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We propose a local conformal autoencoder (LOCA) for standardized data coordinates. LOCA is a deep learning-based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, nonlinear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized, latent variables. We assume a repeated measurement sampling strategy, common in scientific measurements, and present a method for learning an embedding in [Formula: see text] that is isometric to the latent variables of the manifold. The coordinates recovered by our method are invariant to diffeomorphisms of the manifold, making it possible to match between different instrumental observations of the same phenomenon. Our embedding is obtained using LOCA, which is an algorithm that learns to rectify deformations by using a local z-scoring procedure, while preserving relevant geometric information. We demonstrate the isometric embedding properties of LOCA in various model settings and observe that it exhibits promising interpolation and extrapolation capabilities, superior to the current state of the art. Finally, we demonstrate LOCA's efficacy in single-site Wi-Fi localization data and for the reconstruction of three-dimensional curved surfaces from two-dimensional projections., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.)

Objective: We propose an automated nutritional assessment algorithm that provides a method for malnutrition risk prediction with high accuracy and reliability., Methods: The database used for this study was a file of 432 patients, where each patient was described by 4 laboratory parameters and 11 clinical parameters. A malnutrition risk assessment of low (1), moderate (2), or high (3) was assigned by a dietitian for each patient. An algorithm for data organization and classification using characteristic metrics for each patient was developed. For each patient, the algorithm characterized the patients' unique profile and built a characteristic metric to identify similar patients who were mapped into a classification. For each patient, the algorithm characterized the patients' classification., Results: The algorithm assigned a malnutrition risk level for different training sizes that were taken from the data. Our method resulted in average errors (distance between the automated score and the real score) of 0.386, 0.3507, 0.3454, 0.34, and 0.2907 for the 10%, 30%, 50%, 70%, and 90% training sizes, respectively. Our method outperformed the compared method even when our method used a smaller training set than the compared method. In addition, we showed that the laboratory parameters themselves were sufficient for the automated risk prediction and organized the patients into clusters that corresponded to low-, low-moderate-, moderate-, moderate-high-, and high-risk areas. The organization and visualization methods provided a tool for the exploration and navigation of the data points., Conclusion: The problem of rapidly identifying risk and severity of malnutrition is crucial for minimizing medical and surgical complications. These are not easily performed or adequately expedited. We characterized for each patient a unique profile and mapped similar patients into a classification. We also found that the laboratory parameters were sufficient for the automated risk prediction., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Nonlinear independent component analysis is combined with diffusion-map data analysis techniques to detect good observables in high-dimensional dynamic data. These detections are achieved by integrating local principal component analysis of simulation bursts by using eigenvectors of a Markov matrix describing anisotropic diffusion. The widely applicable procedure, a crucial step in model reduction approaches, is illustrated on stochastic chemical reaction network simulations.

We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.

Data fusion and multicue data matching are fundamental tasks of high-dimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is three-fold: First, we present the Laplace-Beltrami approach for computing density invariant embeddings which are essential for integrating different sources of data. Second, we describe a refinement of the Nyström extension algorithm called "geometric harmonics." We also explain how to use this tool for data assimilation. Finally, we introduce a multicue data matching scheme based on nonlinear spectral graphs alignment. The effectiveness of the presented schemes is validated by applying it to the problems of lipreading and image sequence alignment.

Abstract: The single-particle reconstruction problem of electron cryo-microscopy (cryo-EM) is to find the three-dimensional structure of a macromolecule given its two-dimensional noisy projection images at unknown random directions. Ab initio estimates of the 3D structure are often obtained by the “Angular Reconstitution” method, in which a coordinate system is established from three projections, and the orientation of the particle giving rise to each image is deduced from common lines among the images. However, a reliable detection of common lines is difficult due to the low signal-to-noise ratio of the images. In this paper we describe a global self-correcting voting procedure in which all projection images participate to decide the identity of the consistent common lines. The algorithm determines which common line pairs were detected correctly and which are spurious. We show that the voting procedure succeeds at relatively low detection rates and that its performance improves as the number of projection images increases. We demonstrate the algorithm for both simulative and experimental images of the 50S ribosomal subunit. [Copyright &y& Elsevier]

Image coding methods based on adaptive wavelet transform and those employing zerotree quantization have been shown to be successful in recent years. In this paper, we present a general zerotree structure for an arbitrary wavelet packet geometry in an image coding framework. A fast basis selection algorithm which uses a Markov chain based cost estimate of encoding the image using this structure is developed. As a result, our adaptive wavelet zerotree image coder has a relatively low computational complexity, performs comparably to the state-of-the-art image coders and is capable of progressively encoding images. [ABSTRACT FROM AUTHOR]

Studies the paradigm for image representation and image compression using a multilayered algorithm. Construction of wavelet packets; Quantization of wavelet packets coefficients; Consideration of the sequence of library functions.

Abstract: Patch-based de-noising algorithms and patch manifold smoothing have emerged as efficient de-noising methods. This paper provides a new insight on these methods. We show how to extend them to separate oscillatory patterns that could be entangled. A collection of particular patches, that we call reference set, is selected by the user. We define a notion of similarity relative to this reference set that is used to extend the Non-Local Means (see Buades et al., 2005) [1] and the graph-based de-noising method (see Szlam et al., 2008) [12]. [Copyright &y& Elsevier]

Abstract: We introduce a method to re-parameterize massive high dimensional data, generated by nonlinear mixing, into its independent physical parameters. Our method enables the identification of the original parameters and their extension to new observations without any knowledge of the true physical model. The suggested approach in this paper is related to spectral independent components analysis (ICA) via the construction of an anisotropic diffusion kernel whose eigenfunctions comprise the independent components. However, we use a novel anisotropic diffusion process, utilizing only a small observed subset , that approximates the isotropic diffusion on the parametric manifold of the full set Y. We employ a Nyström-type extension of the independent components of to the independent components of Y, and provide a validation scheme for our algorithm parameters choice. We demonstrate our method on synthetic examples and on real application examples. [Copyright &y& Elsevier]

Harmonic analysis and diffusion on discrete data has been shown to lead to state-of-the-art algorithms for machine learning tasks, especially in the context of semi-supervised and transductive learning. The success of these algorithms rests on the assumption that the function(s) to be studied (learned, interpolated, etc.) are smooth with respect to the geometry of the data. In this paper we present a method for modifying the given geometry so the function(s) to be studied are smoother with respect to the modified geometry, and thus more amenable to treatment using harmonic analysis methods. Among the many possible applications, we consider the problems of image denoising and transductive classification. In both settings, our approach improves on standard diffusion based methods. [ABSTRACT FROM AUTHOR]