**2. Data Classification**

Data classification is the process of organizing and categorizing data based on predetermined criteria [7]. It is a crucial aspect of many applications, including data management, data analysis, and information retrieval.

#### *Logistic Regression Algorithm*

Logistic regression is a type of binary classification algorithm that is used to predict the probability of an event occurring [8]. It has been commonly used in machine learning for applications such as spam detection, medical diagnosis, and sentiment analysis [9].

The logistic-regression model maps the input features *x*1, *x*2, ..., *xn* to a predicted output variable *y* that has a value between 0 and 1, representing the probability of the event occurring [10].

The logistic function, also known as the sigmoid function, is used to model the relationship between the input features and the predicted output variable. The sigmoid function is defined as [10]:

$$f(z) = \frac{1}{1 + e^{-z}}$$

where *z* = *w*<sup>0</sup> + *w*1*x*<sup>1</sup> + *w*2*x*<sup>2</sup> + ... + *wnxn* is the linear combination of the input features and their corresponding weights, with *w*<sup>0</sup> as the bias term.

The logistic regression algorithm aims to find the optimal values for the weights *w*0, *w*1, *w*2, ..., *wn* that minimize the error between the predicted output variable and the true output variable [11]. This is achieved by maximizing the likelihood function, which is the probability of the observed data according to the model parameters [12]. The likelihood function for logistic regression is:

$$L(w) = \prod\_{i=1}^{m} f(z\_i)^{y\_i} (1 - f(z\_i))^{1 - y\_i}$$

where *m* is the number of training examples, *yi* is the true output variable for the *i*th example, and *zi* is the linear combination of the input features and weights for the *i*th example [13].

The optimal values for the weights can be found using gradient descent, which involves iteratively updating the weights in the direction of the negative gradient of the likelihood function [14]. The updated rule for the weights is:

$$w\_j := w\_j - \alpha \frac{\partial L(w)}{\partial w\_j}$$

where *α* is the learning rate, and *<sup>∂</sup>L*(*w*) *<sup>∂</sup>wj* is the partial derivative of the likelihood function with respect to the *j*th weight.

The logistic regression algorithm can be summarized in the following steps:


One of the main advantages of logistic regression is its simplicity and ease of implementation. It is a straightforward algorithm that can be easily implemented using standard statistical software [15]. Additionally, logistic regression is highly interpretable, allowing users to understand the contributions of each independent variable to the predicted probability. It is also robust regarding multicollinearity, meaning that it can handle correlated independent variables without producing biased estimates.

However, logistic regression is not without its challenges. One of the main limitations is that it is only suitable for binary classification problems, meaning that it can only predict the likelihood of an event occurring or not occurring [16].

#### **3. Image Detection Technique**

Image detection is a technique used to identify and locate specific objects, features, or patterns within an image. It is a crucial aspect of many applications, including object recognition, facial recognition, and scene comprehension [17]. In the field of healthcare, image detection is used to analyze and interpret medical images, such as X-rays, CT scans, and MRIs. These images provide important diagnostic information that can be used to identify and treat diseases.
