Cluster Point Research Articles

Cooperative Coverage Path Planning for Multi-Mobile Robots Based on Improved K-Means Clustering and Deep Reinforcement Learning

With the increasing complexity of patrol tasks, the use of deep reinforcement learning for collaborative coverage path planning (CPP) of multi-mobile robots has become a new hotspot. Taking into account the complexity of environmental factors and operational limitations, such as terrain obstacles and the scope of the task area, in order to complete the CPP task better, this paper proposes an improved K-Means clustering algorithm to divide the multi-robot task area. The improved K-Means clustering algorithm improves the selection of the first initial clustering point, which makes the clustering process more reasonable and helps to distribute tasks more evenly. Simultaneously, it introduces deep reinforcement learning with a dueling network structure to better deal with terrain obstacles and improves the reward function to guide the coverage process. The simulation experiments have confirmed the advantages of this method in terms of balanced task assignment, improvement in strategy quality, and enhancement of coverage efficiency. It can reduce path duplication and omission while ensuring coverage quality.

Conditional Strong Law of Large Numbers under G-Expectations

In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with lower probability one. Moreover, for conditionally independent random variables with identical conditional distributions, we show the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one.

Strictly frequentist imprecise probability

Strict frequentism defines probability as the limiting relative frequency in an infinite sequence. What if the limit does not exist? We present a broader theory, which is applicable also to data that exhibit diverging relative frequencies. In doing so, we develop a close connection with the theory of imprecise probability: the cluster points of relative frequencies yield a coherent upper prevision. We show that a natural frequentist definition of conditional probability recovers the generalized Bayes rule. Finally, we prove constructively that, for a finite set of elementary events, there exists a sequence for which the cluster points of relative frequencies coincide with a prespecified set which demonstrates the naturalness, and arguably completeness, of our theory.

Reliable Breast Cancer Diagnosis with Deep Learning: DCGAN-Driven Mammogram Synthesis and Validity Assessment

Breast cancer imaging is paramount to quickly detecting and accurately evaluating the disease. The scarcity of annotated mammogram data presents a significant obstacle when building deep learning models that can produce reliable outcomes. This paper proposes a novel approach that utilizes deep convolutional generative adversarial networks (DCGANs) to effectively tackle the issue of limited data availability. The main goal is to produce synthetic mammograms that accurately reproduce the intrinsic patterns observed in real data, enhancing the current dataset. The proposed synthesis method is supported by thorough experimentation, demonstrating its ability to reproduce diverse viewpoints of the breast accurately. A mean similarity assessment with a standard deviation was performed to evaluate the credibility of the synthesized images and establish the clinical significance of the data obtained. A thorough evaluation of the uniformity within each class was conducted, and any deviations from each class’s mean values were measured. Including outlier removal using a specified threshold is a crucial process element. This procedure improves the accuracy level of each image cluster and strengthens the synthetic dataset’s general dependability. The visualization of the class clustering results highlights the alignment between the produced images and the inherent distribution of the data. After removing outliers, distinct and consistent clusters of homogeneous data points were observed. The proposed similarity assessment demonstrates noteworthy effectiveness, eliminating redundant and dissimilar images from all classes. Specifically, there are 505 instances in the normal class, 495 instances in the benign class, and 490 instances in the malignant class out of 600 synthetic mammograms for each class. To check the further validity of the proposed model, human experts visually inspected and validated synthetic images. This highlights the effectiveness of our methodology in identifying substantial outliers.

