An Improved ISOMAP for Visualization and Classification of Multiple Manifolds

Wang, Hongyuan; Xiu-Jie, Ding; Qi-cai, Cheng; Chen, Fuhua

doi:10.1007/978-3-642-42042-9_1

Cited by 8 publications

(2 citation statements)

References 15 publications

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“…The Kernel Isomap can preserve topological stability while tackling the outliers and noises [21]. Moreover [14], they proposed two variant techniques of Isomap visualization, which are the multi-class multi-manifold-Isomap (MCMM-ISOMAP) and Isomap for classification (ISOMAP-C), respectively. The MCMM-ISOMAP and ISOMAP-C and various other techniques have been proposed to overcome the problem of the Isomap algorithm are that it is very slow.…”

Section: Introductionmentioning

confidence: 99%

An Extended Isomap Approach for Nonlinear Dimension Reduction

Yousaf

Rehman

2020

SN COMPUT. SCI.

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Nowadays, Isomap is one of the most popular nonlinear manifold dimension reductions which have applied to the real-world datasets. However, it has various limitations for the high-dimensional and large-scale dataset. Two main limitations of the Isomap are: it may make incorrect links in the neighborhood graph G and high computational cost. In this paper, we have introduced a novel framework, which we called the FastIsomap. The main purpose of the FastIsomap is to increase the accuracy of the graph by using two state-of-the-art algorithms: a randomized division tree and NN-Descent. The basic idea of FastIsomap is to construct an accurate approximated KNN graph from millions and hundreds of dimensional' data points and then project the graph into low-dimensional space. We have compared the FastIsomap framework with the existing Isomap algorithm to verify its efficiency and performance, which provided accurate results of the high and large-dimensional datasets.

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Section: Introductionmentioning

confidence: 99%

An Extended Isomap Approach for Nonlinear Dimension Reduction

Yousaf

Rehman

2020

SN COMPUT. SCI.

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“…For the shortest path problem, Wang et al [19] proposed the Multi-Class Multi-Manifold-Isomap (MCMM-ISOMAP) and Isomap for classification (ISOMAP-C). The MCMM-ISOMAP and ISOMAP-C and an improved Isomap method based on the Dijkstra algorithm with method Fibonacci Heap (Fib-Dij) have been proposed to overcome the shortest path problem [14,20], e.g., by removing the nearest neighboring graphs G of the neighborhood graph or by removing large data points in the shortest path algorithm [14,[18][19][20], which can severely affect the classical Isomap graph [21]. Ying-K Lei et al [22] proposed a greedy approximated algorithm of Minimum Set Coverage (MSC) [23] for the shortest path and MDS problems.…”

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confidence: 99%

FastIsomapVis: A Novel Approach for Nonlinear Manifold Learning

et al. 2020

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The classical Isomap is the most common unsupervised nonlinear manifold method and widely being used in visualizations and dimension reductions. However, when it applied to real-world datasets, it shows shortcomings for the shortest path between all pairs of data points, which are based on the nearest neighborhood G graph via the Dijkstra algorithm, which makes it a very time-consuming step. The other critical problem is the classical Isomap has a lack of topological stability on the nearest neighborhood G graph. In this paper, we propose a novel technique called the FastIsomapVis for the above problems of the classical Isomap. The FastIsomapVis uses hierarchal divide, conquer, and combine approach through two algorithms, which are randomized division tree (KD-tree) and Dijkstra Buckets Double (DKD). The primary aim of the FastIsomapVis is to increase the efficiency and accuracy of the graph. This research paper focuses on transforming the high dimensional datasets into a low dimensional Isomap visualization. The FastIsomapVis makes it easy to construct an accurate K nearest neighborhood G graph and scale high dimensional data points into low dimensional space. Our proposed method is compared to the classical Isomap to verify its effectiveness and provide highly authentic results of the high dimensional datasets. The finding of the current study shows that our proposed method is much fastened than classical Isomap.

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A Hybridisation of Runner-Based and Seed-Based Plant Propagation Algorithms

Sulaiman

Salhi

2016

Nature-Inspired Computation in Engineering

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An Improved ISOMAP for Visualization and Classification of Multiple Manifolds

Cited by 8 publications

References 15 publications

An Extended Isomap Approach for Nonlinear Dimension Reduction

An Extended Isomap Approach for Nonlinear Dimension Reduction

FastIsomapVis: A Novel Approach for Nonlinear Manifold Learning

A Hybridisation of Runner-Based and Seed-Based Plant Propagation Algorithms

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