Multi-view data, in which data of different types are obtained from a common set of samples, is now common in many scientific problems. An important problem in the analysis of multi-view data is identifying interactions between groups of features from different data types. A bimodule is a pair $(A,B)$ of feature sets from two different data types such that the aggregate cross-correlation between the features in $A$ and those in $B$ is large. A bimodule $(A,B)$ is stable if $A$ coincides with the set of features having significant aggregate correlation with the features in $B$, and vice-versa. At the population level, stable bimodules correspond to connected components of the cross-correlation network, which is the bipartite graph whose edges are pairs of features with non-zero cross-correlations. We develop an iterative, testing-based procedure, called BSP, to identify stable bimodules in two moderate- to high-dimensional data sets. BSP relies on permutation-based p-values for sums of squared cross-correlations. We efficiently approximate the p-values using tail probabilities of gamma distributions that are fit using analytical estimates of the permutation moments of the test statistic. Our moment estimates depend on the eigenvalues of the intra-correlation matrices of $A$ and $B$ and as a result, the significance of observed cross-correlations accounts for the correlations within each data type. We carry out a thorough simulation study to assess the performance of BSP, and present an extended application of BSP to the problem of expression quantitative trait loci (eQTL) analysis using recent data from the GTEx project. In addition, we apply BSP to climatology data in order to identify regions in North America where annual temperature variation affects precipitation.

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale data, as the distance varies a lot for clusters with different densities. State of the art(ROSC and CAST ) addresses this limitation by taking the reachability similarity of objects into account. However, we observe that in real-world scenarios, data in the same cluster tend to present in a smooth manner, and previous algorithms never take this into account. Based on this observation, we propose a novel clustering algorithm, which con-siders the smoothness of data for the first time. We first divide objects into a great many tiny clusters. Our key idea is to cluster tiny clusters, whose centers constitute smooth graphs. Theoretical analysis and experimental results show that our clustering algorithm significantly outperforms state of the art. Although in this paper, we singly focus on multi-scale situations, the idea of data smoothness can certainly be extended to any clustering algorithms

Clustering algorithms play a fundamental role as tools in decision-making and sensible automation processes. Due to the widespread use of these applications, a robustness analysis of this family of algorithms against adversarial noise has become imperative. To the best of our knowledge, however, only a few works have currently addressed this problem. In an attempt to fill this gap, in this work, we propose a black-box adversarial attack for crafting adversarial samples to test the robustness of clustering algorithms. We formulate the problem as a constrained minimization program, general in its structure and customizable by the attacker according to her capability constraints. We do not assume any information about the internal structure of the victim clustering algorithm, and we allow the attacker to query it as a service only. In the absence of any derivative information, we perform the optimization with a custom approach inspired by the Abstract Genetic Algorithm (AGA). In the experimental part, we demonstrate the sensibility of different single and ensemble clustering algorithms against our crafted adversarial samples on different scenarios. Furthermore, we perform a comparison of our algorithm with a state-of-the-art approach showing that we are able to reach or even outperform its performance. Finally, to highlight the general nature of the generated noise, we show that our attacks are transferable even against supervised algorithms such as SVMs, random forests and neural networks.

Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of producing exclusive row and column biclusters. We provide a new formulation of the biclustering problem based on the idea of minimizing the empirical clustering risk. We develop and prove a consistency result with respect to the empirical clustering risk. Since the optimization problem is combinatorial in nature, finding the global minimum is computationally intractable. In light of this fact, we propose a simple and novel algorithm that finds a local minimum by alternating the use of an adapted version of the k-means clustering algorithm between columns and rows. We evaluate and compare the performance of our algorithm to other related biclustering methods on both simulated data and real-world gene expression data sets. The results demonstrate that our algorithm is able to detect meaningful structures in the data and outperform other competing biclustering methods in various settings and situations.

Deep Metric Learning (DML) approaches learn to represent inputs to a lower-dimensional latent space such that the distance between representations in this space corresponds with a predefined notion of similarity. This paper investigates how the mapping element of DML may be exploited in situations where the salient features in arbitrary classification problems vary over time or due to changing underlying variables. Examples of such variable features include seasonal and time-of-day variations in outdoor scenes in place recognition tasks for autonomous navigation and age/gender variations in human/animal subjects in classification tasks for medical/ethological studies. Through the use of visualisation tools for observing the distribution of DML representations per each query variable for which prior information is available, the influence of each variable on the classification task may be better understood. Based on these relationships, prior information on these salient background variables may be exploited at the inference stage of the DML approach by using a clustering algorithm to improve classification performance. This research proposes such a methodology establishing the saliency of query background variables and formulating clustering algorithms for better separating latent-space representations at run-time. The paper also discusses online management strategies to preserve the quality and diversity of data and the representation of each class in the gallery of embeddings in the DML approach. We also discuss latent works towards understanding the relevance of underlying/multiple variables with DML.

