Data with Non-Euclidean Geometry and its Characterization

Recently, dealing the Non-Euclidean data and its characterization is considered as one of the major issues by researchers. The first problem arises while distinction of among Euclidean and non-Euclidean geometry. The second problem arises with dealing the Non-Euclidean geometry in true, false and uncertain regions. The third problem arises while investigating some patterns in Non-Euclidean data sets. This paper focused on tackling these issues with some real life examples in data processing, data visualization, knowledge representation, and quantum computing.


Introduction
Data representation and its graphical visualization for knowledge processing tasks is one of the major tasks by research communities [1][2]. In this regard the Euclidean geometry [3] and its postulates help a lot while drawing point, straight line, circle, rectangle or parallel lines [4]. It provided famous theorem that, the angle sum of triangle must be 180 0 as shown in      s theory is extensively studied using NeutroAlgebra [13][14][15] to visualize them via Neutrogeometry [16][17][18]. understood as an example that you want to walk on a defined path to till its End. You become tired after some time and feel emptiness due to which start travelling halfway, before you get halfway started quarter then one-eight, one-sixteen and so on.
It will require infinite number of paths to complete. These types of non geometry where AB and BA do not apply need attention for precise analysis using some Non-Euclidean geometry happened with human cognition when several parallel paths exist from a given point not the straight line as shown in Figure   5.

Non-Euclidean Geometry
This section provides some examples to understand the Non-Euclidean geometry as given below: In this section some Non geometry and its visualization is show better understanding.
pes of data set requires ) vertex and its n items [19]. It needs Euclidean or exponential space to analyze the data in case of large amount.
It is indeed requirement as per current scenario. To achieve this goal, this paper       proposed to deal with these types of data in NeutroGeometry for multi-decision process.

A Method to Deal Non-Euclidean Data
In this section a method is proposed to for characterization of Non-Euclidean data in true, false and NeutroGeometry as follows: Step 1. Let us consider the data with non-Euclidean geometry and its attributes (A).
Step 2. Let A be any non-empty set of a given Non-euclidean geometrical data.
Step 4. In case any map possible then we can characterize them as follows: Step 5. It defined a function f: XY which provides three possibilities: (i) In case a well-defined mapping exists among X and Y then it is called as true regions.
(ii) In case the mapping is undefined or outer-defined mapping among X and Y then it is in false regions.
(iii) It is unknown that the mapping exists or not and what is the value for the mapping among X and Y then the element is in NeutroGeometry.
Step 6. In this way the Non-Euclidean data sets and its characterization can be possible.
Step 7. The similarity among the data sets can be found using the Geodesic distance.
Step 8. The geodesic distance provides shortest path among two non-Euclidean data rather than its straight line distance of Euclidean geometry as shown in Figure 11. Euclidean and Geodesic distance Step 9. The data closed to the defined geodesic distance can be considered as Cluster for knowledge processing tasks.  in the sky and its pattern can be found.

Geometry and its Characterization
Recently, some of the authors paid attention     In this case the Non-Euclidean geometry may provide a new metric for brain drain and dark data analysis [36] quantum space to analyze the momentum of human cognition.   The current paper explores some Non-Euclidean data sets and its characterization.
In near future the author will focus on introducing some new metric to find the pattern in Non-Euclidean geometrical data sets and NeutroGeometrical data sets.

Conclusions
This paper put forward effort towards dealing the Non-Euclidean geometry and its characterization. To achieve this goal, a method has been proposed in Section 3 for its analysis with its illustration in Section 4.
In the future the author will focus on introducing some new techniques to find the pattern in Non-Euclidean data sets and exploring the Neutrogeometry with illustrative examples to distinguish them.
Acknowledgements: Author thanks the editor and other team member of this journal for their valuable time.
Funding: Author declares that, there is no funding for this paper.

Conflicts of Interest: The author declares
there is no conflict of interest.