlike the traditional clustering algorithms where the dataset can be stored and scanned multiple times, clustering streaming data has to satisfy constraints such as limit memory size, real-time response, unknown data statistics and an unknown number of clusters. In this paper, we present a novel online clustering algorithm which can be used to cluster streaming data without knowing the number of clusters a priori. Results on both synthetic and real datasets show that the proposed algorithm produces partitions which are close to what you could get if you clustered the whole data at one time.

We consider the $k$-means clustering problem in the dynamic streaming setting, where points from a discrete Euclidean space $\{1, 2, \ldots, \Delta\}^d$ can be dynamically inserted to or deleted from the dataset. For this problem, we provide a one-pass coreset construction algorithm using space $\tilde{O}(k\cdot \mathrm{poly}(d, \log\Delta))$, where $k$ is the target number of centers. To our knowledge, this is the first dynamic geometric data stream algorithm for $k$-means using space polynomial in dimension and nearly optimal (linear) in $k$.