Nonlinear dimensionality reduction

Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa) itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis. Applications of NLDR Consider a dataset represented as a matrix (or a database table), such that each row represents a set of attributes (or features or dimensions) that describe a particular instance of something. If the number of attributes is large, then the space of unique possible rows is exponentially large. Thus, the larger the dimensionality, the more difficult it becomes to sample th

Optimisation des dimensions d’un capteur de force (CentoNewton)

Dara Haftgoli-Bakhtiari

Les dimensions de la première version du capteur CentoNewton (15,24 mm * 15,24 mm) étant beaucoup trop grandes, une production de plus de capteurs sur le même substrat n’était pas possible (36 capteurs par substrat). Une analyse de son layout a été effectuée pour savoir comment ce capteur a été produit et comment il pouvait être amélioré. Une fois l’analyse de layout terminée, un nouveau layout a été dessiné sur le logiciel dans le but de diminuer ses dimensions et par conséquence augmenter sa productivité. Finalement elle a été diminuée d’un côté jusqu’à 12.7 mm. Une fois layout fini, le nouveau capteur a été produit dans différentes épaisseurs, avec différents diélectriques et différentes pâtes à braser. Après avoir produit ces capteurs, ils ont été vérifiés afin de trouver les défauts additionnels éventuellement existants et non trouvés lors de la première analyse théorique. Ils ont par la suite été soumis à différentes forces pour avoir la réponse de ces capteurs et vérifier leur linéarité. En conclusion, nous avons eu des résultats assez convaincants. L’analyse finale a démontré que notre nouveau capteur reste assez linéaire, en sachant que ce capteur à la base n’est pas un capteur très précis.

2012

Domain adaptation using manifold alignment

Maxime Trolliet

Domain adaptation is a major challenge for future remote sensing applications. Both financial and temporal constraints of data acquisition lead to the developing of new techniques able to use knowledge from alternative sources. Different approaches have been developed by considering the statistical properties of images or by modifying already existing classifiers. We propose a intermediary approach of these two kinds of methods by using a manifold alignment technique constrained by similarity between two images. The two images are mapped in a high dimensional latent space which maximizes the proximity of similar elements, thus allowing classification of the images suffering from label scarcity by using the knowledge of the other image. Such a classification offers improvement compared to various used processes.

2012

Low-dimensional data embedding for scalable astronomical imaging in the SKA telescope era

Vijay Kartik

Astronomy is one of the oldest sciences known to humanity. We have been studying celestial objects for millennia, and continue to peer deeper into space in our thirst for knowledge about our origins and the universe that surrounds us. Radio astronomy -- observing celestial objects at radio frequencies -- has helped push the boundaries on the kind of objects we can study. Indeed, some of the most important discoveries about the structure of our universe, like the cosmic microwave background, and entire classes of objects like quasars and pulsars, were made using radio astronomy. Radio interferometers are telescopes made of multiple antennas spread over a distance. Signals detected at different antennas are combined to provide images with much higher resolution and sensitivity than with a traditional single-dish radio telescope. The Square Kilometre Array (SKA) is one such radio interferometer, with plans to have antennas separated by as much as 3000,km. In its quest for ever-higher resolution and ever-wider coverage of the sky, the SKA heralds a data explosion, with an expected acquisition rate of 5,terabits per second. The high data rate fed into the pipeline can be handled with a two-pronged approach -- (i) scalable, parallel imaging algorithms that fully utilize the latest computing technologies like accelerators and distributed clusters, and (ii) dimensionality reduction methods that embed the high-dimensional telescope data to much smaller sizes without losing information and guaranteeing accurate recovery of the images, thereby enabling imaging methods to scale to big data sizes and alleviating heavy loads on pipeline buffers without compromising on the science goals of the SKA. In this thesis we propose fast and robust dimensionality reduction methods that embed data to very low sizes while preserving information present in the original data. These methods are presented in the context of compressed sensing theory and related signal recovery techniques. The effectiveness of the reduction methods is illustrated by coupling them with advanced convex optimization algorithms to solve a sparse recovery problem. Images thus reconstructed from extremely low-sized embedded data are shown to have quality comparable to those obtained from full data without any reduction. Comparisons with other standard `data compression' techniques in radio interferometry (like averaging) show a clear advantage in using our methods which provide higher quality images from much lower data sizes. We confirm these claims on both synthetic data simulating SKA data patterns as well as actual telescope data from a state-of-the-art radio interferometer. Additionally, imaging with reduced data is shown to have a lighter computational load -- smaller memory footprint owing to the size and faster iterative image recovery owing to the fast embedding. Extensions to the work presented in this thesis are already underway. We propose an `on-line' version of our reduction methods that works on blocks of data and thus can be applied on-the-fly on data as they are being acquired by telescopes in real-time. This is of immediate interest to the SKA where large buffers in the data acquisition pipeline are very expensive and thus undesirable. Some directions to be probed in the immediate future are in transient imaging, and imaging hyperspectral data to test computational load while in a high resolution, multi-frequency setting.

EPFL2018

Low-dimensional data embedding for scalable astronomical imaging in the SKA telescope era

Vijay Kartik

EPFL2018