Extending the concepts of classical signal processing to graphs, a wide array of methods have come to the fore, including filtering, reconstruction, classification, and sampling. Existing approaches in graph signal processing consider a known and static topology, i.e., fixed number of nodes and a fixed edge support. Two types of tasks stand out, namely, topology inference, where the edge support along with their weights are estimated from signals; and data processing, where existing data and the known topology are used to perform different tasks. However, such tasks become quite challenging when the network size and support changes over time. Particularly, these challenges involve adapting to the changing topology, data distributions and dealing with unknown topological information. The latter manifests for example, when new nodes are available to attach to the graph but their connectivity is uncertain as is the case in cold start graph-based recommender systems.
The key contribution of this dissertation is proposing methodologies for signal processing over dynamic networks which are aimed at the two aforementioned tasks. For dynamic networks with incoming nodes, we process signals by introducing a parametric stochastic attachment model. In this model, the incoming nodes connect with probability to existing nodes with certain weights. This uncertainty allows us to model input output relations and allows us to cast them in the context of different graph signal processing tasks. We learn the model attachment parameters in a task-aware setting, allowing us to interpret topology identification in task-aware settings. Separately, we also propose filter design strategies for processing signals both at the incoming and existing nodes using stochastic attachment models.
Another contribution of this dissertation is to extend graph signal processing with graph filters to the scenario where the graph keeps growing in size with streaming data. We propose online graph filter design which updates the filter online, based on incoming nodes. We design this both for scenarios where the incoming node connectivity is known and unknown. In the unknown connectivity case, we study the performance difference between knowing and not knowing the topology and how the stochastic attachment influences it. We also show that by adapting the stochastic attachment, we can learn faster from the data stream.
Finally,we consider the task of topology decomposition and identification for dynamic networks with fixed nodes but changing edge support. We build a tensor of partially observed adjacency matrices corresponding to such a dynamic topology and express this in terms of underlying latent graphs and their temporal signatures. Furthermore, we account for the time-varying graph signals as a prior to aid identifying these latent graphs and missing components of the topology. These latent graphs are individually and collectively expressive and provide interpretable decompositions along with outperforming traditional structure agnostic low-rank decompositions.@en

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in various applications due to their ability to capture complex structural relationships within graph data. However, their inherent black-box nature poses significant challenges to model interpretability, particularly in the context of link prediction tasks. This thesis investigates the explainability of GNNs for link prediction, a critical task in domains such as social network analysis and recommendation systems. We propose an efficient extension of the Zorro explainer, originally designed for node classification, to address the unique challenges of explaining link predictions. Our method leverages top similar nodes for initialization and incorporates techniques to accelerate the greedy search process, ultimately producing binary node and feature masks as explanations. Additionally, we introduce a novel Edge-level RDT-Fidelity metric to better evaluate explainers that generate edge masks, complementing existing metrics like RDT-Fidelity and Sparsity. Experimental results on the Cora and PubMed datasets demonstrate the superior performance and efficiency of our Zorro extension. This work contributes to the growing field of GNN interpretability by providing new methodologies and evaluation frameworks specifically tailored for link prediction.

Analyzing and forecasting multivariate time series using networks is interesting in traffic, energy consumption, or financial forecasting applications. The main challenge is to capture both spatial and temporal dependencies in the data alongside the dynamics of the network itself. Graph Neural Networks (GNNs) have shown reliable performance in network-based data by modeling the connections as a graph. GNNs, using temporal and recurrent structures, are further developed as a prominent tool for processing multivariate time series. However, the dynamics of the network, the evolution of the network over time, and its effect on the data should be studied more. Recent works augment temporal GNNs with graph learning modules to account for the changes in the network; however, often, these methods do not consider the dynamics directly, and all of them stop the graph changing after the training phase. This thesis focuses on an online graph adapting approach to deal with the dynamic data over networks. The proposed method is a hybrid model consisting of a temporal GNN inspired by the physics of dynamic networks, trains its parameters during the training phase, and adapts the graph with the stream of temporal data online. The experiments study the graph adaptation module's role on various benchmark datasets in forecasting tasks, such as traffic, windmill energy, and financial forecasting.