Efficient image restoration with style-guided context cluster and interaction

Recently, convolutional neural networks (CNNs) and vision transformers (ViTs) have emerged as powerful tools for image restoration (IR). Nonetheless, they encountered some limitations due to their characteristics, such as CNNs sacrificing global reception and ViTs requiring large memory and graphics resources. To address these limitations and explore an alternative approach for improved IR performance, we propose two clustering-based frameworks for general IR tasks, which are style-guided context cluster U-Net (SCoC-UNet) and style-guided clustered point interaction U-Net (SCPI-UNet). The SCoC-UNet adopts a U-shaped architecture, comprising position embedding, Encoder, Decoder, and reconstruction block. Specifically, the input low-quality image is viewed as a set of unorganized points, each of which is first given location information by the continuous relative position embedding method. These points are then fed into a symmetric Encoder and Decoder which utilize style-guided context cluster (SCoC) blocks to extract potential context features and high-frequency information. Although SCoC-UNet has obtained decent performance for image restoration, its SCoC block can only capture connectivity at points within the same cluster, which may ignore long-range dependencies in different clusters. To address this issue, we further propose a SCPI-UNet based on SCoC-UNet, which leverages a style-guided clustered point interaction (SCPI) block in place of the SCoC block. The SCPI block utilizes a cross-attention mechanism to establish the connections of feature points between different clusters. Extensive experimental results demonstrate that the proposed SCoC-UNet and SCPI-UNet can handle several typical IR tasks (i.e., JPEG compression artifact reduction, image denoising, and super-resolution) and achieve superior quantitative and qualitative performance over some state-of-the-art methods.

An approach for traffic pattern recognition integration of ship AIS data and port geospatial features

ABSTRACT Recognition of ship traffic patterns can provide insights into the rules of navigation, maneuvering, and collision avoidance for ships at sea. This is essential for ensuring safe navigation at sea and improving navigational efficiency. With the popularization of the Automatic Identification System (AIS), numerous studies utilized ship trajectories to identify maritime traffic patterns. However, the current research focuses on the spatiotemporal behavioral feature clustering of ship trajectory points or segments while lacking consideration for multiple factors that influence ship behavior, such as ship static and maritime geospatial features, resulting in insufficient precision in ship traffic pattern recognition. This study proposes a ship traffic pattern recognition method that considers multi-attribute trajectory similarity (STPMTS), which considers ship static feature, dynamic feature, port geospatial feature, as well as semantic relationships between these features. First, A ship trajectory reconstruction method based on grid compression was introduced to eliminate redundant data and enhance the efficiency of trajectory similarity measurements. Subsequently, to quantify the degree of similarity of ship trajectories, a trajectory similarity measurement method is proposed that combines ship static and dynamic information with port geospatial features. Furthermore, trajectory clustering with hierarchical methods was applied based on the trajectory similarity matrix for dividing trajectories into different clusters. The quality of the similarity measurement results was evaluated by quality criterion to recognize the optimal number of ship traffic patterns. Finally, the effectiveness of the proposed method was verified using actual port ship trajectory data from the Tianjin Port of China, ranging from September to November 2016. Compared with other methods, the proposed method exhibits significant advantages in identifying traffic patterns of ships entering and leaving the port in terms of geometric features, dynamic features, and adherence to navigation rules. This study could serve as an inspiration for a comprehensive exploration of maritime transportation knowledge from multiple perspectives.

Look inside 3D point cloud deep neural network by patch-wise saliency map

The 3D point cloud deep neural network (3D DNN) has achieved remarkable success, but its black-box nature hinders its application in many safety-critical domains. The saliency map technique is a key method to look inside the black-box and determine where a 3D DNN focuses when recognizing a point cloud. Existing point-wise point cloud saliency methods are proposed to illustrate the point-wise saliency for a given 3D DNN. However, the above critical points are alternative and unreliable. The findings are grounded on our experimental results which show that a point becomes critical because it is responsible for representing one specific local structure. However, one local structure does not have to be represented by some specific points, conversely. As a result, discussing the saliency of the local structure (named patch-wise saliency) represented by critical points is more meaningful than discussing the saliency of some specific points. Based on the above motivations, this paper designs a black-box algorithm to generate patch-wise saliency map for point clouds. Our basic idea is to design the Mask Building-Dropping process, which adaptively matches the size of important/unimportant patches by clustering points with close saliency. Experimental results on several typical 3D DNNs show that our patch-wise saliency algorithm can provide better visual guidance, and can detect where a 3D DNN is focusing more efficiently than a point-wise saliency map. Finally, we apply our patch-wise saliency map to adversarial attacks and backdoor defenses. The results show that the improvement is significant.

