<p>We present a technique to identify deviating systems among a group of systems in a</p><p>self-organized way. A compressed representation of each system is used to compute similarity measures, which are combined in an affinity matrix of all systems. Deviation detection and clustering is then used to identify deviating systems based on this affinity matrix.</p><p>The compressed representation is computed with Principal Component Analysis and</p><p>Kernel Principal Component Analysis. The similarity measure between two compressed</p><p>representations is based on the angle between the spaces spanned by the principal</p><p>components, but other methods of calculating a similarity measure are suggested as</p><p>well. The subsequent deviation detection is carried out by computing the probability of</p><p>each system to be observed given all the other systems. Clustering of the systems is</p><p>done with hierarchical clustering and spectral clustering. The whole technique is demonstrated on four data sets of mechanical systems, two of a simulated cooling system and two of human gait. The results show its applicability on these mechanical systems.</p>

A model is developed for the Quanser torsion system available at Control Systems Research Laboratory at Chulalongkorn University. The torsion system is a laboratory equipment that is designed for the study of position control. It consists of a DC motor that drives three inertial loads that are coupled in series with the motor, and where all components are coupled to each other through torsional springs. Several nonlinearities are observed and the most significant one is an offset in the input signal, which is compensated for. Experiments are carried out under feedback as the system is marginally stable. Different input signals are tested and used for system identification. Linear black-box state-space models are then identified using PEM, N4SID and a subspace method made for closed-loop identification, where the last two are the most successful ones. PEM is used in a second step and successfully enhances the parameter estimates from the other algorithms.

We present a technique to identify deviating systems among a group of systems in a self-organized way. A compressed representation of each system is used to compute similarity measures, which are combined in an affinity matrix of all systems. Deviation detection and clustering is then used to identify deviating systems based on this affinity matrix. The compressed representation is computed with Principal Component Analysis and Kernel Principal Component Analysis. The similarity measure between two compressed representations is based on the angle between the spaces spanned by the principal components, but other methods of calculating a similarity measure are suggested as well. The subsequent deviation detection is carried out by computing the probability of each system to be observed given all the other systems. Clustering of the systems is done with hierarchical clustering and spectral clustering. The whole technique is demonstrated on four data sets of mechanical systems, two of a simulated cooling system and two of human gait. The results show its applicability on these mechanical systems.

Subspace clustering identifies the attribute support for each cluster as well as identifying the location and number of clusters. In the most general case, attributes associated with each cluster could be unique. A multi-objective evolutionary method is proposed to identify the unique attribute support of each cluster while detecting its data instances. The proposed algorithm, Symbiotic Evolutionary Subspace Clustering (S-ESC) borrows from symbiosis in the sense that each clustering solution is defined in terms of a host, which is formed by a number of co-evolved cluster centroids (or symbionts). Symbionts define clusters and therefore attribute subspaces, whereas hosts define sets of clusters to constitute a non-degenerate clustering solution. The symbiotic representation of S-ESC is the key to making it scalable to high-dimensional datasets, while a subsampling process makes it scalable to large-scale datasets. Performance of the S-ESC algorithm was found to be robust across a common parameterization utilized throughout.

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This thesis is concerned with subspace identification and its applications for controller performance assessment and process modeling from closed-loop data. A joint input-output closed-loop subspace identification method is developed which provides consistent estimation of the subspace matrices and the noise covariance matrix required for the LQG benchmark curve estimation. Subspace LQG benchmark is also used for performance assessment of the cascade supervisory-regulatory control systems. Three possible scenarios for LQG control design and performance improvement are discussed for this structure. A closed-loop subspace identification method is also provided for estimation of the subspace matrices necessary for performance assessment. A method of direct step model estimation from closed-loop data is provided using subspace identification. The variance calculation required for this purpose can be performed using the proposed method. The variances are used for weighted averaging on the estimated Markov parameters to attenuate the noise influence on the final step response estimation. / Process Control

Indiana University-Purdue University Indianapolis (IUPUI) / Biological functions in cells are highly complicated and heterogenous, and can be reflected by omics data, such as gene expression levels. Detecting subspace structures in omics data and understanding the diversity of the biological processes is essential to the full comprehension of biological mechanisms and complicated biological systems. In this thesis, we are developing novel statistical learning approaches to reveal the subspace structures in omics data. Specifically, we focus on three types of subspace structures: low-rank subspace, sparse subspace and covariates explainable subspace. For low-rank subspace, we developed a semi-supervised model SSMD to detect cell type specific low-rank structures and predict their relative proportions across different tissue samples. SSMD is the first computational tool that utilizes semi-supervised identification of cell types and their marker genes specific to each mouse tissue transcriptomics data, for better understanding of the disease microenvironment and downstream disease mechanism. For sparsity-driven sparse subspace, we proposed a novel positive and unlabeled learning model, namely PLUS, that could identify cancer metastasis related genes, predict cancer metastasis status and specifically address the under-diagnosis issue in studying metastasis potential. We found PLUS predicted metastasis potential at diagnosis have significantly strong association with patient’s progression-free survival in their follow-up data. Lastly, to discover the covariates explainable subspace, we proposed an analytical pipeline based on covariance regression, namely, scCovReg. We utilized scCovReg to detect the pathway level second-order variations using scRNA-Seq data in a statistically powerful manner, and to associate the second-order variations with important subject-level characteristics, such as disease status. In conclusion, we presented a set of state-of-the-art computational solutions for identifying sparse subspaces in omics data, which promise to provide insights into the mechanism in complex diseases.

