Publisher Correction: A science-based approach to classifying light vehicles in Europe: methodology and case studies

Correction to: Scientific Reports 10.1038/s41598-025-90625-9, published online 17 March 2025

The original version of this Article contained display errors in some of the Equations.

As a result, in the Methods section, where:

“In our case, the PDF is represented as f_X|Y (x) where X represents the random variable of interest (e.g., length, width, height), and Y represent the categorical variable defining the vehicle segments (e.g., A, B, C, D, …, N). For example, f_X|Y ₌A(x) represents the PDF of X when Y is in segment A.

To define the similarity of a specific group we determine the conditional probability that, given a vehicle characteristic, the vehicle belongs to a specific segment:

where f_X (x) stands for the marginal probability density functions (PDFs) of the continuous random variable we are interested in. P(Y = y_i) shows the prior probability of each segment, and f_X |Y ₌ y_i (x) represents the PDF of a particular random variable for a specific segment.”

now reads,

In our case, the PDF is represented as  where X represents the random variable of interest (e.g., length, width, height), and Y represent the categorical variable defining the vehicle segments (e.g., A, B, C, D, …, N). For example,  represents the PDF of X when Y is in segment A.

To define the similarity of a specific group, we determine the conditional probability that, given a vehicle characteristic, the vehicle belongs to a specific segment:

where f_X  stands for the marginal probability density functions (PDFs) of the continuous random variable we are interested in. P(Y = y_i) shows the prior probability of each segment, and  represents the PDF of a particular random variable for a specific segment.”

Furthermore, Equation 3

now reads,

And lastly, where

The boundary is again determined by locating the zeros of the difference of the kde of groups y_n and y_m, with the difference that in this case the kde are calculated for two features (f_Xi|Y ₌y_n (x), f_Xj |Y ₌y_n (x)) and are represented by surfaces in the 3d space (a). The zeros of the function, defined by Eq. (4), constitute a 2d domain of features X_i and X_j, which can be approximated by linear functions or piecewise linear functions (b).

now reads,

The boundary is again determined by locating the zeros of the difference of the kde of groups y_n and y_m, with the difference that in this case the kde are calculated for two features and are represented by surfaces in the 3d space (a). The zeros of the function, defined by Eq. (4), constitute a 2d domain of features X_i and X_j, which can be approximated by linear functions or piecewise linear functions (b).

The original Article has been corrected.