The number of high-dimensional datasets recording multiple aspects of a single phenomenon is ever increasing in many areas of science. This is accompanied by a fundamental need for mathematical frameworks that can compare data tabulated as multiple large-scale matrices of di erent numbers of rows. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. This thesis addresses this limitation and de fines a higher-order GSVD (HO GSVD) of N > 2 datasets, that provides a mathematical framework that can compare multiple high-dimensional datasets tabulated as large-scale matrices of different numbers of rows. / text

Since their discovery, organic electronic materials have been of great interest as an alternative active layer material for active area materials in electronic applications. Initially studied as probes or lasing material the field has progressed to the point where both conjugated polymers and small organics have become fashionable objects of current device oriented solid state research. Organic electronic materials are liquid crystalline materials, packing into well-ordered domains when annealed thermally or via solvent annealing. The macromolecular orientation of the molecules in the solid state causes a shift in the electronic properties due to coupling of the dipoles. The amount of interaction between molecules can be correlated to different nanoscale morphologies. Such morphologies can be measured using microscopy techniques and compared to the spectroscopic results. This can then be extrapolated out to infer how the charges move within a film. Cyanine dyes represent an interesting form class of dyes as the molecular packing is strongly affected by hydrophilic and hydrophobic pendent groups, which cause the dye to arrange into a tubular bilayer. Spectroelectrochemistry is used to monitor and controllably oxidize the samples. Using singular value decomposition (SVD) it is possible to extract each electronic species formed during electrochemical oxidation and model the proposed species using semi empirical quantum mechanical calculations. Polyfluorene is a blue luminescent polymer of interest for its high quantum yield. The solution and solid-state conformation has shown two distinct phases. The formation of the secondary phase shows a dependence on the molecular weight. In a poor solvent, as the molecular weight increases, the secondary phase forms easier. In the solid state, the highly efficient blue emission from polyfluorene is degraded by ketone defects. The energy transfer to preexisting ketone defects is increased as the filmed is thermally ordered. Glass transitions of block copolymers are studied using synthetically novel polymers where an environmentally sensitive fluorescent reporter is placed within various regions of a self-assembled film. Different dynamics are observed within the block of the film then specifically at the interface of two blocks. / text

Στόχος της εργασίας είναι η μελέτη πιθανοτικών αλγορίθμων για προσεγγιστική επίλυση προβλημάτων του επιστημονικού υπολογισμού. Τα προβλήματα τα οποία θα μας απασχολήσουν είναι ο πολλαπλασιασμός μητρών, ο υπολογισμός της διάσπασης ιδιαζουσών τιμών (SVD) ενός μητρώου και ο υπολογισμός μιας "συμπιεσμένης" διάσπασης ενός μητρώου. / -

The goal of this research was to improve the speed and accuracy of reporting by clinical radiologists. By applying a technique known as eigenimage processing to chest radiographs, abnormal findings were enhanced and a classification scheme developed. Results confirm that the method is feasible for clinical use. Eigenimage processing is a popular face recognition routine that has only recently been applied to medical images, but it has not previously been applied to full size radiographs. Chest radiographs were chosen for this research because they are clinically important and are challenging to process due to their large data content. It is hoped that the success with these images will enable future work on other medical images such as those from CT and MRI. Eigenimage processing is based on a multivariate statistical method which identifies patterns of variance within a training set of images. Specifically it involves the application of a statistical technique called principal components analysis to a training set. For this research, the training set was a collection of 77 normal radiographs. This processing produced a set of basis images, known as eigenimages, that best describe the variance within the training set of normal images. For chest radiographs the basis images may also be referred to as 'eigenchests'. Images to be tested were described in terms of eigenimages. This identified patterns of variance likely to be normal. A new image, referred to as the remainder image, was derived by removing patterns of normal variance, thus making abnormal patterns of variance more conspicuous. The remainder image could either be presented to clinicians or used as part of a computer aided diagnosis system. For the image sets used, the discriminatory power of a classification scheme approached 90%. While the processing of the training set required significant computation time, each test image to be classified or enhanced required only a few seconds to process. Thus the system could be integrated into a clinical radiology department.

The deep web contains a massive number of collections that are mostly invisible to search engines. These collections often contain high-quality, structured information that cannot be crawled using traditional methods. An important problem is selecting which of these collections to search. Automatic collection selection methods try to solve this problem by suggesting the best subset of deep web collections to search based on a query. A few methods for deep Web collection selection have proposed in Collection Retrieval Inference Network system and Glossary of Servers Server system. The drawback in these methods is that they require communication between the search broker and the collections, and need metadata about each collection. This thesis compares three different sampling methods that do not require communication with the broker or metadata about each collection. It also transforms some traditional information retrieval based techniques to this area. In addition, the thesis tests these techniques using INEX collection for total 18 collections (including 12232 XML documents) and total 36 queries. The experiment shows that the performance of sample-based technique is satisfactory in average.

