Abstract
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.
Highlights
Information visualization is an emerging research area, which helps users in sense-making, investigation, and representation from analysis results and original data [1]
We propose a FastIsomapVis method for high-dimensional and large-scale data, which differs from the existing method; our method uses the accuracy of K nearest neighbor graph (KNN) graphs to provide 100% accurate results without investing in many trees
We present unique algorithms for the construction of the KNearest-Neighbor (KNN) graphs, and our FastIsomapVis method is based on the below algorithms
Summary
Information visualization is an emerging research area, which helps users in sense-making, investigation, and representation from analysis results and original data [1]. The information becomes computationally unmanageable when it has numerous dimensions, and many data points are large. In many fields of research, such as data mining, machine learning, computer vision, information visualization [2,3,4], and the information visualization community [5,6,7], there is an urgent requirement to discover a representation of lowdimensional data to high dimensional data [8]. In the process of dimensionality reduction, the most critical point is not to affect the inherent framework of the large, high-dimensional data; for instance, it is important to keep dissimilar datasets far apart and similar datasets closer to each other, in the low dimensional space [9]. The machine learning technique provides dimensionality reduction, accompanied by minimal information loss
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