Functional singular value decomposition and multi-resolution anomaly detection

This dissertation has two major parts. The first part discusses the connections and differences between the statistical tool of Principal Component Analysis (PCA) and the related numerical method of Singular Value Decomposition (SVD), and related visualization methods. The second part proposes a Multi-Resolution Anomaly Detection (MRAD) method for time series with long range dependence (LRD). PCA is a popular method in multivariate analysis and in Functional Data Analysis (FDA). Compared to PCA, SVD is more general, because it not only provides a direct approach to calculate the principal components (PCs), but also simultaneously yields the PCAs for both the row and the column spaces. SVD has been used directly to explore and analyze data sets, and has been shown to be an insightful analysis tool in many fields. However, the connection and differences between PCA and SVD have seldom been explored from a statistical view point. Here we explore the connections and differences between PCA and SVD, and extend the usual SVD method to variations including different centerings based on various types of means. A generalized scree plot is developed to provide a visual aid for selection of different centerings. Several matrix views of the SVD components are introduced to explore different features in data, including SVD surface plots, image plots, rotation movies, and curve movies. These methods visualize both column and row information of a two-way matrix simultaneously, relate the matrix to relevant curves, and show local variations and interactions between columns and rows. Several toy examples are designed iii to compare the different types of centerings, and three real applications are used to illustrate the matrix views. In the field of Internet traffic anomaly detection, different types of network anomalies exist at different time scales. This motivates anomaly detection methods that effectively exploit multiscale properties. Because time series of Internet measurements exhibit long range dependence (LRD) and self-similarity (SS), the classical outlier detection methods base on short-range dependent time series may not be suitable for identifying network anomalies. Based on a time series collected at a single scale (the finest scale), we aggregate to form time series of various scales, and propose a MRAD procedure to find anomalies which appear at different time scales. We show that this MRAD method is more conservative than a typical outlier detection method based on a given scale, and has larger power on average than any single scale outlier detection method based on some reasonable assumptions. Asymptotic distribution of the test statistic is developed as well. An MRAD map is developed to show candidate anomalies and the corresponding significance probabilities (p values). This method can be easily extended to be implemented in real time. Simulations and real examples are reported as well, to illustrate the usefulness of the MRAD method. Keywords: Principal Component Analysis, Functional Data Analysis, Exploratory Data Analysis, Network Intrusion Detection, Outlier detection, Level Shift, Multiscale analysis, Long Range Dependence, Multiple Comparison, p values, Time Series, false discovery rate

Accounting and Statistical Analyses for Sustainable Development

In this Open Access publication Claudia Lemke develops a comprehensive Multi-Level Sustainable Development Index (MLSDI) that is applicable to micro, meso, and macro objects by conducting methodological and empirical research. Multi-level comparability is crucial because the Sustainable Development Goals (SDGs) at macro level can only be achieved if micro and meso objects contribute. The author shows that a novel information-theoretic algorithm outperforms established multivariate statistical weighting methods such as the principal component analysis (PCA). Overcoming further methodological shortcomings of previous sustainable development indices, the MLSDI avoids misled managerial and political decision making

Information-based Preprocessing of PLC Data for Automatic Behavior Modeling

Cyber-physical systems (CPS) offer immense optimization potential for manufacturing processes through the availability of multivariate time series data of actors and sensors. Based on automated analysis software, the deployment of adaptive and responsive measures is possible for time series data. Due to the complex and dynamic nature of modern manufacturing, analysis and modeling often cannot be entirely automated. Even machine- or deep learning approaches often depend on a priori expert knowledge and labelling. In this paper, an information-based data preprocessing approach is proposed. By applying statistical methods including variance and correlation analysis, an approximation of the sampling rate in event-based systems and the utilization of spectral analysis, knowledge about the underlying manufacturing processes can be gained prior to modeling. The paper presents, how statistical analysis enables the pruning of a dataset's least important features and how the sampling rate approximation approach sets the base for further data analysis and modeling. The data's underlying periodicity, originating from the cyclic nature of an automated manufacturing process, will be detected by utilizing the fast Fourier transform. This information-based preprocessing method will then be validated for process time series data of cyber-physical systems' programmable logic controllers (PLC)

Data-analysis strategies for image-based cell profiling

Image-based cell profiling is a high-throughput strategy for the quantification of phenotypic differences among a variety of cell populations. It paves the way to studying biological systems on a large scale by using chemical and genetic perturbations. The general workflow for this technology involves image acquisition with high-throughput microscopy systems and subsequent image processing and analysis. Here, we introduce the steps required to create high-quality image-based (i.e., morphological) profiles from a collection of microscopy images. We recommend techniques that have proven useful in each stage of the data analysis process, on the basis of the experience of 20 laboratories worldwide that are refining their image-based cell-profiling methodologies in pursuit of biological discovery. The recommended techniques cover alternatives that may suit various biological goals, experimental designs, and laboratories' preferences.Peer reviewe

Data Analytics and Performance Enhancement in Edge-Cloud Collaborative Internet of Things Systems

Based on the evolving communications, computing and embedded systems technologies, Internet of Things (IoT) systems can interconnect not only physical users and devices but also virtual services and objects, which have already been applied to many different application scenarios, such as smart home, smart healthcare, and intelligent transportation. With the rapid development, the number of involving devices increases tremendously. The huge number of devices and correspondingly generated data bring critical challenges to the IoT systems. To enhance the overall performance, this thesis aims to address the related technical issues on IoT data processing and physical topology discovery of the subnets self-organized by IoT devices. First of all, the issues on outlier detection and data aggregation are addressed through the development of recursive principal component analysis (R-PCA) based data analysis framework. The framework is developed in a cluster-based structure to fully exploit the spatial correlation of IoT data. Specifically, the sensing devices are gathered into clusters based on spatial data correlation. Edge devices are assigned to the clusters for the R-PCA based outlier detection and data aggregation. The outlier-free and aggregated data are forwarded to the remote cloud server for data reconstruction and storage. Moreover, a data reduction scheme is further proposed to relieve the burden on the trunk link for data uploading by utilizing the temporal data correlation. Kalman filters (KFs) with identical parameters are maintained at the edge and cloud for data prediction. The amount of data uploading is reduced by using the data predicted by the KF in the cloud instead of uploading all the practically measured data. Furthermore, an unmanned aerial vehicle (UAV) assisted IoT system is particularly designed for large-scale monitoring. Wireless sensor nodes are flexibly deployed for environmental sensing and self-organized into wireless sensor networks (WSNs). A physical topology discovery scheme is proposed to construct the physical topology of WSNs in the cloud server to facilitate performance optimization, where the physical topology indicates both the logical connectivity statuses of WSNs and the physical locations of WSN nodes. The physical topology discovery scheme is implemented through the newly developed parallel Metropolis-Hastings random walk based information sampling and network-wide 3D localization algorithms, where UAVs are served as the mobile edge devices and anchor nodes. Based on the physical topology constructed in the cloud, a UAV-enabled spatial data sampling scheme is further proposed to efficiently sample data from the monitoring area by using denoising autoencoder (DAE). By deploying the encoder of DAE at the UAV and decoder in the cloud, the data can be partially sampled from the sensing field and accurately reconstructed in the cloud. In the final part of the thesis, a novel autoencoder (AE) neural network based data outlier detection algorithm is proposed, where both encoder and decoder of AE are deployed at the edge devices. Data outliers can be accurately detected by the large fluctuations in the squared error generated by the data passing through the encoder and decoder of the AE