Business processes evolve over time to adapt to changing business environments. This requires continuous monitoring of business processes to gain insights into whether they conform to the intended design or deviate from it. The situation when a business process changes while being analysed is denoted as Concept Drift. Its analysis is concerned with studying how a business process changes, in terms of detecting and localising changes and studying the effects of the latter. Concept drift analysis is crucial to enable early detection and management of changes, that is, whether to promote a change to become part of an improved process, or to reject the change and make decisions to mitigate its effects. Despite its importance, there exists no comprehensive framework for analysing concept drift types, affected process perspectives, and granularity levels of a business process. This article proposes the CONcept Drift Analysis in Process Mining (CONDA-PM) framework describing phases and requirements of a concept drift analysis approach. CONDA-PM was derived from a Systematic Literature Review (SLR) of current approaches analysing concept drift. We apply the CONDA-PM framework on current approaches to concept drift analysis and evaluate their maturity. Applying CONDA-PM framework highlights areas where research is needed to complement existing efforts.

Nonnegative matrix factorization is usually powerful for learning the "shallow" parts-based representation, but it clearly fails to discover deep hierarchical information within both the basis and representation spaces. In this paper, we technically propose a new enriched prior based Dual-constrained Deep Semi-Supervised Coupled Factorization Network, called DS2CF-Net, for learning the hierarchical coupled representations. To ex-tract hidden deep features, DS2CF-Net is modeled as a deep-structure and geometrical structure-constrained neural network. Specifically, DS2CF-Net designs a deep coupled factorization architecture using multi-layers of linear transformations, which coupled updates the bases and new representations in each layer. To improve the discriminating ability of learned deep representations and deep coefficients, our network clearly considers enriching the supervised prior by the joint deep coefficients-regularized label prediction, and incorporates enriched prior information as additional label and structure constraints. The label constraint can enable the samples of the same label to have the same coordinate in the new feature space, while the structure constraint forces the coefficient matrices in each layer to be block-diagonal so that the enhanced prior using the self-expressive label propagation are more accurate. Our network also integrates the adaptive dual-graph learning to retain the local manifold structures of both the data manifold and feature manifold by minimizing the reconstruction errors in each layer. Extensive experiments on several real databases demonstrate that our DS2CF-Net can obtain state-of-the-art performance for representation learning and clustering.

Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited. In this work, a system developed for a leading provider of cloud computing combining both user segmentation and demand forecasting is presented. It consists of a TDA-based clustering method for time series inspired by a popular managerial framework for customer segmentation and extended to the case of clusterwise regression using matrix factorization methods to forecast demand. Increasing customer loyalty and producing accurate forecasts remain active topics of discussion both for researchers and managers. Using a public and a novel proprietary data set of commercial data, this research shows that the proposed system enables analysts to both cluster their user base and plan demand at a granular level with significantly higher accuracy than a state of the art baseline. This work thus seeks to introduce TDA-based clustering of time series and clusterwise regression with matrix factorization methods as viable tools for the practitioner.

Machine learning is an important Artificial Intelligence technique that can perform a task effectively by learning through experience. According to Forbes, machine learning will replace 25% of the jobs within the next 10 years. One of the most popular real-world applications of Machine Learning is classification. It corresponds to a task that occurs commonly in everyday life. For example, a hospital may want to classify medical patients into those who are at high, medium or low risk of acquiring a certain illness, an opinion polling company may wish to classify people interviewed into those who are likely to vote for each of several political parties or are undecided, or we may wish to classify a student project as distinction, merit, pass or fail.

More and more diseases have been found to be strongly correlated with disturbances in the microbiome constitution, e.g., obesity, diabetes, or some cancer types. Thanks to modern high-throughput omics technologies, it becomes possible to directly analyze human microbiome and its influence on the health status. Microbial communities are monitored over long periods of time and the associations between their members are explored. These relationships can be described by a time-evolving graph. In order to understand responses of the microbial community members to a distinct range of perturbations such as antibiotics exposure or diseases and general dynamical properties, the time-evolving graph of the human microbial communities has to be analyzed. This becomes especially challenging due to dozens of complex interactions among microbes and metastable dynamics. The key to solving this problem is the representation of the time-evolving graphs as fixed-length feature vectors preserving the original dynamics. We propose a method for learning the embedding of the time-evolving graph that is based on the spectral analysis of transfer operators and graph kernels. We demonstrate that our method can capture temporary changes in the time-evolving graph on both created synthetic data and real-world data. Our experiments demonstrate the efficacy of the method. Furthermore, we show that our method can be applied to human microbiome data to study dynamic processes.