Low-Dimensional Data Representation in Data Analysis

Bernstein, Alexander; Kuleshov, Alexander P.

doi:10.1007/978-3-319-11656-3_5

Cited by 8 publications

(8 citation statements)

References 21 publications

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“…Asymptotic expansion and uniform large deviation results are obtained for the considered random variable. The problem statement is motivated by manifold learning problems (Roweis and Saul, 2000;Zhang and Zha, 2004;Bernstein and Kuleshov, 2014).…”

Section: Resultsmentioning

confidence: 99%

“…Chosen descriptions of the neighborhoods (local descriptions of the DM) are computed. Examples of such descriptions: Saul (2000); the neighborhood U N (X n , k) is used here • An applying of the Principal Component Analysis (PCA) Jolliffe (2002) to the neighborhood U N (X n , ε) results in an p×q orthogonal matrix Q PCA (X n ) whose columns are the PCA principal eigenvectors corresponding to the q largest PCA eigenvalues (Zhang and Zha, 2004;Bernstein and Kuleshov, 2014). These matrices determine q-dimensional linear spaces L PCA (X n ) = Span(Q PCA (X n )) in the p ℝ which, under certain conditions, accurately approximate the tangent spaces…”

Section: Second Step: Neighborhoods Descriptionsmentioning

confidence: 99%

“…Fortunately, in many applications, especially in imaging and medical ones, the real high-dimensional data occupy only a very small part in the high dimensional 'observation space' p ℝ whose intrinsic dimension q is small (usually, ) q p ≪ Donoho (2000;Verleysen, 2003). Thus, various Dimensionality Reduction (Feature extraction) algorithms whose goal is a finding of a low-dimensional parameterization of high-dimensional data can be used as a first key step in solutions of such 'high-dimensional' tasks by transforming the data into their low-dimensional representations (features) preserving certain chosen subject-driven data properties (Bengio et al, Bernstein and Kuleshov, 2014;Kuleshov and Bernstein, 2016. Then the low-dimensional features can be used in reduced learning procedures instead of initial high-dimensional vectors avoiding the curse of dimensionality Kuleshov and Bernstein (2014): 'dimensionality reduction may be necessary to discard redundancy and reduce the computational cost of further operations' Lee and Verleysen (2007).…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Properties of Local Sampling on Manifold

Yanovich¹

2016

Journal of Mathematics and Statistics

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In many applications, the real high-dimensional data occupy only a very small part in the high dimensional 'observation space' whose intrinsic dimension is small. The most popular model of such data is Manifold model which assumes that the data lie on or near an unknown manifold Data Manifold, (DM) of lower dimensionality embedded in an ambient high-dimensional input space (Manifold assumption about highdimensional data). Manifold Learning is a Dimensionality Reduction problem under the Manifold assumption about the processed data and its goal is to construct a low-dimensional parameterization of the DM (global low-dimensional coordinates on the DM) from a finite dataset sampled from the DM. Manifold assumption means that local neighborhood of each manifold point is equivalent to an area of low-dimensional Euclidean space. Because of this, most of Manifold Learning algorithms include two parts: 'local part' in which certain characteristics reflecting low-dimensional local structure of neighborhoods of all sample points are constructed and 'global part' in which global low-dimensional coordinates on the DM are constructed by solving certain convex optimization problem for specific cost function depending on the local characteristics. Statistical properties of 'local part' are closely connected with local sampling on the manifold, which is considered in the study.

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Section: Resultsmentioning

confidence: 99%

Section: Second Step: Neighborhoods Descriptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic Properties of Local Sampling on Manifold

Yanovich¹

2016

Journal of Mathematics and Statistics

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“…Thus, the curse of dimensionality phenomenon is often an obstacle for using ML techniques. To avoid this phenomenon, various universal dimensionality reduction methods Burges (2010); Sorzano et al (2014); Bernstein and Kuleshov (2014); Chernova and Burnaev (2015) and/or specific neuroimaging-oriented feature selection methods Mwangi et al (2014) are used for extracting low-dimensional features from high-dimensional neuroimaging data. After that, ML algorithms are applied to these features.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning pipeline for discovering neuroimaging-based biomarkers in neurology and psychiatry

Bernstein¹,

Burnaev²,

Kondratyeva³

et al. 2018

Preprint

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We consider a problem of diagnostic pattern recognition/classification from neuroimaging data. We propose a common data analysis pipeline for neuroimaging-based diagnostic classification problems using various ML algorithms and processing toolboxes for brain imaging. We illustrate the pipeline application by discovering new biomarkers for diagnostics of epilepsy and depression based on clinical and MRI/fMRI data for patients and healthy volunteers.

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“…The typical machine learning pipeline consists of the following steps: data collection, model training, and inference [23], [24]. For resource constrained embedded devices, an important aspect to be considered is an appropriate data processing, which allows for a low-dimensional representation of the data [25]. Low-dimensional data allows for the design of the less computationally complex algorithm.…”

mentioning

confidence: 99%

Analysis of Edge-Optimized Deep Learning Classifiers for Radar-Based Gesture Recognition

et al. 2021

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The increasing significance of technology in daily lives led to the need for the development of convenient methods of human-computer interaction (HCI). Given that the existing HCI approaches exhibit various limitations, hand gesture recognition-based HCI may serve as a more intuitive mode of humanmachine interaction in many situations. In addition, the system has to be deployable on low-power devices for applicability in broadly defined Internet of Things (IoT) and smart home solutions. Recent advances exhibit the potential of deep learning models for gesture classification, whereas they are still limited to high-performance hardware. Embedded neural network accelerators are constrained in terms of available memory, central processing unit (CPU) clock speed, graphics processing unit (GPU) performance, and a number of supported operations. The aforementioned problems are addressed in this paper by namely two approaches -simplifying the signal processing pipeline to avoid recurrent structures and efficient topological design. This paper employs an intuitive scheme allowing for the generation of the data in the compressed form from the sequence of range-Doppler images (RDI). Thus, it allows for the design of a neural classifier avoiding the usage of recurrent layers. The proposed framework has been optimized for Intel ® Neural Compute Stick 2 (Intel ® NCS 2), at the same time achieving promising classification accuracy of 97.57%. To confirm the robustness of the proposed algorithm, five independent persons have been involved in the algorithm testing process.

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Low-Dimensional Data Representation in Data Analysis

Cited by 8 publications

References 21 publications

Asymptotic Properties of Local Sampling on Manifold

Asymptotic Properties of Local Sampling on Manifold

Machine Learning pipeline for discovering neuroimaging-based biomarkers in neurology and psychiatry

Analysis of Edge-Optimized Deep Learning Classifiers for Radar-Based Gesture Recognition

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