Estimating Dependency, Monitoring and Knowledge Discovery in High-Dimensional Data Streams

Data Mining – known as the process of extracting knowledge from massive data sets – leads to phenomenal impacts on our society, and now affects nearly every aspect of our lives: from the layout in our local grocery store, to the ads and product recommendations we receive, the availability of treatments for common diseases, the prevention of crime, or the efficiency of industrial production processes. However, Data Mining remains difficult when (1) data is high-dimensional, i.e., has many attributes, and when (2) data comes as a stream. Extracting knowledge from high-dimensional data streams is impractical because one must cope with two orthogonal sets of challenges. On the one hand, the effects of the so-called "curse of dimensionality" bog down the performance of statistical methods and yield to increasingly complex Data Mining problems. On the other hand, the statistical properties of data streams may evolve in unexpected ways, a phenomenon known in the community as "concept drift". Thus, one needs to update their knowledge about data over time, i.e., to monitor the stream. While previous work addresses high-dimensional data sets and data streams to some extent, the intersection of both has received much less attention. Nevertheless, extracting knowledge in this setting is advantageous for many industrial applications: identifying patterns from high-dimensional data streams in real-time may lead to larger production volumes, or reduce operational costs. The goal of this dissertation is to bridge this gap. We first focus on dependency estimation, a fundamental task of Data Mining. Typically, one estimates dependency by quantifying the strength of statistical relationships. We identify the requirements for dependency estimation in high-dimensional data streams and propose a new estimation framework, Monte Carlo Dependency Estimation (MCDE), that fulfils them all. We show that MCDE leads to efficient dependency monitoring. Then, we generalise the task of monitoring by introducing the Scaling Multi-Armed Bandit (S-MAB) algorithms, extending the Multi-Armed Bandit (MAB) model. We show that our algorithms can efficiently monitor statistics by leveraging user-specific criteria. Finally, we describe applications of our contributions to Knowledge Discovery. We propose an algorithm, Streaming Greedy Maximum Random Deviation (SGMRD), which exploits our new methods to extract patterns, e.g., outliers, in high-dimensional data streams. Also, we present a new approach, that we name kj-Nearest Neighbours (kj-NN), to detect outlying documents within massive text corpora. We support our algorithmic contributions with theoretical guarantees, as well as extensive experiments against both synthetic and real-world data. We demonstrate the benefits of our methods against real-world use cases. Overall, this dissertation establishes fundamental tools for Knowledge Discovery in high-dimensional data streams, which help with many applications in the industry, e.g., anomaly detection, or predictive maintenance. To facilitate the application of our results and future research, we publicly release our implementations, experiments, and benchmark data via open-source platforms

Multi-purpose exploratory mining of complex data

Due to the increasing power of data acquisition and data storage technologies, a large amount of data sets with complex structure are collected in the era of data explosion. Instead of simple representations by low-dimensional numerical features, such data sources range from high-dimensional feature spaces to graph data describing relationships among objects. Many techniques exist in the literature for mining simple numerical data but only a few approaches touch the increasing challenge of mining complex data, such as high-dimensional vectors of non-numerical data type, time series data, graphs, and multi-instance data where each object is represented by a finite set of feature vectors. Besides, there are many important data mining tasks for high-dimensional data, such as clustering, outlier detection, dimensionality reduction, similarity search, classification, prediction and result interpretation. Many algorithms have been proposed to solve these tasks separately, although in some cases they are closely related. Detecting and exploiting the relationships among them is another important challenge. This thesis aims to solve these challenges in order to gain new knowledge from complex high-dimensional data. We propose several new algorithms combining different data mining tasks to acquire novel knowledge from complex high-dimensional data: ROCAT (Relevant Overlapping Subspace Clusters on Categorical Data) automatically detects the most relevant overlapping subspace clusters on categorical data. It integrates clustering, feature selection and pattern mining without any input parameters in an information theoretic way. The next algorithm MSS (Multiple Subspace Selection) finds multiple low-dimensional subspaces for moderately high-dimensional data, each exhibiting an interesting cluster structure. For better interpretation of the results, MSS visualizes the clusters in multiple low-dimensional subspaces in a hierarchical way. SCMiner (Summarization-Compression Miner) focuses on bipartite graph data, which integrates co-clustering, graph summarization, link prediction, and the discovery of the hidden structure of a bipartite graph data on the basis of data compression. Finally, we propose a novel similarity measure for multi-instance data. The Probabilistic Integral Metric (PIM) is based on a probabilistic generative model requiring few assumptions. Experiments demonstrate the effectiveness and efficiency of PIM for similarity search (multi-instance data indexing with M-tree), explorative data analysis and data mining (multi-instance classification). To sum up, we propose algorithms combining different data mining tasks for complex data with various data types and data structures to discover the novel knowledge hidden behind the complex data