This thesis investigates the application of multi-agent reinforcement learning (MARL) to the optimization of radar waveforms. Radar technology is crucial in fields such as aviation, maritime navigation, and defense, but faces challenges such as interference, clutter, and the need for high resolution and accuracy. Cognitive radar, which adapts to environmental changes in real-time, offers a promising solution. This research aims to explore the potential of MARL in optimizing radar waveforms and examines whether incorporating domain knowledge can enhance performance.

The radar waveform optimization problem is framed within the Decentralized Partially Observable Markov Decision Process (Dec-POMDP) framework, defining the radar environment, agents' observations and actions, and reward functions. The study experiments with different architectures, including decentralized actors with a centralized critic. The centralized critic, having access to global state information, helps stabilize the learning process and mitigate non-stationarity and credit assignment problems. The use of GNNs as a centralized critic is proposed to leverage graph data sparsity, enhancing scalability.

The proposed models are trained and tested in a radar-tracking scenario, evaluated in terms of Pareto optimality and optimization times. The results show that both Independent Actor-Critic (IAC) and Independent Actor with Centralized Critic (IACC) models outperform traditional methods in terms of probability of detection, waveform duration, and optimization speed. The findings highlight the effectiveness of MARL approaches in optimizing radar waveforms, emphasizing the benefits of centralized critics for robustness and coordination. However, the choice of architecture significantly impacts performance, and while GNNs offer potential scalability advantages, their integration of domain knowledge did not yield significant improvements in this study. This research lays a foundation for future exploration of MARL and GNNs in radar waveform optimization.

GNNs are a powerful tool for learning tasks on data with a graph structure. However, the topology of the graph in which GNNs are trained is often subject to change due to random, external perturbations. This research investigates the relationship between 5 topological properties of graphs (assortativity, density, edge connectivity, closeness centrality, diameter) and how stable GNNs trained on graphs with different topological properties are against different perturbations. The analysis is conducted by first synthetically generating graphs with different topological properties and training a GNN using the generated graphs. The synthetic graphs are then perturbed, and the relative change in the GNNs' output is measured. These results are further supported by conducting the same process on three popular GNN datasets: Cora, CiteSeer and PubMed citations. Finally, relationships between the graph properties under investigation and GNN stability are inferred using the results obtained from both synthetic and real-world datasets.

Graph Neural Networks are widely used as useful tools to investigate graphs because they can learn from the topological structure of graphs. In practical applications, the graph’s structure can change over time, have errors or be subject to adversarial attacks. These perturbations negatively impact the accuracy of the neural network. The theoretical stability of graph neural networks has been analysed already and in this paper, the stability of graph neural networks is investigated experimentally. The performance of different perturbation strategies is compared to see how different perturbations impact stability.

Graph Neural Networks (GNNs) have emerged as a powerful tool for learning from relational data. The real-world graphs such models are trained on are susceptible to changes in their topology. A growing body of work in the field of GNNs' stability to topology perturbations is trying to characterise how models respond to those changes, providing valuable insights that have enhanced the robustness of GNNs to adversarial attacks. The past work in this field, however, has only approached stability analysis using spectral graph theory, which is not applicable to all kinds of GNN models. In this paper, we aim to extend the past work in GNN stability by proposing an algorithm for analysing the stability of GNNs with model-agnostic GNN explainability tools instead of the mathematical framework of spectral graph theory. We demonstrate that the outputs of explainability tools can encode useful insights into the stability of GNNs and present a case study on using those insights to analyse node removal, edge removal, and edge weight perturbations.

Graph Neural Network holds significant impor- tance in various applications. Pioneering research has demonstrated state-of-the-art performance in practical applications such as Fraud Detection, Recommender Systems, or Traffic Forecasting by utilizing various Graph Neural Networks (GNNs) architectures. For these applications, one of the most important properties that needs to hold is the stability of GNN under stochastic perturbation as real-life networks undergo changes in topology on a frequent basis. However, it remains unclear how different architectures preserve this property under different perturbations. In this research, we aim to shed light on if this stability property undergoes drastic changes in the graph underlying topology, and if it affects the overall performance of the GNN in Traffic Forecasting problems. We demonstrate that the architectures differ in the stability property measured by different metrics, while some archi- tectures retains their state-of-the-art performance, providing useful insight on the analysis of stability property on different graph neural network archi- tectures in Traffic Forecasting problem.

Graph Neural Networks (GNN) are Machine Learning models which are trained on graph data in order to handle complex state-of-the-art tasks such as recommender systems and molecular property prediction. However, the graphs that these models are trained on can be perturbed in various ways post training resulting in reductions in performance. This study compares the stability of various Graph Neural Network task types (Node Classification, Link Prediction, and Graph Classification) by investigating each of their performances across a range of perturbation severities performed on graphs. Further experiments explore whether this performance ranking changes for different types of perturbations and GNN architectures. Through results, it is shown that there is a noticeable difference in stability between the investigated tasks. However, it is also shown that under certain conditions, such as different types of perturbations or architectures, the performance ranking may shift. This paper highlights weak points in GNNs that should be explored for stronger defenses against potential attacks.

Accurate forecasts are essential for integrating wind energy into the power grid. With wind energy's growing role in the renewable mix, precise short-term generation forecasts are increasingly vital. Turbine-level forecasts are critical for optimal wind farm operation, control, and planning. However, the wind's unpredictability and the complex interactions between turbines make forecasting challenging. Existing methods either depend on resource-intensive physical models or overlook turbine interactions, resulting in isolated, overly simplistic models.

This master's thesis explores the use of Graph Neural Networks (GNNs) in conjunction with Recurrent Neural Networks (RNNs) for wind power generation forecasting in wind farms. The result is an integrated approach that can learn the interactions between turbines through GNNs to handle the temporal dynamics of the data through RNNs.

The research begins with an in-depth overview of wind turbines and their arrangement in wind farms, highlighting the importance and challenges of Wind Power Forecasting (WPF). It establishes that the spatial configuration of turbines complicates power generation estimation, especially over different time horizons. Graphs are introduced as an effective way to represent the interconnections between turbines. Various methods for constructing these graphs are reviewed, focusing on predefined heuristics and their limitations in adapting to changing wind farm characteristics.

The core of this thesis is the AG-LSTM Network, a model that integrates RNNs and GNNs for short-term WPF for turbines within a wind farm. It utilizes historical power generation data, a variety of future and past covariates, and static turbine-specific features. The model is based on an encoder-decoder architecture with an Adaptive Graph Long-Short Term Memory Cell (AG-LSTM), which generates a dynamic adjacency matrix representing the farm's state at each moment. This matrix combines the input features and hidden states across turbines, resulting in an embedding that is transformed into the power forecast.

Through comprehensive experiments and analyses, the AG-LSTM Network proves to be more accurate than state-of-the-art methods on two real-life datasets when future covariates are unavailable. Further experiments demonstrate the quality of the forecast and break down the contribution of the different choices regarding its architecture. The results underscore the potential of hybrid neural network architectures in enhancing WPF, providing a valuable tool for the renewable energy sector.

In conclusion, this research contributes to the renewable energy field by proposing a novel hybrid neural network model that effectively addresses the complexities of short-term WPF. Future work could explore further exploitation of future covariates and the robustness of the model against incomplete input data.

The Deep Neural Network (DNN) has become a widely popular machine learning architecture thanks to its ability to learn complex behaviors from data. Standard learning strategies for DNNs however rely on the availability of large, labeled datasets. Self-Supervised Learning (SSL) is a style of learning that allows models to also use unlabeled data for training, which is typically much more abundant.
SSL is being applied many different data domains such as images and natural language. One such a domain is the domain of graph data. A graph is a data structure describing a network of nodes connected by edges. Graphs are a natural way of presenting many forms of data such as molecules, social networks, and 3D meshes.
The style of SSL that has found the most success on graphs is Contrastive Learning (CL). In CL, an encoder is trained to produce semantically rich representations from unlabeled input data by smartly separating task-relevant information in the input from task-irrelevant information. The encoder backbone most commonly used for Graph Contrastive Learning (GCL) is the Graph Convolutional Neural Network (GCNN).
While GCNNs are the state of the art on many graph data tasks, they suffer from underfitting when made too deep. This is especially a problem for GCL as it prevents encoder complexity to scale with the large availability of unlabeled data.
In this thesis, we investigate this underfitting behavior through the lens of GCNN stability. Stability refers to a model's ability to continue producing consistent outputs, even when its inputs are perturbed slightly. Theoretical work has shown that stability guarantees for GCNNs weaken when their complexity is increased. We confirm experimentally that, in many cases, GCNNs indeed grow less stable when made more complex. This a relevant finding given that learning stable representations is a prerequisite to CL. Additionally, we show in our experiments that, even when trained using CL, stability discrepancies between different GCNN architectures do not disappear. This, in turn, suggests that GCNN architectures with poorer stability may also produce poorer representations. We confirm experimentally that, on at least one dataset, poor stability as a result of architectural complexity can indeed be correlated to a degradation in representation quality.
With this result we provide an additional explanation as to why deeper GCNNs are often found to perform worse in GCL settings. These insights can, in turn, motivate the design of model architectures for GCL that do not suffer from this trade-off between complexity and representation quality.

Machine learning (ML) systems for computer vision applications are widely deployed in decision-making contexts, including high-stakes domains such as autonomous driving and medical diagnosis. While largely accelerating the decision-making process, those systems have been found to suffer from a severe issue of reliability, i.e., they can easily fail on serving data that are slightly different from the data captured during their training phase. Such an issue has resulted in undesired outcomes with safety, ethical, and societal concerns across various applications, such as numerous examples of semi-automatic cars causing accidents on the road.
In this thesis, we hence develop a system in order to support ML practitioners in debugging their computer vision models, even before deploying them and having access to serving data.

We take inspiration from prior ongoing works in order to formulate the current diagnosis problem, identify its challenges, and envision a human-computation-based solution. We then thoroughly analyse the requirements for developing a system instantiating the solution, actually design such a system, and implement it in a well-functioning, full-fledged, highly-modular, and easily-customizable system.
The solution is based on the definition of human computation operations, that, altogether, allow to a) identify the mechanisms a human would expect the model to learn in an ideal world, b) identify the mechanisms the model has actually learned (via annotations of saliency maps), and c) to compare these two sets of mechanisms to conclude about the good behavior of the model. The solution is especially made to account for certainty issues in the work of the human workers, and to handle ambiguous granularities in the concepts the model might have learned.
To the best of our knowledge, our work is the first system that allows an ML practitioner to first identify their own goals for debugging a model (among a large diversity of goals), accounting for their limited monetary budget, then to configure a debugging session according to these goals, and finally to fully-automatically run the system with such configuration to obtain a model debugging report.

Finally, we conduct a thorough investigation of our system. First, we set-up to understand the correctness and informativeness of the outputs, by running the system with various configurations on different models trained using various datasets, for which the biases are more or less controlled. This first evaluation particularly shows that the outputs and its implementation are correct. With these outputs, we are able to identify the biases that have been injected in the model, as well as to learn about previously unknown behaviors of highly-common models that are used by many practitioners.
Second, we evaluate the cost-effectiveness of running the system. For that, we ran tests in two settings: when the human workers might make mistakes (e.g., due to a lack of expertise, the complexity of the task, or inattention), and when human workers are fully accurate. We vary the configurations of the system (e.g., the order in which the human operations are conducted, the number of workers allocated at the start of the debugging session) within the two settings, and we observe how the number of human operations needed evolve, in order to reach correct system outputs. We find that the system's output is potentially relevant, informative and complete. The system output provide an in depth analysis of the model's behaviour and unravel what the model comprehends, where it falls short, and what it should ideally have grasped.

All in all, in this thesis, we build the system and thoroughly evaluate it. While we identify a number of conceptual and practical limitations of this system (e.g., difficulty to annotate concepts, potentially high cost), our work constitutes a first step towards developing complete solutions to help practitioners debug their system. We encourage readers to build on our work, in order to further optimize our system for cost. Note that we make all our code publicly available for anyone to re-use our system, or reproduce our experiments.

One of the contributing factors to climate change is the release of gases, particularly carbon dioxide (CO2), which is amplified by the expanding E-commerce industry. E-commerce enterprises heavily depend on recommender systems as a means to incentivize consumers towards making product purchases. This master's thesis investigates the positive impacts of presenting information regarding carbon dioxide (CO2) emissions values on user behavior and recommendation accuracy within sustainable recommender systems. Through the creation of a new dataset, CarEmissions, this study explores whether displaying emission values influences sustainable choices in recommendations. Findings demonstrate that recommendation models trained without CO2 values consistently outperform those with CO2 values, enhancing both accuracy and greenness. This suggests that the inclusion of CO2 values introduces variability to user ratings, thereby influencing recommendation outcomes. Furthermore, this research examines correlations between user demographics, knowledge, and ratings, revealing insights into the lack of significant links. Additionally, it assesses the differences in recommendation quality between datasets with and without CO2 values, highlighting the advantages of omitting CO2 values in enhancing recommendation performance. While considering the limitations inherent to domain-specific data and convenience sampling, the thesis outlines avenues for refining data collection and exploring automated strategies for balancing recommendation accuracy and greenness. By advancing the understanding of user behavior and ethical considerations in sustainable recommender systems, this study contributes to the evolving landscape of technology-driven sustainable consumption.