Energy-efficient access point clustering and power allocation in cell-free massive MIMO networks: a hierarchical deep reinforcement learning approach

Cell-free massive multiple-input multiple-output (CF-mMIMO) has attracted considerable attention due to its potential for delivering high data rates and energy efficiency (EE). In this paper, we investigate the resource allocation of downlink in CF-mMIMO systems. A hierarchical depth deterministic strategy gradient (H-DDPG) framework is proposed to jointly optimize the access point (AP) clustering and power allocation. The framework uses two-layer control networks operating on different timescales to enhance EE of downlinks in CF-mMIMO systems by cooperatively optimizing AP clustering and power allocation. In this framework, the high-level processing of system-level problems, namely AP clustering, enhances the wireless network configuration by utilizing DDPG on the large timescale while meeting the minimum spectral efficiency (SE) constraints for each user. The low layer solves the link-level sub-problem, that is, power allocation, and reduces interference between APs and improves transmission performance by utilizing DDPG on a small timescale while meeting the maximum transmit power constraint of each AP. Two corresponding DDPG agents are trained separately, allowing them to learn from the environment and gradually improve their policies to maximize the system EE. Numerical results validate the effectiveness of the proposed algorithm in term of its convergence speed, SE, and EE.

Nonparametric Bayesian functional clustering with applications to racial disparities in breast cancer

AbstractAs we have easier access to massive data sets, functional analyses have gained more interest. However, such data sets often contain large heterogeneities, noises, and dimensionalities. When generalizing the analyses from vectors to functions, classical methods might not work directly. This paper considers noisy information reduction in functional analyses from two perspectives: functional clustering to group similar observations and thus reduce the sample size and functional variable selection to reduce the dimensionality. The complicated data structures and relations can be easily modeled by a Bayesian hierarchical model due to its flexibility. Hence, this paper proposes a nonparametric Bayesian functional clustering and peak point selection method via weighted Dirichlet process mixture (WDPM) modeling that automatically clusters and provides accurate estimations, together with conditional Laplace prior, which is a conjugate variable selection prior. The proposed method is named WDPM‐VS for short, and is able to simultaneously perform the following tasks: (1) Automatic cluster without specifying the number of clusters or cluster centers beforehand; (2) Cluster for heterogeneously behaved functions; (3) Select vibrational peak points; and (4) Reduce noisy information from the two perspectives: sample size and dimensionality. The method will greatly outperform its comparison methods in root mean squared errors. Based on this proposed method, we are able to identify biological factors that can explain the breast cancer racial disparities.

Probing cosmology via the clustering of critical points

ABSTRACT Exclusion zones in the cross-correlations between critical points (peak-void, peak-wall, filament-wall, and filament-void) of the density field define quasi-standard rulers that can be used to constrain dark matter and dark energy cosmological parameters. The average size of the exclusion zone is found to scale linearly with the typical distance between extrema. The latter changes as a function of the matter content of the universe in a predictable manner, but its comoving size remains essentially constant in the linear regime of structure growth on large scales, unless the incorrect cosmology is assumed in the redshift–distance relation. This can be used to constrain the dark energy parameters when considering a survey that scans a range of redshifts. The precision of the parameter estimation is assessed using a set of cosmological simulations, and is found to be a 4σ detection of a change in matter content of 5 per cent, or about 3.8σ detection of 50 per cent shift in the dark energy parameter using a full sky survey up to redshift 0.5.

What can we learn from a master plot of energy rate versus mass for a very wide variety of (complex) systems?