On the challenges and opportunities in visualization for machine learning and knowledge extraction: A research agenda

We describe a selection of challenges at the intersection of machine learning and data visualization and outline a subjective research agenda based on professional and personal experience. The unprecedented increase in the amount, variety and the value of data has been significantly transforming the way that scientific research is carried out and businesses operate. Within data science, which has emerged as a practice to enable this data-intensive innovation by gathering together and advancing the knowledge from fields such as statistics, machine learning, knowledge extraction, data management, and visualization, visualization plays a unique and maybe the ultimate role as an approach to facilitate the human and computer cooperation, and to particularly enable the analysis of diverse and heterogeneous data using complex computational methods where algorithmic results are challenging to interpret and operationalize. Whilst algorithm development is surely at the center of the whole pipeline in disciplines such as Machine Learning and Knowledge Discovery, it is visualization which ultimately makes the results accessible to the end user. Visualization thus can be seen as a mapping from arbitrarily high-dimensional abstract spaces to the lower dimensions and plays a central and critical role in interacting with machine learning algorithms, and particularly in interactive machine learning (iML) with including the human-in-the-loop. The central goal of the CD-MAKE VIS workshop is to spark discussions at this intersection of visualization, machine learning and knowledge discovery and bring together experts from these disciplines. This paper discusses a perspective on the challenges and opportunities in this integration of these discipline and presents a number of directions and strategies for further research

MultiLink Analysis: Brain Network Comparison via Sparse Connectivity Analysis

Abstract The analysis of the brain from a connectivity perspective is revealing novel insights into brain structure and function. Discovery is, however, hindered by the lack of prior knowledge used to make hypotheses. Additionally, exploratory data analysis is made complex by the high dimensionality of data. Indeed, to assess the effect of pathological states on brain networks, neuroscientists are often required to evaluate experimental effects in case-control studies, with hundreds of thousands of connections. In this paper, we propose an approach to identify the multivariate relationships in brain connections that characterize two distinct groups, hence permitting the investigators to immediately discover the subnetworks that contain information about the differences between experimental groups. In particular, we are interested in data discovery related to connectomics, where the connections that characterize differences between two groups of subjects are found. Nevertheless, those connections do not necessarily maximize the accuracy in classification since this does not guarantee reliable interpretation of specific differences between groups. In practice, our method exploits recent machine learning techniques employing sparsity to deal with weighted networks describing the whole-brain macro connectivity. We evaluated our technique on functional and structural connectomes from human and murine brain data. In our experiments, we automatically identified disease-relevant connections in datasets with supervised and unsupervised anatomy-driven parcellation approaches and by using high-dimensional datasets

