2. The BireyselValue name, conditions and showcase

2.1.         Meaning of the name BireyselValue

The similarity check between the individual traits of a class and the observation to be classified, outlined above in \ref{867500}, implies two things: the observations in the same class coincide with one another and have similar characteristics; moreover, the individual traits of a class form the backbone of the BireyselValue method to predict the class of the given observation. To this end, those individual traits must be sought from observations that are in the same class. Since the personal characteristics of the observations in the same class are the input to form the individual traits of that class, the name Bireysel was used for this method. In the Turkish language, the word “Bireysel” has the same meaning as “personal” or “individual” as in the English language. The second part of the name “Value” is self-explanatory.

2.2. Conditions

Two conditions are required for the BireyselValue method to be employed:
2.2.1. The training dataset of size \(m\times n\) must have \(m\ge80\), and \(n\ge2\).
2.2.2. The \(k\) classes must be \(\ge2\). In addition, each class must have \(m_{c_s}\ge40\)\(m_{c_s}\) corresponds to the number of observations in a class.

2.3. Showcases

To demonstrate the use of the BireyselValue method, this paper will present an example of a training dataset with a size of \(m=120\) observations and \(n=5\) variables, which means that 600 entries are measured. Furthermore, the training dataset has \(k=3\) classes as \(C=(1,2,3)\).

3. Proposed Method

In this section, the three stages of the proposed method, named BireyselValue, are presented. The building stage is presented in \ref{921392}, the training stage is presented in \ref{625657}, and the prediction stage is presented in \ref{500846}.

3.1 The Building Stage  

In this stage, four steps are involved in creating five parameters; the sequence of the steps is as follows:

3.1.1. Step one

The norm of the training dataset is captured using the Euclidean norm, which is the square root of the sum of every squared entry in the training dataset. The result is a scalar value named parameter_1, which is referred to as \(v_{norm}\). The calculation of the norm is formulated as follows:
\(\begin{equation} \label{eq:1} \sqrt{\sum_{r=1}^m\sum_{a=1}^n〖x_{ra}〗^{2}} \end{equation}\)           

Next, parameter_1 in Equation (1) is used to scale the training dataset; every entry \(x_{ra}\) in the training dataset is divided by parameter_1. As a result, the scaled version of the training dataset is referred to as __dsFig. (\ref{323202}) illustrates the outcome from this step using the showcase example in (\ref{993524}).