Globally convergent homotopy methods are used to solve difficult nonlinear systems of equations by tracking the zero curve of a homotopy map. Homotopy curve tracking involves solving a sequence of linear systems, which often vary greatly in difficulty. In this research, a popular iterative solution tool, GMRES(k), is adapted to deal with the sequence of such systems. The proposed adaptive strategy of GMRES(k) allows tuning of the restart parameter k based on the GMRES convergence rate for the given problem. Adaptive GMRES(k) is shown to be superior to several other iterative techniques on analog circuit simulation problems and on postbuckling structural analysis problems. Developing parallel techniques for robust but expensive sequential computations, such as globally convergent homotopy methods, is important. The design of these techniques encompasses the functionality of the iterative method (adaptive GMRES(k)) implemented sequentially and is based on the results of a parallel performance analysis of several implementations. An implementation of adaptive GMRES(k) with Householder reflections in its orthogonalization phase is developed. It is shown that the efficiency of linear system solution by the adaptive GMRES(k) algorithm depends on the change in problem difficulty when the problem is scaled. In contrast, a standard GMRES(k) implementation using Householder reflections maintains a constant efficiency with increase in problem size and number of processors, as concluded analytically and experimentally. The supporting numerical results are obtained on three distributed memory homogeneous parallel architectures: CRAY T3E, Intel Paragon, and IBM SP2. / Ph. D.

Dados de alta dimensão são tipicamente tratados como pertencentes a um único subespaço do espaço onde estão imersos. Entretanto, dados utilizados em aplicações reais estão usualmente distribuídos entre subespaços independentes e com dimensões distintas. Um objeto de estudo surge a partir dessa afirmação: como essa distribuição em subespaços independentes pode auxiliar tarefas de visualização? Por outro lado, se o dado parece estar embaralhado nesse espaço de alta dimensão, como visualizar seus padrões e realizar tarefas como classificação? Podemos, por exemplo, mapear esse dado num outro espaço utilizando uma função capaz de o desembaralhar, de modo que os padrões intrínsecos fiquem mais claros e, assim, facilitando nossa tarefa de visualização ou classificação. Essa Tese apresenta dois estudos que abordam ambos os problemas. Para o primeiro, utilizamos técnicas de subspace clustering para definir, quando existente, a estrutura de subespaços do dado e estudamos como essa informação pode auxiliar em visualizações utilizando projeções multidimensionais. Para o segundo problema, métodos de kernel, bastante conhecidos na literatura, são as ferramentas a nos auxiliar. Utilizamos a medida de similaridade do kernel para desenvolver uma nova técnica de projeção multidimensional capaz de lidar com dados imersos no espaço de características induzido implicitamente pelo kernel. / High-dimensional data are typically handled as laying in a single subspace of the original space. However, data involved in real applications are usually spread around in distinct subspaces which may have different dimensions. We would like to study how the subspace structure information can be used to improve visualization tasks. On the other hand, what if the data is tangled in this high-dimensional space, how to visualize its patterns or how to accomplish classification tasks? One could, for example, map the data in another high-dimensional space using amapping capable of untangle the data making the patterns clear, rendering the visualization or classification an easy task. This dissertation presents an study for both problems pointed out above. For the former, we use subspace clustering techniques to define, when it exists, a subspace structure, studying how this information can be used to support visualization tasks based on multidimensional projections. For the latter problem we employ kernel methods, well known in the literature, as a tool to assist visualization tasks. We use a similarity measure given by the kernel to develop acompletely new multidimensional projection technique capable of dealing with data embedded in the implicit feature space defined by the kernel.

Data mining in high dimensionality almost inevitably faces the consequences of increasing sparsity and declining differentiation between points. This is problematic because we usually exploit these differences for approaches such as clustering and outlier detection. In addition, the exponentially increasing sparsity tends to increase false negatives when clustering. In this thesis, we address the problem of solving high-dimensional problems using low-dimensional solutions. In clustering, we provide a new framework MAXCLUS for finding candidate subspaces and the clusters within them using only two-dimensional clustering. We demonstrate this through an implementation GCLUS that outperforms many state-of-the-art clustering algorithms and is particularly robust with respect to noise. It also handles overlapping clusters and provides either `hard' or `fuzzy' clustering results as desired. In order to handle extremely high dimensional problems, such as genome microarrays, given some sample-level diagnostic labels, we provide a simple but effective classifier GSEP which weights the features so that the most important can be fed to GCLUS. We show that this leads to small numbers of features (e.g. genes) that can distinguish the diagnostic classes and thus are candidates for research for developing therapeutic applications. In the field of outlier detection, several novel algorithms suited to high-dimensional data are presented (T*ENT, T*ROF, FASTOUT). It is shown that these algorithms outperform the state-of-the-art outlier detection algorithms in ranking outlierness for many datasets regardless of whether they contain rare classes or not. Our research into high-dimensional outlier detection has even shown that our approach can be a powerful means of classification for heavily overlapping classes given sufficiently high dimensionality and that this phenomenon occurs solely due to the differences in variance among the classes. On some difficult datasets, this unsupervised approach yielded better separation than the very best supervised classifiers and on other data, the results are competitive with state-of-the-art supervised approaches.kern-1pt The elucidation of this novel approach to classification opens a new field in data mining, classification through differences in variance rather than spatial location. As an appendix, we provide an algorithm for estimating false negative and positive rates so these can be compensated for.