3.1.2. Logistic Regression

An LR algorithm is formed from regression analyses, deriving a linear relationship amongs<sup>t</sup> the LCFs by using coefficients [22]. This algorithm, which is derived from statistics, produces a regression output in the form of a mathematical function, and can calculate the probability of the occurrence of landslides. The sigmoid function or logistic function, which is used in this algorithm, is where the name of LR originates. The sigmoid function in 'S' shape is a core part of LR, which sets an asymptote, based on the positive or negative values of *x*. For positive values of *x*, an asymptote is set to *y* = 1, and for negative values of *x*, asymptote is set for *y* = 0.

The algorithm is easy to implement and does not require any hyper parameter tuning. The model finds its application in LSM due to this simplicity and its usage of probability to predict the solution. A non-linear relationship is established with the landslide and nonlandslide points and LCFs and finds a fitting function. The probability of the occurrence of landslides *P*(*L*) is calculated by LR as follows:

$$P\left(L\right) = \frac{\varepsilon^{\mathbf{x}}}{1 + \varepsilon^{\mathbf{x}}} \tag{2}$$

where, *x* is a linear fitting function, using the LCFs, given by:

$$z = a\_0 + a\_1 C\_1 + a\_2 C\_2 + \dots + a\_n C\_n \tag{3}$$

where, *a*0 is the intercept, *a*1, *a*2 ... *an* are the regression coefficients, and *C*1, *C*2, ... *Cn* are the LCFs. For dependent variables in binary form and large input data with minimum duplicates and minimum multi collinearity, the algorithm can produce satisfactory results in LSM [23].