Mass and energy rate (ER) data have been collected for a wide variety of (complex) systems from the biological, cultural, and cosmological realms. They range from the cytochrome oxidase protein (10-22 kg and 6x10-19 W) to the observable universe (1.5x1053 kg and 1048 W) and, thus, span 75 mass and 66 ER orders of magnitude. Many of these systems are relevant for the big history (BH) narrative, i.e., the development of complexity over “big time” from the Big Bang up to the human society on Earth of today. The purpose of this paper is not per se to describe their history though, but to explore a master plot of ER vs. mass. Notably, the development of systems over big time has followed a rather tortuous path criss-crossing over this ER vs. mass master plot. The true mass of the system as a whole is used (for example trees including the non-living wood, living organisms including their intrinsic water, and social systems including the built constructs), because these inactive parts are essential for the performance of the system and facilitate its ER. A double logarithmic master plot of all ER vs. mass data shows clusters of data points. To some extent, this provides quantitative support for the distinction between the (sub-)realms, which is based on a qualitative description of their material structure and energy processing. In the master plot, small systems with low mass and ER converge into larger systems with larger mass and ER, which is typically accompanied by a decrease of the energy rate density (ERD = ER/mass). Correlation of ER with mass for various groups of systems demonstrates both sub- and supra-linear scaling with the power law β constant varying between 0.5 and 4.0, showing that the mechanisms of self-organisation are quite different for the corresponding system groups. The combination of convergence and scaling with β always larger than zero explains why the ER & mass data points fall in a diagonal band with a width of 17 orders of magnitude.
 ER and mass have changed over wide ranges during the evolution of groups of systems, suggesting that evolution can be viewed as a process of systems exploring a larger ER vs. mass area until they run into ER and/or mass limitations. Indeed, there is a diagonal ER vs. mass limit for stable systems in all realms, corresponding to an ERD value of around 105 W/kg. Systems with ER & mass combinations above this limit, such as bombs, super-novae and cosmological transients, are unstable and “explosive”. This raises the interesting question of whether such an ERD maximum puts a limit on the development of complexity over big time. It seems that the low, right side of the master plot is empty. However, it is argued here that it is full of systems with low ER, such as dormant, living organisms, technological systems with their power adjusted or even switched off, as well as cooling, cosmological objects. Such systems are typically considered of less interest in a BH context, but they are viewed here as simple, complex systems which are out of equilibrium with matter, energy and information stored in their structure. While ERD appears to increase with the ‘advancement’ of systems over big time [5,51,52], there are quite some confounding factors regarding the efficacy of ERD as a metric for complexity in BH. For example, ERD decreases during the lifetime of a human and the human society (the mass of human-made constructs has grown faster than the global energy consumption), as well as during the evolution of living organisms and stars, whereas complexity is considered to increase. High ERD values of system parts may be illustrative for the complexity of the larger system, but are not representative for ERD of the system itself. Machines with an increased efficiency of energy conversion have a lower ERD, but could be considered more complex. The smallest and largest ERD values observed for the various realms appear to correlate with activity level and reciprocally with size, which do not per se reflect complexity. It is hoped that the raw data collected and the major trends observed in this paper will offer new insights into various aspects of the evolution of the universe over big time, and serve as an important resource for other related studies.

Video-Based Identification and Prediction Techniques for Stable Vessel Trajectories in Bridge Areas.

In recent years, the global upswing in vessel-bridge collisions underscores the vital need for robust vessel track identification in accident prevention. Contemporary vessel trajectory identification strategies often integrate target detection with trajectory tracking algorithms, employing models like YOLO integrated with DeepSORT or Bytetrack algorithms. However, the accuracy of these methods relies on target detection outcomes and the imprecise boundary acquisition method results in erroneous vessel trajectory identification and tracking, leading to both false positives and missed detections. This paper introduces a novel vessel trajectory identification framework. The Co-tracker, a long-term sequence multi-feature-point tracking method, accurately tracks vessel trajectories by statistically calculating the translation and heading angle transformation of feature point clusters, mitigating the impact of inaccurate vessel target detection. Subsequently, vessel trajectories are predicted using a combination of Long Short-Term Memory (LSTM) and a Graph Attention Neural Network (GAT) to facilitate anomaly vessel trajectory warnings, ensuring precise predictions for vessel groups. Compared to prevalent algorithms like YOLO integrated with DeepSORT, our proposed method exhibits superior accuracy and captures crucial heading angle features. Importantly, it effectively mitigates the common issues of false positives and false negatives in detection and tracking tasks. Applied in the Three Rivers area of Ningbo, this research provides real-time vessel group trajectories and trajectory predictions. When the predicted trajectory suggests potential entry into a restricted zone, the system issues timely audiovisual warnings, enhancing real-time alert functionality. This framework markedly improves vessel traffic management efficiency, diminishes collision risks, and ensures secure navigation in multi-target and wide-area vessel scenarios.

New kind of vector space via Ş-Proximit structure

This paper describes the basic aim of Ş -proximit space for non-empty sets. The relationship between approach space and Ş-proximit space has been clarified. This paper demonstrates that all metric spaces are Ş-proximit spaces. But the opposite is not always true. We define SA-contraction and present various features and the results. In addition, we define new Ş-proximit normed space. We demonstrate that any proximit normed space is normed. But the opposite is not always true. We define the concepts of the Ş -proximit semigroup, Ş-proximit group, and Ş-proximit vector space via instances of problem-solving techniques. We also discussed the definitions of Cauchy sequence, cluster point, Ş -convergent sequence, and Ş -complete.

Informatization Teaching Mode of Intellectual Property Law Course Based on Clustering Algorithm

Abstract The traditional intellectual property law course cannot adapt to the needs of cultivating students’ active learning ability, practical ability and innovation ability in the digital era due to the teaching concept, teaching means, teaching method and assessment form. This study proposes an information-based teaching model, which builds a course knowledge organization model using a formal expression language, through atomized knowledge points and knowledge granularity. The k-means algorithm has been improved from the perspective of center selection and constraint rules to adapt to the characteristics of the intellectual property law course and complete the clustering and extraction of knowledge points. The frequent item-based method analyzes the students’ answers and generates the corresponding association rules to further develop the analysis of learning situations. For a college law school study, it was found that 925 simultaneous wrong answers and 8152 simultaneous correct answers were successfully mined using clustering. In applying this college students’ evaluation scores of this information technology teaching in terms of content design, presentation design, structural design and relationship design of knowledge clustering are 0.796, 0.818, 0.788, 0.794, and overall good results are achieved.

Estimation of plant's morphological parameters using terrestrial laser scanning-based three-dimensional point cloud data

The yield of crop is very important for sustainable agriculture to meet continuously growing demand of food. The morphological parameters, such as plant height (PH), projected leaf area (PLA), and plant volume (PV) are important metrics to estimate crop yield. In this paper, a multi-step methodology is proposed to estimate parameters PH, PLA and PLA using state-of-the-art three-dimensional (3D) mapping technique: terrestrial laser scanning (TLS). The proposed methodology consists of three well-designed steps: pre-processing, ground filtering and clustering, and estimation of plant's morphological parameters. In pre-processing TLS-derived laser scans acquired from multiple scan stations to cover the selected agricultural test site registered and coordinate transformation is performed to convert the TLS point cloud into total station (TS)-based locally defined coordinate system. The second step transformed point cloud data is processed to generate ground and non-ground points, where subsequently Euclidean clustering is employed to generate clusters of non-ground points. The clustered data is cleaned based on geometrical constraints and cabbage plant's clusters are extracted, which are processed using height-based analysis and convex hull algorithm to estimate PH, PLA and PLA of each cluster. The proposed methodology performance was evaluated using TLS point cloud data of selected agricultural field of cabbage plants, and PH, PLA and PLA estimation was performed at RMSE of 0.005 m, 0.012 m2 and 0.0063 m3 respectively. The proposed methodology is efficient and easy to implement step-wise approach from data collection to processing for plant's geometrical analysis, thus it has potential to be used as one of the industrial tools for precision agriculture.

Simulation of proton-induced primary displacement damage in GaAs under different ambient temperatures

The performance of on-orbit GaAs-based solar cells is susceptible to the displacement damage effect. The proton-induced primary displacement damage in GaAs on a geosynchronous equatorial orbit (GEO) was simulated and analyzed by combining the Monte Carlo (MC) and molecular dynamics (MD) methods. The MC simulation provided the distribution of primary knock-on atoms (PKAs) in GaAs induced by GEO-related protons to the MD simulation. In MD simulations, the effects of radiation fluence and ambient temperature on the displacement damage were considered. The simulation results showed that GEO-related protons generated a significant number of PKAs within an energy range of below 10 keV in GaAs. The high-fluence radiation emulated by the binary PKA could generate more point defects and cluster defects in GaAs than the low-fluence radiation emulated by single PKAs. As compared to room temperature (300 K), both a low (100 K) and high (500 K) ambient temperature could deteriorate the displacement damage. In addition, a high ambient temperature of 500 K could induce widespread thermal spikes in GaAs as compared to 100 and 300 K. This work can provide useful insight into the proton-induced displacement damage in GaAs and the radiation hardening of GaAs-based photoelectric devices in space.

A Multimodal Biometric Recognition Method Based on Federated Learning

Recently, multimodal authentication methods based on deep learning have been widely explored in biometrics. Nevertheless, the contradiction between the data privacy protection and the requirement of sufficient data when model optimizing has become increasingly prominent. To this end, we proposes a multimodal biometric federated learning framework (FedMB) to realize the multiparty joint training of identity authentication models with different modal data while protecting the users’ data privacy. Specifically, a personalized multimodal biometric recognition model fully trained by each participant is first obtained to improve the authentication performance, using modal point clustering with class‐first federated learning methods on the service side with the modal. Then a complementary multimodal biometric recognition strategy is implemented to build a complementary modal model. Finally, the fusion participant local model, with the modal model and complementary modal model, is trained by all participants again to obtain a more personalized modal model. The experimental results have demonstrated that the proposed FedMB can either protect the data privacy or utilize the data from all participants to train the personalized biometric recognition model to improve identity authentication performance.

A secured image based three factor user authentication system

Graphical User Authentication (GUA) is an image-based password system that leverages the human tendency to remember visuals more effectively. This methodology enables users to effortlessly generate and recall passwords. The three important parameters for any graphical based password system are Usability, Randomness and Security. Usability deals with the system adaptability, memorability, flexibility, User satisfaction etc. On the other side randomness is about Hotspot Coverage, Click Point Clustering, Spatial Patterns, J-statistics etc. This paper is an attempt to initially develop an image-based authentication system that is usable, venerable in terms of randomness. In addition, it is necessary to build a strong security authentication process where the attackers are unable to access the system. The past research study claims the diversity between the usability and security aspect. The focus of this research study is to analyze the impact of various security attacks on the proposed system and the possible solution to avoid them.

DLOAM: Real-time and Robust LiDAR SLAM System Based on CNN in Dynamic Urban Environments

Dynamic object detection, state estimation, and map-building are crucial for autonomous robot systems and intelligent transportation applications in urban scenarios. Most current LiDAR Simultaneous Localization and Mapping (SLAM) systems operate on the assumption that the observed environment is static. However, the overall accuracy and robustness of a SLAM system can be compromised by dynamic objects in the environment. Aiming at the problem of inaccurate odometry estimation and wrong mapping caused by the existing LiDAR SLAM method which cannot detect the dynamic objects, we study the SLAM problem of robots and unmanned vehicles equipped with LiDAR traveling in the dynamic urban scenes. We propose a fast LiDAR-only model-free dynamic objects detection method, which uses the spatial and temporal information of point cloud through a convolutional neural network (CNN), and the detection accuracy is improved by 35 use spatial information. We further integrate it into a state-of-the-art LiDAR SLAM framework to improve the SLAM performance. Firstly, the range image constructed by LiDAR point cloud is used for ground extraction and non-ground point clustering. Then, the motion of objects in the scene is estimated by the difference between adjacent frames, and the segmented objects are further divided into dynamic objects and static objects by their motion features. After that, the stable feature points are extracted from the static objects. Finally, the pose transformation of adjacent frames is solved by matching feature point pairs. We evaluated the accuracy and robustness of our system on datasets with different challenging dynamic environments, and the results show our system has significant improvements in accuracy and robustness of odometry and mapping, while still maintain real-time performance, which is sufficient for autonomous robot systems and intelligent transportation applications in urban scenarios.

Ideal/balance point clustering algorithm

Generally clustering is one of the largest used ML techniques to group data points of similar type together. Mostly while grouping data points based upon few popular traditional clustering algorithms like KNN, K-means etc. only the magnitudes of those data points are considered. The deviation of those data points from a particular point said to be the center point or the balance point of the entire dataset is not considered that much, but Here in this Ideal Balance Point clustering algorithm the degree of deviation of all the data points from the balance point is primarily considered. By using such a methodology, we may be able to form clusters of data points based on their degrees of deviation from the Ideal Balance Point of the entire dataset. The Ideal Balance Point of the dataset is actually the centroid of the plane on which the datapoints are distributed. Here in the Ideal Balance Point clustering algorithm the user may also manually feed-in the Ideal Balance Point for the dataset based on the requirement or as per the practical idealness of the circumstance and nature of the dataset. Generally, this idea is derived from the theory that an object has all its’ mass equally distributed on the centroid. Hence the plane formed by the distribution of the data points is considered as an object and the centroid of it is assumed to be the point where the entire data points are directed into, but the ideal balance point for the data may also differ as per real life scenario, thus the feature of feeding in the balance point is also given in this Ideal Balance Point clustering algorithm.