Multimodal Data Fusion and Quantitative Analysis for Medical Applications

Medical big data is not only enormous in its size, but also heterogeneous and complex in its data structure, which makes conventional systems or algorithms difficult to process. These heterogeneous medical data include imaging data (e.g., Positron Emission Tomography (PET), Computerized Tomography (CT), Magnetic Resonance Imaging (MRI)), and non-imaging data (e.g., laboratory biomarkers, electronic medical records, and hand-written doctor notes). Multimodal data fusion is an emerging vital field to address this urgent challenge, aiming to process and analyze the complex, diverse and heterogeneous multimodal data. The fusion algorithms bring great potential in medical data analysis, by 1) taking advantage of complementary information from different sources (such as functional-structural complementarity of PET/CT images) and 2) exploiting consensus information that reflects the intrinsic essence (such as the genetic essence underlying medical imaging and clinical symptoms). Thus, multimodal data fusion benefits a wide range of quantitative medical applications, including personalized patient care, more optimal medical operation plan, and preventive public health. Though there has been extensive research on computational approaches for multimodal fusion, there are three major challenges of multimodal data fusion in quantitative medical applications, which are summarized as feature-level fusion, information-level fusion and knowledge-level fusion: • Feature-level fusion. The first challenge is to mine multimodal biomarkers from high-dimensional small-sample multimodal medical datasets, which hinders the effective discovery of informative multimodal biomarkers. Specifically, efficient dimension reduction algorithms are required to alleviate "curse of dimensionality" problem and address the criteria for discovering interpretable, relevant, non-redundant and generalizable multimodal biomarkers. • Information-level fusion. The second challenge is to exploit and interpret inter-modal and intra-modal information for precise clinical decisions. Although radiomics and multi-branch deep learning have been used for implicit information fusion guided with supervision of the labels, there is a lack of methods to explicitly explore inter-modal relationships in medical applications. Unsupervised multimodal learning is able to mine inter-modal relationship as well as reduce the usage of labor-intensive data and explore potential undiscovered biomarkers; however, mining discriminative information without label supervision is an upcoming challenge. Furthermore, the interpretation of complex non-linear cross-modal associations, especially in deep multimodal learning, is another critical challenge in information-level fusion, which hinders the exploration of multimodal interaction in disease mechanism. • Knowledge-level fusion. The third challenge is quantitative knowledge distillation from multi-focus regions on medical imaging. Although characterizing imaging features from single lesions using either feature engineering or deep learning methods have been investigated in recent years, both methods neglect the importance of inter-region spatial relationships. Thus, a topological profiling tool for multi-focus regions is in high demand, which is yet missing in current feature engineering and deep learning methods. Furthermore, incorporating domain knowledge with distilled knowledge from multi-focus regions is another challenge in knowledge-level fusion. To address the three challenges in multimodal data fusion, this thesis provides a multi-level fusion framework for multimodal biomarker mining, multimodal deep learning, and knowledge distillation from multi-focus regions. Specifically, our major contributions in this thesis include: • To address the challenges in feature-level fusion, we propose an Integrative Multimodal Biomarker Mining framework to select interpretable, relevant, non-redundant and generalizable multimodal biomarkers from high-dimensional small-sample imaging and non-imaging data for diagnostic and prognostic applications. The feature selection criteria including representativeness, robustness, discriminability, and non-redundancy are exploited by consensus clustering, Wilcoxon filter, sequential forward selection, and correlation analysis, respectively. SHapley Additive exPlanations (SHAP) method and nomogram are employed to further enhance feature interpretability in machine learning models. • To address the challenges in information-level fusion, we propose an Interpretable Deep Correlational Fusion framework, based on canonical correlation analysis (CCA) for 1) cohesive multimodal fusion of medical imaging and non-imaging data, and 2) interpretation of complex non-linear cross-modal associations. Specifically, two novel loss functions are proposed to optimize the discovery of informative multimodal representations in both supervised and unsupervised deep learning, by jointly learning inter-modal consensus and intra-modal discriminative information. An interpretation module is proposed to decipher the complex non-linear cross-modal association by leveraging interpretation methods in both deep learning and multimodal consensus learning. • To address the challenges in knowledge-level fusion, we proposed a Dynamic Topological Analysis framework, based on persistent homology, for knowledge distillation from inter-connected multi-focus regions in medical imaging and incorporation of domain knowledge. Different from conventional feature engineering and deep learning, our DTA framework is able to explicitly quantify inter-region topological relationships, including global-level geometric structure and community-level clusters. K-simplex Community Graph is proposed to construct the dynamic community graph for representing community-level multi-scale graph structure. The constructed dynamic graph is subsequently tracked with a novel Decomposed Persistence algorithm. Domain knowledge is incorporated into the Adaptive Community Profile, summarizing the tracked multi-scale community topology with additional customizable clinically important factors

Mapping Big Data into Knowledge Space with Cognitive Cyber-Infrastructure

Big data research has attracted great attention in science, technology, industry and society. It is developing with the evolving scientific paradigm, the fourth industrial revolution, and the transformational innovation of technologies. However, its nature and fundamental challenge have not been recognized, and its own methodology has not been formed. This paper explores and answers the following questions: What is big data? What are the basic methods for representing, managing and analyzing big data? What is the relationship between big data and knowledge? Can we find a mapping from big data into knowledge space? What kind of infrastructure is required to support not only big data management and analysis but also knowledge discovery, sharing and management? What is the relationship between big data and science paradigm? What is the nature and fundamental challenge of big data computing? A multi-dimensional perspective is presented toward a methodology of big data computing.Comment: 59 page

Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment