The Experts below are selected from a list of 22236 Experts worldwide ranked by ideXlab platform
Longbing Cao - One of the best experts on this subject based on the ideXlab platform.
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a convergence theorem for graph shift type algorithms
Pattern Recognition, 2015Co-Authors: Xuhui Fan, Longbing CaoAbstract:The Robust Graph mode seeking by Graph Shift (Liu and Yan, 2010) (RGGS) algorithm represents a recent promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the RGGS algorithm, leaving the question as to whether an algorithm works for solid reasons. In this paper, we propose a generic theoretical framework consisting of three key Graph Shift (GS) components: the simplex of a generated sequence set, the monotonic and continuous objective function and Closed Mapping. We prove that the GS-type algorithms built on such components can be transformed to fit Zangwill?s theory, and the sequence set generated by the GS procedures always terminates at a local maximum, or at worst, contains a subsequence which converges to a local maximum of the similarity measure function. The framework is verified by theoretical analysis and experimental results of several typical GS-type algorithms. HighlightsWe theoretically analyze the behaviors of the RGGS algorithm.We prove that the RGGS algorithm is convergent with Zangwill?s theory.A convergence proof framework is built to apply to other GS-type algorithms.
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a convergence theorem for the graph shift type algorithms
arXiv: Machine Learning, 2013Co-Authors: Xuhui Fan, Longbing CaoAbstract:Graph Shift (GS) algorithms are recently focused as a promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the GS Algorithm. In this paper, we propose a generic theoretical framework consisting of three key GS components: simplex of generated sequence set, monotonic and continuous objective function and Closed Mapping. We prove that GS algorithms with such components can be transformed to fit the Zangwill's convergence theorem, and the sequence set generated by the GS procedures always terminates at a local maximum, or at worst, contains a subsequence which converges to a local maximum of the similarity measure function. The framework is verified by expanding it to other GS-type algorithms and experimental results.
Xuhui Fan - One of the best experts on this subject based on the ideXlab platform.
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a convergence theorem for graph shift type algorithms
Pattern Recognition, 2015Co-Authors: Xuhui Fan, Longbing CaoAbstract:The Robust Graph mode seeking by Graph Shift (Liu and Yan, 2010) (RGGS) algorithm represents a recent promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the RGGS algorithm, leaving the question as to whether an algorithm works for solid reasons. In this paper, we propose a generic theoretical framework consisting of three key Graph Shift (GS) components: the simplex of a generated sequence set, the monotonic and continuous objective function and Closed Mapping. We prove that the GS-type algorithms built on such components can be transformed to fit Zangwill?s theory, and the sequence set generated by the GS procedures always terminates at a local maximum, or at worst, contains a subsequence which converges to a local maximum of the similarity measure function. The framework is verified by theoretical analysis and experimental results of several typical GS-type algorithms. HighlightsWe theoretically analyze the behaviors of the RGGS algorithm.We prove that the RGGS algorithm is convergent with Zangwill?s theory.A convergence proof framework is built to apply to other GS-type algorithms.
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a convergence theorem for the graph shift type algorithms
arXiv: Machine Learning, 2013Co-Authors: Xuhui Fan, Longbing CaoAbstract:Graph Shift (GS) algorithms are recently focused as a promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the GS Algorithm. In this paper, we propose a generic theoretical framework consisting of three key GS components: simplex of generated sequence set, monotonic and continuous objective function and Closed Mapping. We prove that GS algorithms with such components can be transformed to fit the Zangwill's convergence theorem, and the sequence set generated by the GS procedures always terminates at a local maximum, or at worst, contains a subsequence which converges to a local maximum of the similarity measure function. The framework is verified by expanding it to other GS-type algorithms and experimental results.
Florin A. Radu - One of the best experts on this subject based on the ideXlab platform.
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– Normed spaces (Sect. 1.1). – Completness, Banach spaces (Sect. 1.2).
2016Co-Authors: Florin A. RaduAbstract:– Continuous functions, contractions (Sect. 1.3), Banach fix point theorem. Applications (Sect. 4.2). – Compactness and finite dimensional spaces (Sect. 1.4). – Linear and continuous functions (Sect. 1.5). Applications (Sect. 4.3). – Zorn’s lemma, Hamel bases and the Hahn-Banach theorem (Sect. 1.6). Quotient spaces. – The interior Mapping and Closed Mapping theorems (Sect. 1.7). – Baire theorem and uniform boundedness (Sect. 1.8) – Weak convergence (Sect. 1.9). – Reflexive spaces (Sect. 1.10). 2 Hilbert spaces (Chapter 2 in [1]) – Geometry (Sect. 2.1)
Seyedahmad Ahmadi - One of the best experts on this subject based on the ideXlab platform.
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towards computerized diagnosis of neurological stance disorders data mining and machine learning of posturography and sway
Journal of Neurology, 2019Co-Authors: Seyedahmad Ahmadi, Gerome Vivar, Johann Frei, Sergej Nowoshilow, Stanislav Bardins, Thomas Brandt, Siegbert KrafczykAbstract:We perform classification, ranking and Mapping of body sway parameters from static posturography data of patients using recent machine-learning and data-mining techniques. Body sway is measured in 293 individuals with the clinical diagnoses of acute unilateral vestibulopathy (AVS, n = 49), distal sensory polyneuropathy (PNP, n = 12), anterior lobe cerebellar atrophy (CA, n = 48), downbeat nystagmus syndrome (DN, n = 16), primary orthostatic tremor (OT, n = 25), Parkinson's disease (PD, n = 27), phobic postural vertigo (PPV n = 59) and healthy controls (HC, n = 57). We classify disorders and rank sway features using supervised machine learning. We compute a continuous, human-interpretable 2D map of stance disorders using t-stochastic neighborhood embedding (t-SNE). Classification of eight diagnoses yielded 82.7% accuracy [95% CI (80.9%, 84.5%)]. Five (CA, PPV, AVS, HC, OT) were classified with a mean sensitivity and specificity of 88.4% and 97.1%, while three (PD, PNP, and DN) achieved a mean sensitivity of 53.7%. The most discriminative stance condition was ranked as "standing on foam-rubber, eyes Closed". Mapping of sway path features into 2D space revealed clear clusters among CA, PPV, AVS, HC and OT subjects. We confirm previous claims that machine learning can aid in classification of clinical sway patterns measured with static posturography. Given a standardized, long-term acquisition of quantitative patient databases, modern machine learning and data analysis techniques help in visualizing, understanding and utilizing high-dimensional sensor data from clinical routine.
Siegbert Krafczyk - One of the best experts on this subject based on the ideXlab platform.
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towards computerized diagnosis of neurological stance disorders data mining and machine learning of posturography and sway
Journal of Neurology, 2019Co-Authors: Seyedahmad Ahmadi, Gerome Vivar, Johann Frei, Sergej Nowoshilow, Stanislav Bardins, Thomas Brandt, Siegbert KrafczykAbstract:We perform classification, ranking and Mapping of body sway parameters from static posturography data of patients using recent machine-learning and data-mining techniques. Body sway is measured in 293 individuals with the clinical diagnoses of acute unilateral vestibulopathy (AVS, n = 49), distal sensory polyneuropathy (PNP, n = 12), anterior lobe cerebellar atrophy (CA, n = 48), downbeat nystagmus syndrome (DN, n = 16), primary orthostatic tremor (OT, n = 25), Parkinson's disease (PD, n = 27), phobic postural vertigo (PPV n = 59) and healthy controls (HC, n = 57). We classify disorders and rank sway features using supervised machine learning. We compute a continuous, human-interpretable 2D map of stance disorders using t-stochastic neighborhood embedding (t-SNE). Classification of eight diagnoses yielded 82.7% accuracy [95% CI (80.9%, 84.5%)]. Five (CA, PPV, AVS, HC, OT) were classified with a mean sensitivity and specificity of 88.4% and 97.1%, while three (PD, PNP, and DN) achieved a mean sensitivity of 53.7%. The most discriminative stance condition was ranked as "standing on foam-rubber, eyes Closed". Mapping of sway path features into 2D space revealed clear clusters among CA, PPV, AVS, HC and OT subjects. We confirm previous claims that machine learning can aid in classification of clinical sway patterns measured with static posturography. Given a standardized, long-term acquisition of quantitative patient databases, modern machine learning and data analysis techniques help in visualizing, understanding and utilizing high-dimensional sensor data from clinical routine.