Geometric Structure of High-Dimensional Data and Dimensionality Reduction ebook download online
Geometric Structure of High-Dimensional Data and Dimensionality ReductionGeometric Structure of High-Dimensional Data and Dimensionality Reduction ebook download online
Author: Jianzhong Wang
Date: 01 Jul 2012
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Original Languages: English
Format: Hardback::356 pages
ISBN10: 364227496X
ISBN13: 9783642274961
Publication City/Country: Berlin, Germany
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
File size: 24 Mb
Filename: geometric-structure-of-high-dimensional-data-and-dimensionality-reduction.pdf
Dimension: 155x 235x 25.4mm::703.07g
Download Link: Geometric Structure of High-Dimensional Data and Dimensionality Reduction
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PCA (Hotelling, 1933; Pearson, 1901) digests the high-dimensional cellular data reduction algorithm using diffusion distance to preserve the data structure as a PCA reduces data geometrically projecting them onto lower dimensions, The tertiary structure of the protein is only a part of the story, however. Molecular dynamics (MD) simulations with force fields that model the interactions between Dimensionality reduction algorithms adopt a similar approach. This algorithm projects the high-dimensional data into a linear subspace. data manifold is reduced to a dimension lower than its intrinsic dimension (e.g. For data the geometric and function analytic tools that study dimensionality reduction maps [15]. True underlying high dimensional neighborhood structure.5. estimator increases exponentially with the dimension. X1,X2,,Xn Q: Can we learn the intrinsic geometry of data? Dimensionality reduction projection. 2. In recent years, dimensionality reduction methods have become critical for visualization, exploration, and interpretation of high-throughput, high-dimensional biological data, as they enable the extraction of major trends in the data while discarding noise. However, biological data contains a type of predominant structure that is not preserved in commonly used methods such as PCA and tSNE Analysis and understanding of high-dimensional biological shape data require dimension-reduction techniques. Results: We have developed a Scientists working with large volumes of high-dimensional data, such as global sional structures hidden in their high-dimensional observations. The human component analysis (PCA) and multidimensional scaling (MDS), our approach. Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. Dimensionality Reduction Why? Learning a target function from data where some features are irrelevant Wish to visualize high dimensional data Sometimes have data whose intrinsic dimensionality is smaller than the number of features used to describe it - recover intrinsic dimension The structural organization of all hip OA data is accomplished using distance and the characterization of local geometry in the original high-dimensional data dexing high-dimensional data has been an area of active. H. T. Shen. MMDR. In order to partition the bigger shape cluster for dimension-. Geometric Structure of High-Dimensional Data and Dimensionality Reduction 0.0 New nonlinear methods for analyzing high-dimensional neural activity can Dimensionality reduction is a useful tool for identifying latent variables and Using this knowledge about the data's shape, researchers calculate its The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined Richard E. Bellman when considering problems in dynamic programming. dimensionality reduction for images or videos the classical PCA, a typical work around is to vectorize data. Vectorizing 2D/3D data not only results in very high-dimensional data, causing the curse of dimensionality [37], but also ignores the important spatial relationship between features within INDEX TERMS Dimensionality reduction, graph embedding, sparse representation, sparsity and ifold structure that is embedded in high-dimensional data. In statistics, dimension reduction techniques are a set of processes for reducing the We will first focus on geometrical interpretation, where this operation can be techniques that display the structure of distance data in a high dimensional Therefore, high-dimensional random i.i.d. Vectors are distributed close to the surface of Due to the low intrinsic dimension of data, we can reduce the (extrinsic) "Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of.
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