# Gaussian Processes for Signal Processing and Representation in Control Engineering
## 6 Decision Support for Bike-Sharing System  
Bike-sharing systems are widely used across the globe especially in major cities. Their main use is in improving healthy and convenient transport for citizens. People can just rent a bike at any station and return it at any other. The significant problem with this system is the high usage of single stations which results in a lack of bikes or not enough free docks to return one. System operators try to solve it by reacting in real time to high demand and manually repositioning bikes between stations. This solution cannot properly handle this problem as it is always too late to make an action after the jammed station was observed [32]. To efficiently operate such a system, the authors of [32] proposed a complex model to predict citywide usage of bikes in the near future which allows the prevention of problems before they occur. The whole proposition of Hierarchical Consistency Prediction (HCP) consists of:  
* Adaptive Transition Contraint (AdaTC)--which is a clustering algorithm used to cluster station into groups. This makes the rent and transition more regular within each cluster;
* Similarity-based Gaussian Process Regressor (SGPR)--which is a variation of GP used to predict how many bikes will be rented in different scale locations (e.g., single station, cluster etc. );
* General Least Square (GLS)--which is used to collectively improve obtained predictions;
* Transition based Inference (TINF)--which is designed to infer citywide bike return demand on predicted rent demands. Figure 4 shows a whole framework which includes all mentioned parts. First, the AdaTC clusters' whole data based on station locations and bike usage patters. Then 3-level hierarchy model (HCP) is formulated. SGPR is used to make a check-out prediction based on available data and GLS improves it to final check-out form. At the end, the TINF method impact system is used with check-in prediction [32]. For us the most interesting part is the usage of Gaussian Process variation. The authors started with the use of the basic GP regression model, with the most common settings:  
\[\mu(f)=0 \tag{24}\]  
\[\kappa(f_{1},f_{2})=a^{2}\times\exp\left(-\sigma_{4}^{-2}\times(f_{1}-f_{2})^{ 2}\right), \tag{25}\]  
where \(\mu\) is mean, \(\kappa\) covariance function and \(a,\sigma\) are parameters. Then to a specific location the \(M\)-similar matrix training set in a target period \(f_{t+1}\) is created:  
\[H_{t+1}=\Big{\{}\Big{(}f_{1}^{t+1},x_{1}^{t+1}\Big{)},\Big{(}f_{2}^{t+1},x_{2 }^{t+1}\Big{)},\ldots,\Big{(}f_{M}^{t+1},x_{M}^{t+1}\Big{)}\Big{\}}. \tag{26}\]  
SGPR is an extension of GPR, which allows us to predict the value of function in \(f_{t+1}\) in a certain location based on \(H_{t+1}\). The authors also base some formulas on [1]. SGRP hyperparameters are learned by minimizing the total regression error on its validations set. Taking into account the specify of every locations, the authors learnt SGPR separately for each of them. Otherwise, the prediction accuracy could be negatively impacted [32]. In conclusion, GP was used in a slightly different form in order to adapt it to the problem, but overall usage was the same as usual. To sum up, the authors conducted a series of tests on real data which confirmed the effectiveness of their model, and they would like to generalize the model in the future. In [33] we encounter a similar problem of bike-sharing difficulties connected to high-demand on stations. In addition to a general solution, they take into account the limiting effect of supply on demand. In order to accomplish that, the authors propose to implement censored likelihood which is able to train supply-aware models. In addition, the Gaussian Process model is used for time-series analysis of bike rentals, in order to calculate bike-sharing demand prediction. Both solutions are combined together to obtain satisfactory results.