A transportation service must be sustainable, respectful of the environment, and socially and economically responsible. These requirements make metro networks the ideal candidate as the most efficient mean of transport in our society. Now, a correct management of this type of infrastructures entails the analysis of the structure and robustness of these networks. This allows us to detect malfunctions and, above all, to design in the most appropriate way the expansion of subway networks. This is one of the major challenges facing the study of transport networks in sustainable smart cities. In this sense, the complex network analysis provides us with the necessary scientific tools to perform both quantitative and qualitative analysis of metro networks. This work deals with Madrid metro network, which is the largest in Spain. The main structural and topological characteristics, and robustness features of Madrid metro network were studied. The results obtained were analyzed and some conclusions were derived.

With the growth of cities, urban traffic has increased and traffic congestion has become a serious problem. Due to their characteristics, metro systems are one of the most used public transportation networks in big cities. So, optimization and planning of metro networks are challenges which governments must focus on. The objective of this study was to analyze Madrid metro network using graph theory. Through complex network theory, the main structural and topological properties of the network as well as robustness characteristics were obtained. Furthermore, to inspect these results, multivariate analysis techniques were employed, specifically HJ-Biplot. This analysis tool allowed us to explore relationships between centrality measures and to classify stations according to their centrality. Therefore, it is a multidisciplinary study that includes network analysis and multivariate analysis. The study found that closeness and eccentricity were strongly negatively correlated. In addition, the most central stations were those located in the city center, that is, there is a relationship between centrality and geographic location. In terms of robustness, a highly agglomerated community structure was found.

The present paper focuses on the analysis of large data sets from public transport networks, more specifically, on how to predict urban bus passenger demand. A series of steps are proposed to ease the understanding of passenger demand. First, given the large number of stops in the bus network, these are divided into clusters and then different models are fitted for a representative of each of the clusters. The aim is to compare and combine the predictions associated with traditional methods, such as exponential smoothing or ARIMA, with machine learning methods, such as support vector machines or artificial neural networks. Moreover, support vector machine predictions are improved by incorporating explanatory variables with temporal structure and moving averages. Finally, through cointegration techniques, the results obtained for the representative of each group are extrapolated to the rest of the series within the same cluster. A case study in the city of Salamanca (Spain) is presented to illustrate the problem.

Classical Partial Least Squares Regression (PLSR) models were developed primarily for continuous data, allowing dimensionality reduction while preserving relationships between predictors and responses. However, their application to binary data is limited. This study introduces Binary Partial Least Squares Regression (BPLSR), a novel extension of the PLSR methodology designed specifically for scenarios involving binary predictors and responses. BPLSR adapts the classical PLSR framework to handle the unique properties of binary datasets. A key feature of this approach is the introduction of a triplot representation that integrates logistic biplots. This visualization tool provides an intuitive interpretation of relationships between individuals and variables from both predictor and response matrices, enhancing the interpretability of binary data analysis. To illustrate the applicability and effectiveness of BPLSR, the method was applied to a real-world dataset of strains of Colletotrichum graminicola, a pathogenic fungus. The results demonstrated the ability of the method to represent binary relationships between predictors and responses, underscoring its potential as a robust analytical tool. This work extends the capabilities of traditional PLSR methods and provides a practical and versatile solution for binary data analysis with broad applications in diverse research areas.