# High-Dimensional Data Analysis Using Parameter Free Algorithm Data Point Positioning Analysis
###### Abstract
[12] presented a novel supervised multi-view hash model that utilized deep learning and a multi-view stability evaluation method to enhance hash learning. The approach included multi-data fusion methods and a memory network to reduce computing resources during retrieval. The proposed method outperformed state-of-the-art single-view and multi-view hashing methods on three datasets, showing its potential for improving hash learning. In [13], the authors proposed a group-based nuclear norm and learning graph (GNNLG) model for image restoration, which exploits patch similarity and low-rank properties. An optimized learning strategy was developed to impose smoothing priors on the denoised depth image. The authors used the alternating direction method of multipliers to improve speed and convergence. Experimental results showed that the proposed method outperformed state-of-the-art denoising methods. In Reference [14], the authors proposed a task-adaptive attention module for image captioning that learned implicit non-visual clues and alleviated misleading problems. The authors also introduced diversity regularization to enhance the expression ability of the module. The experiments on the MSCOCO captioning dataset showed that using the proposed module with a vanilla Transformer-based image captioning model improved performance. The authors of [15] proposed a precise NR IQA scheme with two steps: distortion identification and targeted quality evaluation. They used Inception-ResNet-v2 to train a classifier and designed a specific approach to quantify image distortion. The method outperformed state-of-the-art NR IQA methods in the experiments, indicating its potential for practical applications. A popular strategy for dealing with overfitting in clustering is to reduce within-cluster variation. In the case of clustering, a common way to deal with overfitting is to minimize within-cluster variance [16]. The authors of [17] proposed a technique where they merged DBSCAN with affinity propagation (APSCAN), enabling users to benefit from both methods. The density contains two pieces of data: radius and number. Radius is the average distance from the exemplar to all points, and the number is the number of points that are located inside the radius neighborhood. Both parameters--radius and number--have been employed in the strategy as an alternative to Eps and MinPts. The evolutionary parameter-free clustering algorithm (EPFC) was developed by [PERSON] and [PERSON] [18]; the average value of nearest neighbor points is calculated based on all datasets. Depending on the computed distance between each data point and its closest neighbor, one of two decisions will be determined, i.e., to divide the group or combine the data points. In [19], a parameter-free approach was described, where the radius was determined automatically based on the window size and data distribution. It may be more efficient to sample a group of solutions rather than search for the solution space entirely when faced with all obstacles at once, including high dimensionality, high nonlinearity, parameter interaction, and disturbances due to randomness. Most of the previously investigated clustering methods for data mining used manual parameter selection to find the cluster from the raw data. Moreover, the methods used in high-dimension datasets provided comparatively lower performances. To address this concern, this study developed a novel clustering method (DPPA) to find the cluster from the raw dataset. The proposed method has been tested using the well-reputed publicly available dataset. The key contributions of this paper are as follows:  
1. In this study, we propose a new non-parametric clustering algorithm (DPPA), which can calculate 1-NN and Max-NN by analyzing the positions of data in the dataset without any initial manual parameter assignment. 2. We use two well-known publicly available datasets to evaluate the proposed method to find clusters.