Judgements of and sensitivity to style are ubiquitous. People become sensitive to the structural regularities of complex or “polymorphous” categories through exposure to individual examples, which allows them respond to new items that are of the same style as those previously experienced. This thesis investigates whether a dimension reduction mechanism could account for how people learn about the structure of complex categories. That is, whether through experience, people extract the primary dimensions of variation in a category and use these to analyse and categorise subsequent instances. We used Singular Value Decomposition (SVD) as the method of dimension reduction, which yields the main dimensions of variation of pixel-based stimuli (eigenvectors). We then tested whether a simple autoassociative network could learn to distinguish paintings by Picasso and Braque which were reconstructed from only these primary dimensions of variation. The network could correctly classify the stimuli, and its performance was optimal with reconstructions based on just the first few eigenvectors. Then we reconstructed the paintings using either just the first 10 (early reconstructions) or all 1,894 eigenvectors (full reconstructions), and asked human participants to categorise the images. We found that people could categorise the images with either the early or full reconstructions. Therefore, people could learn to distinguish category membership based on the reduced set of dimensions obtained from SVD. This suggests that a dimension reduction mechanism analogous to SVD may be operating when people learn about the structure and regularities in complex categories.

Judgements of and sensitivity to style are ubiquitous. People become sensitive to the structural regularities of complex or “polymorphous” categories through exposure to individual examples, which allows them respond to new items that are of the same style as those previously experienced. This thesis investigates whether a dimension reduction mechanism could account for how people learn about the structure of complex categories. That is, whether through experience, people extract the primary dimensions of variation in a category and use these to analyse and categorise subsequent instances. We used Singular Value Decomposition (SVD) as the method of dimension reduction, which yields the main dimensions of variation of pixel-based stimuli (eigenvectors). We then tested whether a simple autoassociative network could learn to distinguish paintings by Picasso and Braque which were reconstructed from only these primary dimensions of variation. The network could correctly classify the stimuli, and its performance was optimal with reconstructions based on just the first few eigenvectors. Then we reconstructed the paintings using either just the first 10 (early reconstructions) or all 1,894 eigenvectors (full reconstructions), and asked human participants to categorise the images. We found that people could categorise the images with either the early or full reconstructions. Therefore, people could learn to distinguish category membership based on the reduced set of dimensions obtained from SVD. This suggests that a dimension reduction mechanism analogous to SVD may be operating when people learn about the structure and regularities in complex categories.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23323号 / 情博第759号 / 新制||情||129(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 矢ヶ崎 一幸, 准教授 辻本 諭 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The Polar Decomposition (PD) of a dense matrix is an important operation in linear algebra, while being a building block for solving the Symmetric Eigenvalue Problem (SEP) and computing the Singular Value Decomposition (SVD). It can be directly calculated through the SVD itself, or iteratively using the QR Dynamically-Weighted Halley (QDWH) algorithm. The former is difficult to parallelize due to the preponderant number of memory-bound operations during the bidiagonal reduction. The latter is an iterative method, which performs more floating-point operations than the SVD approach, but exposes at the same time more parallelism. Looking at the roadmap of the hardware technology scaling, algorithms perform- ing floating-point operations on locally cached data should be favored over those requiring expensive horizontal data movement. In this context, this thesis investigates new high-performance algorithmic designs of QDWH algorithm to compute the PD. Originally introduced by Nakatsukasa et al. [1, 2], our algorithmic contributions include mixed precision techniques, task-based formulations, and parallel asynchronous executions. Moreover, by making the PD competitive, its application to the SEP and the SVD becomes practical. In particular, we introduce for the first time new algorithms for partial SVD decomposition using QDWH. By the same token, we extend the QDWH to support partial eigen decomposition for SEP. We present new high-performance implementations of the QDWH-based algorithms relying on fine-grained computations, which allows exploiting the sparsity of the underlying data structure. To demonstrate performance efficiency, portability and scalability, we conduct benchmarking campaigns on some of the latest shared/distributed-memory systems. Our QDWH-based algorithm implementations outperform the state-of-the-art numerical libraries by up to 2.8x and 12x on shared and distributed-memory, respectively. The task-based QDWH has been integrated into the Chameleon library (https://gitlab.inria.fr/solverstack/chameleon) for support on shared-memory systems with hardware accelerators. It is also currently being used by astronomers from the Subaru telescope located at the summit of Mauna Kea, Hawaii, USA. The distributed-memory software library of QDWH and its SVD extension are freely available under modified-BSD license at https: //github.com/ecrc/qdwh.git and https://github.com/ecrc/ksvd.git, respectively. Both software libraries have been integrated into the Cray Scientific numerical library LibSci v17.11.1 and v19.02.1.

Recommender System (RS) has become one of the most important component for many companies, such as YouTube and Amazon. A recommender system consists of a series of algorithms which predict and recommend products to users. This report covers the selection of many open source recommender system projects, and movie predictions are made using the selected recommender system. Based on the predictions, a comparison was made between precision and an improved precision algorithm. The selected RS uses singular value decomposition in the field of collaborative filtering. Based on the recommendation results produced by the RS, the comparison between precision and the improved precision algorithms showed that the result of improved precision is slightly higher than precision in different cutoff values and different dimensions of eigenvalues. / Rekommendationssystem har blivit en av de viktigaste beståndsdelar för många företag, såsom YouTube och Amazon. Ett rekommendationssystem består av en serie av algoritmer som förutsäger och rekommenderar produkter till användare. Denna rapport omfattar valet av många öppen källkod rekommendationssystem projekt, och filmprognoser görs med det valda rekommendationssystemet. Baserat på filmprognoser, gjordes en jämförelse mellan precision och en förbättrad precision algoritmer. Det valda rekommendationssystemet använder singulärvärdesuppdelning som kollaborativ filtrering. Baserat på rekommendationsresultat som produceras av rekommendationssystemet, jämförelsen mellan precision och den förbättrade precisions algoritmer visade att resultatet av förbättrad precision är något högre än precision i olika brytvärden och olika dimensioner av egenvärden.