We study Frank-Wolfe algorithms -- standard, pairwise, and away-steps -- for efficient optimization of Dominant Set Clustering. We present a unified and computationally efficient framework to employ the different variants of Frank-Wolfe methods, and we investigate its effectiveness via several experimental studies. In addition, we provide explicit convergence rates for the algorithms in terms of the so-called Frank-Wolfe gap. The theoretical analysis has been specialized to the problem of Dominant Set Clustering and is thus more easily accessible compared to prior work.

Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures, computer graphics, numerical simulation, cryptographics and can be used to make various algorithms cache-oblivious. In this paper, we describe some details of the Hilbert-curve. We define the Hilbert-curve in terms of a finite automaton of Mealy-type which determines from the two-dimensional coordinate space the Hilbert order value and vice versa in a logarithmic number of steps. And we define a context-free grammar to generate the whole curve in a time which is linear in the number of generated coordinate/order value pairs, i.e. a constant time per coordinate pair or order value. We also review two different strategies which enable the generation of curves without the usual restriction to square-like grids where the side-length is a power of two. Finally, we elaborate on a few applications, namely matrix multiplication, Cholesky decomposition, the Floyd-Warshall algorithm, k-Means clustering, and the similarity join.

This article considers "sketched learning," or "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is first constructed by computing carefully chosen nonlinear random features (e.g., random Fourier features) and averaging them over the whole dataset. Parameters are then learned from the sketch, without access to the original dataset. This article surveys the current state-of-the-art in sketched learning, including the main concepts and algorithms, their connections with established signal-processing methods, existing theoretical guarantees---on both information preservation and privacy preservation, and important open problems.

In the R code above, the bluered() function [in gplots package] is used to generate a smoothly varying New What you'll learn to create colorful heatmaps showing the relationship between species and also gene expression levels between samples how to cluster species/genes in the data sets Requirements Description In this video the student will be able to use clustering methods to find clusters in his data. He will also be able to make nice-looking heatmaps using the heatmap and the pheatmap command. Clustering topics such as k-means clustering, PAM clustering, Silhouette plots, and elbow plots will be covered. Minimal familiarity with R coding is required. In this video the student will be able to use clustering methods to find clusters in his data.

We consider a set of points sampled from an unknown probability measure on a Euclidean space, each of which points belongs to one of the finitely many classes. We study the question of querying the class label at a very small number of judiciously chosen points so as to be able to attach the appropriate class label to every point in the set. Our approach is to consider the unknown probability measure as a convex combination of the conditional probabilities for each class. Our technique involves the use of a highly localized kernel constructed from Hermite polynomials, and use them to create a hierarchical estimate of the supports of the constituent probability measures. We do not need to make any assumptions on the nature of any of the probability measures nor know in advance the number of classes involved. We give theoretical guarantees measured by the $F$-score for our classification scheme. Examples include classification in hyper-spectral images, separation of distributions, and MNIST classification.

Autonomous driving systems validation remains one of the biggest challenges car manufacturers must tackle in order to provide safe driverless cars. The high complexity stems from several factors: the multiplicity of vehicles, embedded systems, use cases, and the very high required level of reliability for the driving system to be at least as safe as a human driver. In order to circumvent these issues, large scale simulations reproducing this huge variety of physical conditions are intensively used to test driverless cars. Therefore, the validation step produces a massive amount of data, including many time-indexed ones, to be processed. In this context, building a structure in the feature space is mandatory to interpret the various scenarios. In this work, we propose a new co-clustering approach adapted to high-dimensional time series analysis, that extends the standard model-based co-clustering. The FunCLBM model extends the recently proposed Functional Latent Block Model and allows to create a dependency structure between row and column clusters. This structured partition acts as a feature selection method, that provides several clustering views of a dataset, while discriminating irrelevant features. In this workflow, times series are projected onto a common interpolated low-dimensional frequency space, which allows to optimize the projection basis. In addition, FunCLBM refines the definition of each latent block by performing block-wise dimension reduction and feature selection. We propose a SEM-Gibbs algorithm to infer this model, as well as a dedicated criterion to select the optimal nested partition. Experiments on both simulated and real-case Renault datasets shows the effectiveness of the proposed tools and the adequacy to our use case.

Highlight: This post can come as a very interesting and surprising one. You will see how we can apply a machine learning algorithm on the pixel intensity color with a so-called K-means clustering algorithm. In this way, we would be able to create a compressed version of our image that will have much fewer colors. The picture will be preserved in a lower color resolution, whereas the number of pixels will remain the same. This technique is very exciting, so we hope that you will enjoy it.

Cluster-based information retrieval is one of the Information retrieval(IR) tools that organize, extract features and categorize the web documents according to their similarity. Unlike traditional approaches, cluster-based IR is fast in processing large datasets of document. To improve the quality of retrieved documents, increase the efficiency of IR and reduce irrelevant documents from user search. in this paper, we proposed a (K-means) - Hierarchical Parallel Genetic Algorithms Approach (HPGA) that combines the K-means clustering algorithm with hybrid PG of multi-deme and master/slave PG algorithms. K-means uses to cluster the population to k subpopulations then take most clusters relevant to the query to manipulate in a parallel way by the two levels of genetic parallelism, thus, irrelevant documents will not be included in subpopulations, as a way to improve the quality of results. Three common datasets (NLP, CISI, and CACM) are used to compute the recall, precision, and F-measure averages. Finally, we compared the precision values of three datasets with Genetic-IR and classic-IR. The proposed approach precision improvements with IR-GA were 45% in the CACM, 27% in the CISI, and 25% in the NLP. While, by comparing with Classic-IR, (k-means)-HPGA got 47% in CACM, 28% in CISI, and 34% in NLP.

Finding meaningful clusters in drive-by-download malware data is a particularly difficult task. Malware data tends to contain overlapping clusters with wide variations of cardinality. This happens because there can be considerable similarity between malware samples (some are even said to belong to the same family), and these tend to appear in bursts. Clustering algorithms are usually applied to normalised data sets. However, the process of normalisation aims at setting features with different range values to have a similar contribution to the clustering. It does not favour more meaningful features over those that are less meaningful, an effect one should perhaps expect of the data pre-processing stage. In this paper we introduce a method to deal precisely with the problem above. This is an iterative data pre-processing method capable of aiding to increase the separation between clusters. It does so by calculating the within-cluster degree of relevance of each feature, and then it uses these as a data rescaling factor. By repeating this until convergence our malware data was separated in clear clusters, leading to a higher average silhouette width.

The quality of learned features by representation learning determines the performance of learning algorithms and the related application tasks (such as high-dimensional data clustering). As a relatively new paradigm for representation learning, Concept Factorization (CF) has attracted a great deal of interests in the areas of machine learning and data mining for over a decade. Lots of effective CF based methods have been proposed based on different perspectives and properties, but note that it still remains not easy to grasp the essential connections and figure out the underlying explanatory factors from exiting studies. In this paper, we therefore survey the recent advances on CF methodologies and the potential benchmarks by categorizing and summarizing the current methods. Specifically, we first re-view the root CF method, and then explore the advancement of CF-based representation learning ranging from shallow to deep/multilayer cases. We also introduce the potential application areas of CF-based methods. Finally, we point out some future directions for studying the CF-based representation learning. Overall, this survey provides an insightful overview of both theoretical basis and current developments in the field of CF, which can also help the interested researchers to understand the current trends of CF and find the most appropriate CF techniques to deal with particular applications.