The edge flow reconstruction task improves the integrity and accuracy of edge flow data by recovering corrupted or incomplete signals. This can be solved by a regularized optimization problem, and the corresponding regularizers are chosen based on prior knowledge. However, obtaining prior information is challenging in some fields. Thus, we consider exploiting the learning ability of neural networks to acquire prior knowledge. In this paper, we propose a new optimization problem for the simplicial edge flow reconstruction task, the simplicial ElasticNet, which is a regularized optimization problem that combines the advantages of the L1 and L2 norm. It is solved iteratively by the multi-block ADMM algorithm, and the convergence conditions are illustrated. By unrolling the simplicial ElasticNet's iterative steps, we propose a neural network with high interpretability and low requirement for the number of training data for the reconstruction task of simplicial edge flows. The unrolling network replaces the fixed parameters in the iterative algorithm with the learnable weights in the neural networks, thus exploiting the neural network's learning capability while preserving the iterative algorithm's interpretability. The core component of this unrolling network is simplicial convolutional filters with learnable weights to aggregate information from the edge flow neighbors, thus enhancing the learning and expressive ability of the network. We conduct extensive experiments on real-world and artificial datasets to validate the proposed approach. It is demonstrated that the simplicial unrolling network is significantly more advantageous than the traditional iterative algorithms and standard non-model-based neural networks in the case of limited training data.

In this thesis we develop a Bayesian approach to graph contrastive learning and propose a new uncertainty measure based on the disagreement in likelihood due to different positive samples. Moreover, we extend contrastive learning to simplicial complexes and show that it can be used to generate high-quality representations of edge flow data.

Water distribution networks (WDNs) provide drinking water to urban and rural consumers through a network of pipes that transport water from reservoirs to junctions. Water utilities rely on tools such as EPANET to simulate and analyse the performance of water distribution networks (WDNs). EPANET solves the flow continuity and headloss equations through pressurised piped networks under steady-state conditions. The EPANET solver applies the iterative Global Gradient Algorithm (GGA) of until convergence to determine unknown flows and pressures at the same time. Despite the widespread success of GGA, the speed of the algorithm may hinder several applications that require many simulations, especially for large networks.

To overcome these issues, researchers often resort to surrogate models, also known as metamodels, to significantly reduce the simulating times while approximating the behaviour of hydrodynamic models. Machine learning methods are increasingly being used as surrogate models for WDN analysis. Among these, the multi-layer perceptron (MLP) is the preferred metamodeling choice. MLPs provide a fast alternative to hydrodynamic models, but may lack the desired level of accuracy for complex case studies and applications. This is due to the lack of domain knowledge. Domain knowledge in WDNs can be divided into the topology of the network and the physical equations that govern the system. Recently, researchers have expanded MLPs to include domain knowledge in the form of the topology of the system. These new machine learning-based surrogates are called GNNs. However, GNNs present the problem that they lack speed compared to MLPs and still do not include information on the physical equations of the system.

For this reason, we propose applying algorithm unrolling to the GGA to include information on the physical equations that govern WDNs. Algorithm unrolling (AU) is a promising technique within the field of model-based deep learning that provides an alternative to traditional data-driven methods for approximating the output of iterative algorithms. This approach involves deconstructing the iterative algorithm used to solve the optimisation problem of interest into blocks that can be represented as layers in a neural network. Our architecture identifies two steps in the GGA and designs layers of a deep neural network following the steps of the GGA. In addition, the architecture includes information of the system features, those that remain constant throughout the steps of the GGA. We do so by adding residual connections to the variables. We evaluate the proposed metamodel by predicting the heads of five WDNs with varying characteristics and present an ablation study to understand the effect of the different components of our architecture. Our results show that our metamodel improved the accuracies with respect to MLPs and GNNs while being up to 2000 times faster than EPANET. We believe that the increase in accuracy with respect to the state-of-the-art baselines and the increase in speed with respect to EPANET justify the use of this metamodel for applications in the field of WDNs that rely on many simulations of EPANET.

