Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized

. Partial alignments of the data sets---obtained from prior knowledge of their manifold structure or from pairwise correspondences of subsets of labeled examples--- are completed by integrating supervised signals with unsupervised frameworks for manifold learning. As an illustration

semantically relevant clustering of data. We show that PM yields superior results when measuring the alignment between the generated clusters and the nominal class labeling of the data set. We found that while gross motions were easily clustered by both methods, the lack of preservation of structural

High dimensional data that lies on or near a low dimensional manifold can be described by a collection of local linear models. Such a description, however, does not provide a global parameterization of the manifold---arguably an important goal of unsupervised learning. In this paper, we show how

semantically useful clustering of relevant data. We show that PM yields superior results when measuring the alignment between the generated clusters over a range of K-values (number of clusters) and the nominal class labelling of the data set. A key result is that unsupervised clustering with PM yields

data volume, few methods can integrative and efficiently find the principal low-dimensional manifold of the high-dimensional cancer multi-omics data. Results: In this study, we proposed a novel low-rank approximation based integrative probabilistic model to fast find the shared principal subspace

m]]l]]s¶D]]¿÷mB]iv]b]oD]m¶¨]iv]§]iv]r]j]t¿rv]]irj]]t]]m] / | ap]]r¿]ÎNy]s¶D]]mb¶r]ix} Û]Ix]]rd]mb]} p—N]t]o%ism] in]ty]m] / || Û]Is]¡uÎc]rN]]riv]nd]p]*N]m]st¶ I always bow to Śri ̄ Śāradāmbā, the limitless ocean of the nectar of compassion, who bears a rosary, a vessel of nectar, the symbol of knowledge and a book in Her lotus hands. Dedicated to the Lotus Feet of the revered Sadguru. This thesis presents a new active mask (AM) framework and an algorithm for segmenta-tion of digital images, particularly those of punctate patterns from fluorescence microscopy. Fluorescence microscopy has greatly facilitated the task of understanding complex sys-tems at cellular and molecular levels in recent years. Segmentation, an important yet dif-ficult problem, is often the first processing step following acquisition. Our team previously demonstrated that a stochastic active contour based algorithm together with the concept of

of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically pow-ered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles

Ultracold atoms in optical lattices provide a highly control-lable environment for the clean experimental realization of various model Hamiltonians from condensed matter and statistical physics. For example, the two-component Bose-Hubbard model, which re-duces to an anisotropic spin-1/2 Heisenberg model in a certain limit and thus allows for the study of quantum magnetism, can be im-plemented by using bosons with two different internal states that couple differently to an optical lattice potential. In this thesis, I present our first experiments with two-component hyperfine-state mixtures of ultracold 87Rb atoms in a state-dependent optical lat-tice, both in the strongly correlated regime and in the context of nonlinear atom optics. For the production of 87Rb Bose-Einstein condensates we have developed a moving-coil transporter apparatus featuring a mag-netic TOP trap which serves as a “phase-space funnel ” to load a

ii iii CHRISTOPHER CHARLES WEIGLE: Displays for Exploration and Comparison of Nested