We present a nonparametric Bayesian method for disease subtype discovery in multi-dimensional cancer data. Our method can simultaneously analyse a wide range of data types, allowing for both agreement and disagreement between their underlying clustering structure. It includes feature selection and infers the most likely number of disease subtypes, given the data. We apply the method to 277 glioblastoma samples from The Cancer Genome Atlas, for which there are gene expression, copy number variation, methylation and microRNA data. We identify 8 distinct consensus subtypes and study their prognostic value for death, new tumour events, progression and recurrence. The consensus subtypes are prognostic of tumour recurrence (log-rank p-value of $3.6 \times 10^{-4}$ after correction for multiple hypothesis tests). This is driven principally by the methylation data (log-rank p-value of $2.0 \times 10^{-3}$) but the effect is strengthened by the other 3 data types, demonstrating the value of integrating multiple data types. Of particular note is a subtype of 47 patients characterised by very low levels of methylation. This subtype has very low rates of tumour recurrence and no new events in 10 years of follow up. We also identify a small gene expression subtype of 6 patients that shows particularly poor survival outcomes. Additionally, we note a consensus subtype that showly a highly distinctive data signature and suggest that it is therefore a biologically distinct subtype of glioblastoma. The code is available from https://sites.google.com/site/multipledatafusion/

An intrinsic problem of classifiers based on machine learning (ML) methods is that their learning time grows as the size and complexity of the training dataset increases. For this reason, it is important to have efficient computational methods and algorithms that can be applied on large datasets, such that it is still possible to complete the machine learning tasks in reasonable time. In this context, we present in this paper a more accurate simple process to speed up ML methods. An unsupervised clustering algorithm is combined with Expectation, Maximization (EM) algorithm to develop an efficient Hidden Markov Model (HMM) training. The idea of the proposed process consists of two steps. In the first step, training instances with similar inputs are clustered and a weight factor which represents the frequency of these instances is assigned to each representative cluster. Dynamic Time Warping technique is used as a dissimilarity function to cluster similar examples. In the second step, all formulas in the classical HMM training algorithm (EM) associated with the number of training instances are modified to include the weight factor in appropriate terms. This process significantly accelerates HMM training while maintaining the same initial, transition and emission probabilities matrixes as those obtained with the classical HMM training algorithm. Accordingly, the classification accuracy is preserved. Depending on the size of the training set, speedups of up to 2200 times is possible when the size is about 100.000 instances. The proposed approach is not limited to training HMMs, but it can be employed for a large variety of MLs methods.

We present a principled approach for detecting overlapping temporal community structure in dynamic networks. Our method is based on the following framework: find the overlapping temporal community structure that maximizes a quality function associated with each snapshot of the network subject to a temporal smoothness constraint. A novel quality function and a smoothness constraint are proposed to handle overlaps, and a new convex relaxation is used to solve the resulting combinatorial optimization problem. We provide theoretical guarantees as well as experimental results that reveal community structure in real and synthetic networks. Our main insight is that certain structures can be identified only when temporal correlation is considered and when communities are allowed to overlap. In general, discovering such overlapping temporal community structure can enhance our understanding of real-world complex networks by revealing the underlying stability behind their seemingly chaotic evolution.

This paper describes a machine induction program (WITT) that attempts to model human categorization. Properties of categories to which human subjects are sensitive includes best or prototypical members, relative contrasts between putative categories, and polymorphy (neither necessary or sufficient features). This approach represents an alternative to usual Artificial Intelligence approaches to generalization and conceptual clustering which tend to focus on necessary and sufficient feature rules, equivalence classes, and simple search and match schemes. WITT is shown to be more consistent with human categorization while potentially including results produced by more traditional clustering schemes. Applications of this approach in the domains of expert systems and information retrieval are also discussed.

The original k-means clustering method works only if the exact vectors representing the data points are known. Therefore calculating the distances from the centroids needs vector operations, since the average of abstract data points is undefined. Existing algorithms can be extended for those cases when the sole input is the distance matrix, and the exact representing vectors are unknown. This extension may be named relational k-means after a notation for a similar algorithm invented for fuzzy clustering. A method is then proposed for generalizing k-means for scenarios when the data points have absolutely no connection with a Euclidean space.

Two features of microtext that challenge language processing tools are addressed in the context of linking messages in the emergency response domain. First, the effect of very short texts on several classifiers is estimated by comparing the results when classifiers are applied to the full text of news reports vs. only the headlines. These experiments demonstrate a decrease of 5 - 20% in accuracy. A second challenging feature of microtexts is their accumulation in real time, which can be massive for sources such as Twitter. A dynamic hierarchical clustering algorithm that clusters messages as they accumulate is described, and a preliminary experiment in clustering tweets is demonstrated.

A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density manifolds) describing the data. The number of manifolds, as well as the shape and dimension of each manifold is automatically inferred. We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function. We show that our model is effective for density estimation, performs better than infinite Gaussian mixture models at recovering the true number of clusters, and produces interpretable summaries of high-dimensional datasets.

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations between the data points followed by spectral clustering. A probabilistic performance analysis shows that this algorithm succeeds even when the subspaces intersect, and when the dimensions of the subspaces scale (up to a log-factor) linearly in the ambient dimension. Moreover, we prove that the algorithm also succeeds for data points that are subject to erasures with the number of erasures scaling (up to a log-factor) linearly in the ambient dimension. Finally, we propose a simple scheme that provably detects outliers.

Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented by three distance functions and to identify the optimal distance function for clustering methods. The proposed K-Means algorithm is compared with K-Means, Static Weighted K-Means (SWK-Means) and Dynamic Weighted K-Means (DWK-Means) algorithm by using Davis Bouldin index, Execution Time and Iteration count methods. Experimental results show that the proposed K-Means algorithm performed better on Iris and Wine dataset when compared with other three clustering methods.

Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and undirected graphs that form a global multilayer graph, where the common vertex set represents the entities and the edges on different layers capture the similarities of the entities in term of the different modalities. In this paper, we address the problem of analyzing multi-layer graphs and propose methods for clustering the vertices by efficiently merging the information provided by the multiple modalities. To this end, we propose to combine the characteristics of individual graph layers using tools from subspace analysis on a Grassmann manifold. The resulting combination can then be viewed as a low dimensional representation of the original data which preserves the most important information from diverse relationships between entities. We use this information in new clustering methods and test our algorithm on several synthetic and real world datasets where we demonstrate superior or competitive performances compared to baseline and state-of-the-art techniques. Our generic framework further extends to numerous analysis and learning problems that involve different types of information on graphs.