Whereas in the past, Distribution Systems played a passive role in connecting customers to electricity, Distribution System Operators (DSOs) will have to take in the future a more active role in monitoring and regulating the network to deal with the new behaviors and dynamics of the system brought by the energy transition. State Estimation, a task traditionally reserved for Transmission System Operators (TSOs), is, therefore, a needed tool for DSOs to properly monitor the distribution grid in the future. However, the implementation of Distribution System State Estimation (DSSE) faces several challenges. The distribution system lacks observability to get satisfying estimation accuracy, the denser network increases the complexity of the estimation process, and the lack of labeled data makes training Machine Learning alternatives difficult. To tackle these issues, we propose the Deep Statistical Solver for Distribution System State Estimation (DSS2), a Deep Learning model based on the Graph Neural Network (GNN) architecture and the Physic-Informed Machine Learning (PIML) framework.

The DSS2 model is based on the Deep Statistical Solver (DSS) framework, which seamlessly models power systems into GNN using Hyper-Heterogeneous Multi Graphs (H2MG), and emphasizes semi-supervised learning by learning to optimize, using optimization problem as a loss function. This thesis extends the DSS framework to the DSSE problem, using the traditional State Estimation algorithm as an optimization problem to learn, and incorporating the power flow equations in the loss function. This model is trained through a semi-supervised approach to learn the physics of the problem and alleviate the need for labels and uses the Deep Learning tools to improve accuracy and robustness in the DSSE task.

Case studies on 14-bus, 70-bus, and 179-bus networks show promising results, with the model outperforming the traditional WLS algorithm while showing better robustness. The model also competed in performance against supervised models and showed to be more suitable for the semi-supervised learning approach than simpler GNN architectures.

Side-Channel Attacks (SCA) attempt to recover the secret cryptographic key from an electronic device by exploiting the unintended physical leakages of said device. With the devices that are being attacked becoming more sophisticated, so is SCA. In the past few years, the focus of the research in the field of SCA shifted towards the application of the powerful method of Deep Learning (DL). DL SCA methods can operate in a similar way as before seen methods in the profiled setting, such as Template Attack. In the profiled setting, SCA first creates a profile on a copy of the target device, to then subsequently use that same profile to perform a more powerful attack on the target device. DL SCA has proven to be quite the effective method, even showcasing its success against implementations utilising countermeasures. However, as DL SCA is fairly novel there still exist gaps in the knowledge we have of how to make DL SCA effective in all possible situations. Most research bases itself on software-based implementations, whilst rarely hardware-based implementations are discussed as they are often seen as more difficult to attack. Our contribution in this work is to showcase the difference in difficulty between hardware-based implementations and software-based implementations that both use countermeasures. We explore the attack performance of several state-of-the-art methods on hardware-based implementations with countermeasures and give insight into why their performance is the way it is. We also attempt to make a base methodology for attacking hardware-based implementations, both with and without countermeasures, as the current field of research is lacking this. Showcasing our suggested methodology, we achieve better than state-of-the-art results on a hardware-based implementation with countermeasures and competitive with the state-of-the-art results on a hardware-based implementation without countermeasures.

We all know the possible consequences of global warming, rising temperatures, flooded cities and destroyed ecosystems. One of the causes is the emission of gases, predominantly CO2, which is increased by the growing E-commerce market. E-commerce companies rely on recommender systems to stimulate users to purchase products. We are convinced that we can use the core strength of recommender systems, influencing decision making, to steer users towards eco-friendly choices. Therefore, in this thesis, we research how greenness can be integrated into recommender systems. We present the first recommender system dataset that includes greenness, we benchmark several recommendation algorithms and we propose a strategy to increase recommendation greennness. To create the dataset, we annotate an existing recipe recommendation dataset with recipe greenness. For our benchmarking experiment, we propose metrics to measure recommendation greenness, which we use to show that no recommendation algorithm is fundamentally greener than others. Lastly, we propose a re-ranking method for improving the greenness of recommendation rankings. We use the method to explore the trade-off between accuracy and greenness and we show that it is possible improve the greenness of recommender systems significantly with little loss of accuracy.