## 2 Supervised Approach for Land Use  
In this section, we introduce the concept of supervised learning as an alternative to traditional unsupervised methods for solving the place identification problem. Supervised classification offers several advantages to place identification through learning patterns from correctly labeled training data. It does so by learning from a data set with both input features and labels or outputs to predict labels for completely new, unseen data. Unlike clustering, domain expertise is explicitly provided for supervised learning through labeled examples, so careful separation of the training test from the test set should be made available. This structured approach lets the model learn specific patterns that distinguish between various types of places based on real examples rather than relying on inherent similarities in the data. For this case, we need a set of representative patterns of cells correctly classified. To do this, we select a subgrid of the area under study that contains patterns or cells (\(x_{i}\)) with the labels (\(y_{i}\)) that we want to identify \(T=(x_{i},y_{i})\) such that we can infer a function \(h(x_{i})=y_{i}\) and its capability can be evaluated to classify unlabeled patterns (\(x_{i}^{\prime}\)). Multi-class classification [25, 26] is a type of supervised learning where an algorithm is trained to categorize data points into more than two distinct classes. Unlike binary classification, which has to deal with only two classes, multi-class classification contains more labels and usually requires more complicated models that can handle a variety of outcomes. Support vector machines (SVM) [26], specifically support vector classification implementation (SVC) [28], represent one powerful approach to supervised classification. SVMs work in such a manner that they find the optimal hyperplane, which maximizes the margin between the classes in feature space. SVMs apply kernel functions to handle non-linear classification problems by implicitly mapping data to higher-dimensional spaces where linear separation is possible. This makes SVMs particularly suitable for place identification tasks where the relationship between features (such as temporal patterns or mobility characteristics) and place categories may be complex and non-linear. We use the most common kernel functions in SVM:  
* The linear kernel computes the dot product between feature vectors. This is applicable if data are linearly separable in the original feature space. * The polynomial kernel extends the linear kernel by incorporating polynomial terms to enable the capture of higher-order patterns based on the degree of the polynomial. * The radial basis function (RBF) kernel is a widely used kernel that maps data points into an infinite-dimensional space. It is particularly effective for datasets where the relationship between features is non-linear. * The sigmoid kernel resembles the activation function in neural networks and is useful for certain types of data. The similarity between two data points is computed using the hyperbolic tangent function. The k-nearest neighbors (kNN) classifier, as introduced in [29], stands out as one of the most intuitive and effective approaches to supervised classification. This algorithm classifies new data points by identifying the majority class among their k closest neighbors in the feature space. Despite its simplicity, kNN consistently delivers competitive performance in various classification tasks. The main challenge is to choose an appropriate value of k since this parameter has a high impact on the performance of the model and, therefore, has to be tuned carefully depending on dataset characteristics. We apply the kNN algorithm using three different distance metrics to assess its performance under different data characteristics:  
* Manhattan distance: This metric calculates the absolute differences between coordinates along each dimension, summing them to calculate the total distance.