Mathematical Foundations of the Self Organized Neighbor Embedding ({SONE}) for Dimension Reduction and Visualization

Abstract. In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NE-XOM) for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE).Ittreatsthecomponents, likedatasimilarity measures andneighborhood functions, independently and easily changeable. And it enables the utilization of different divergences, based on the theory of Fréchet derivatives. In this way we propose a new dimension reduction and visualization algorithm, which can be easily adapted to the user specific request and the actual problem.

Mathematical Foundations of the Self Organized Neighbor Embedding (SONE) for Dimension Reduction and Visualization

Bunte K, Schleif F-M, Villmann T. Mathematical Foundations of the Self Organized Neighbor Embedding (SONE) for Dimension Reduction and Visualization. In: Proceedings of ESANN 2011. Ciaco - i6doc.com; 2011: 29-34

Statistical Physics of Design

Modern life increasingly relies on complex products that perform a variety of functions. The key difficulty of creating such products lies not in the manufacturing process, but in the design process. However, design problems are typically driven by multiple contradictory objectives and different stakeholders, have no obvious stopping criteria, and frequently prevent construction of prototypes or experiments. Such ill-defined, or "wicked" problems cannot be "solved" in the traditional sense with optimization methods. Instead, modern design techniques are focused on generating knowledge about the alternative solutions in the design space. In order to facilitate such knowledge generation, in this dissertation I develop the "Systems Physics" framework that treats the emergent structures within the design space as physical objects that interact via quantifiable forces. Mathematically, Systems Physics is based on maximal entropy statistical mechanics, which allows both drawing conceptual analogies between design problems and collective phenomena and performing numerical calculations to gain quantitative understanding. Systems Physics operates via a Model-Compute-Learn loop, with each step refining our thinking of design problems. I demonstrate the capabilities of Systems Physics in two very distinct case studies: Naval Engineering and self-assembly. For the Naval Engineering case, I focus on an established problem of arranging shipboard systems within the available hull space. I demonstrate the essential trade-off between minimizing the routing cost and maximizing the design flexibility, which can lead to abrupt phase transitions. I show how the design space can break into several locally optimal architecture classes that have very different robustness to external couplings. I illustrate how the topology of the shipboard functional network enters a tight interplay with the spatial constraints on placement. For the self-assembly problem, I show that the topology of self-assembled structures can be reliably encoded in the properties of the building blocks so that the structure and the blocks can be jointly designed. The work presented here provides both conceptual and quantitative advancements. In order to properly port the language and the formalism of statistical mechanics to the design domain, I critically re-examine such foundational ideas as system-bath coupling, coarse graining, particle distinguishability, and direct and emergent interactions. I show that the design space can be packed into a special information structure, a tensor network, which allows seamless transition from graphical visualization to sophisticated numerical calculations. This dissertation provides the first quantitative treatment of the design problem that is not reduced to the narrow goals of mathematical optimization. Using statistical mechanics perspective allows me to move beyond the dichotomy of "forward" and "inverse" design and frame design as a knowledge generation process instead. Such framing opens the way to further studies of the design space structures and the time- and path-dependent phenomena in design. The present work also benefits from, and contributes to the philosophical interpretations of statistical mechanics developed by the soft matter community in the past 20 years. The discussion goes far beyond physics and engages with literature from materials science, naval engineering, optimization problems, design theory, network theory, and economic complexity.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163133/1/aklishin_1.pd

Modern applications of machine learning in quantum sciences

In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning

Modern applications of machine learning in quantum sciences

In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.Comment: 268 pages, 87 figures. Comments and feedback are very welcome. Figures and tex files are available at https://github.com/Shmoo137/Lecture-Note

Study on the Method of Constructing a Statistical Shape Model and Its Application to the Segmentation of Internal Organs in Medical Images

In image processing, segmentation is one of the critical tasks for diagnostic analysis and image interpretation. In the following thesis, we describe the investigation of three problems related to the segmentation algorithms for medical images: Active shape model algorithm, 3-dimensional (3-D) statistical shape model building and organic segmentation experiments. For the development of Active shape models, the constraints of statistical model reduced this algorithm to be difficult for various biological shapes. To overcome the coupling of parameters in the original algorithm, in this thesis, the genetic algorithm is introduced to relax the shape limitation. How to construct a robust and effective 3-D point model is still a key step in statistical shape models. Generally the shape information is obtained from manually segmented voxel data. In this thesis, a two-step procedure for generating these models was designed. After transformed the voxel data to triangular polygonal data, in the first step, attitudes of these interesting objects are aligned according their surface features. We propose to reflect the surface orientations by means of their Gauss maps. As well the Gauss maps are mapped to a complex plane using stereographic projection approach. The experiment was run to align a set of left lung models. The second step is identifying the positions of landmarks on polygonal surfaces. This is solved by surface parameterization method. We proposed two simplex methods to correspond the landmarks. A semi-automatic method attempts to “copy” the phasic positions of pre-placed landmarks to all the surfaces, which have been mapped to the same parameterization domain. Another automatic corresponding method attempts to place the landmarks equidistantly. Finally, the goodness experiments were performed to measure the difference to manually corresponded results. And we also compared the affection to correspondence when using different surface mapping methods. The third part of this thesis is applying the segmentation algorithms to solve clinical problems. We did not stick to the model-based methods but choose the suitable one or their complex according to the objects. In the experiment of lung regions segmentation which includes pulmonary nodules, we propose a complementary region growing method to deal with the unpredictable variation of image densities of lesion regions. In the experiments of liver regions, instead of using region growing method in 3-D style, we turn into a slice-by-slice style in order to reduce the overflows. The image intensity of cardiac regions is distinguishable from lung regions in CT image. But as to the adjacent zone of heart and liver boundary are generally blurry. We utilized a shape model guided method to refine the segmentation results.3-D segmentation techniques have been applied widely not only in medical imaging fields, but also in machine vision, computer graphic. At the last part of this thesis, we resume some interesting topics such as 3-D visualization for medical interpretation, human face recognition and object grasping robot etc.九州工業大学博士学位論文 学位記番号:工博甲第353号　学位授与年月日:平成25年9月27日Chapter 1: Introduction|Chapter 2: Framework of Medical Image Segmentation|Chapter 3: 2-D Organic Regions Using Active Shape Model and Genetic Algorithm|Chapter 4: Alignment of 3-D Models|Chapter 5: Corespondence of 3-D Models|Chapter 6:Experiments of Organic Segmentation|Chapter 7: Visualization Technology and Its Applications|Chapter 8: Conclusions and Future Works九州工業大学平成25年