## 3 Proposed Architecture
### Problem Description and Notation  
In this context, the linear classification of agriculture commodity forecasting initially classifies different commodities and predicts their future prices based on a predictor function that is linear in nature. For this purpose, we need to combine weight with the value of a commodity-dependent variable. Further, nonlinear operations for future predictions regarding commodities prices can be involved in the entire process.  
\[Linear=[X\;(features)]+Weight\;(w),\;Y\;(classification) \tag{1}\]  
\[Link\;Function=Calculate\;Gradients \tag{2}\]  
\[Compute\;Cost=Analysis\;(Link\;Function). \tag{3}\]  
In Equation (1), the linear equation associates an individual feature with a connected weight. The reason behind this equation is to call it logistic regression, which is a more generalized linear model. The link function provides a data converter platform, where we can define the range of parameters, such as (0,1) for computing efficient cost and dependencies, as elaborated in Equation (2), whereas Equation (3) demonstrates the link function, which is an activation function, and 'a' is the defined value as follows:  
After this linear process of commodity classification, logistic regression is applied to the range of two dependent variables (A and B). Therefore, A is defined as a matrix of values with an '\(n\)' number of features extracted in the '\(i\)th' iteration. Similarly, B is defined as a vector with dependent features of'm.' According to the gathered values of agricultural commodities, we create a customized weight matrix, which is as follows:  
\[\mathit{Linear}\ (l)=w_{0}+w_{1}*a_{1}+w_{2}*a_{2}+\ldots+w_{n}*a_{n} \tag{4}\]  
The link function is calculated after the multiplication of randomly generated features for forecast prices:  
\[\mathit{Link}\ Function\ (LF)=\left[\frac{1}{(1+e^{a})}\right] \tag{5}\]  
However, the cost of the '\(i\)th' iteration of the price prediction is calculated as:  
\[\mathit{Cost}\ (c)=(1-n)\sum_{j=1}^{j=n}LF^{\prime}\log(LF)+\left(1-LF^{\prime} \right)*\log(1-LF) \tag{6}\]  
After this whole process, we calculate the derivation of the calculated cost of \(LF^{\prime}\) with the updated weight for efficient future prediction of commodity prices:  
\[\mathit{Gradients}\ (g)=\sum_{j=1}^{j=n}\left(LF^{\prime}-LF\right)*mj \tag{7}\]  
\[\mathit{Update}\ Weight\ \left(w^{\prime}\right)=wj-(a*g) \tag{8}\]  
The main objective of using the linear-logistic regression method is to create a linear boundary-based classification and decision system that separates two classes based on conditional probability:  
\[\mathit{Probablity}\ (P)=\left(LF^{\prime}=1\ \middle|a;w\right) \tag{9}\]  
We initiate the future prediction of classification by tuning the decision boundary of '+' features, where '1' and '0' are classified as factors related to the class-based decision boundary, and therefore, the equation is:  
\[\mathit{Probablity}\ (P)=\left(LF^{\prime}=0\ \middle|a;w\right) \tag{10}\]  
Logistic regression evaluates the probability of commodity prices for a particular set of defined data points, such as agricultural-related crop production information, belonging to either class '0,' equal to the previous predictive class, or class '1,' equal to the current predictive class. The value of \(a\) and \(w\) is changed in every classification phase to obtain an accurate price forecast of each commodity efficiently. We evaluate a set of values obtained from negative (\(-\)ve) to positive (\(+\)ve) infinity according to the previous and current prices in the linear model. For this purpose, we narrow down the score to a range of (0,1) as the probability (for prediction).  
The exponent of the activation function is justified as the probability, which is always '>0.' The limit of this linear-logistic regression is set at values less than 1, for the purpose of dividing the value in the numerator by the value of '>1.'