This paper introduces a method to explain the individual classification decisions of any classification algorithm, particularly focusing on nonlinear models. The authors propose a framework that defines local explanation vectors as class probability gradients, which help understand the prediction results for single data instances. These vectors highlight the features that are most influential in changing the predicted label. The method is applicable to various classification methods, including Gaussian Process Classification (GPC), Support Vector Machines (SVM), and k-Nearest Neighbors (k-NN). The paper demonstrates the effectiveness of the method through several applications, such as classifying Iris flowers using k-NN, distinguishing digits "two" and "eight" using SVM, and explaining mutagenicity classification using GPC. The results show that the explanation vectors can provide insights into the decision-making process, even in complex datasets like chemical compounds. The authors also discuss the limitations of the approach, such as handling zero derivatives and the assumption of stationarity in the data. Overall, the method offers a valuable tool for understanding the predictions of nonlinear classifiers.This paper introduces a method to explain the individual classification decisions of any classification algorithm, particularly focusing on nonlinear models. The authors propose a framework that defines local explanation vectors as class probability gradients, which help understand the prediction results for single data instances. These vectors highlight the features that are most influential in changing the predicted label. The method is applicable to various classification methods, including Gaussian Process Classification (GPC), Support Vector Machines (SVM), and k-Nearest Neighbors (k-NN). The paper demonstrates the effectiveness of the method through several applications, such as classifying Iris flowers using k-NN, distinguishing digits "two" and "eight" using SVM, and explaining mutagenicity classification using GPC. The results show that the explanation vectors can provide insights into the decision-making process, even in complex datasets like chemical compounds. The authors also discuss the limitations of the approach, such as handling zero derivatives and the assumption of stationarity in the data. Overall, the method offers a valuable tool for understanding the predictions of nonlinear classifiers.