Arno Knobbe

Guus Toussaint, Arno Knobbe

Many systems in our world age, degrade or otherwise move slowly but steadily in a certain direction. When monitoring such systems by means of sensors, one often assumes that some form of `age' is latently present in the data, but perhaps the available sensors do not readily provide this useful information. The task that we study in this paper is to extract potential proxies for this `age' from the available multi-variate time series without having clear data on what `age' actually is. We argue that when we find a sensor, or more likely some discovered function of the available sensors, that is sufficiently monotonic, that function can act as the proxy we are searching for. Using a carefully defined grammar and optimising the resulting equations in terms of monotonicity, defined as the absolute Spearman's Rank Correlation between time and the candidate formula, the proposed approach generates a set of candidate features which are then fitted and assessed on monotonicity. The proposed system is evaluated against an artificially generated dataset and two real-world datasets. In all experiments, we show that the system is able to combine sensors with low individual monotonicity into latent features with high monotonicity. For the real-world dataset of InfraWatch, a structural health monitoring project, we show that two features with individual absolute Spearman's $ρ$ values of $0.13$ and $0.09$ can be combined into a proxy with an absolute Spearman's $ρ$ of $0.95$. This demonstrates that our proposed method can find interpretable equations which can serve as a proxy for the `age' of the system.

Guus Toussaint, Arno Knobbe

Equation Discovery techniques have shown considerable success in regression tasks, where they are used to discover concise and interpretable models (\textit{Symbolic Regression}). In this paper, we propose a new ED-based binary classification framework. Our proposed method EDC finds analytical functions of manageable size that specify the location and shape of the decision boundary. In extensive experiments on artificial and real-life data, we demonstrate how EDC is able to discover both the structure of the target equation as well as the value of its parameters, outperforming the current state-of-the-art ED-based classification methods in binary classification and achieving performance comparable to the state of the art in binary classification. We suggest a grammar of modest complexity that appears to work well on the tested datasets but argue that the exact grammar -- and thus the complexity of the models -- is configurable, and especially domain-specific expressions can be included in the pattern language, where that is required. The presented grammar consists of a series of summands (additive terms) that include linear, quadratic and exponential terms, as well as products of two features (producing hyperbolic curves ideal for capturing XOR-like dependencies). The experiments demonstrate that this grammar allows fairly flexible decision boundaries while not so rich to cause overfitting.

D. B. Steffelbauer, E. J. M. Blokker, S. G. Buchberger et al.

Socio-economic characteristics are influencing the temporal and spatial variability of water demand - the biggest source of uncertainties within water distribution system modeling. Improving our knowledge on these influences can be utilized to decrease demand uncertainties. This paper aims to link smart water meter data to socio-economic user characteristics by applying a novel clustering algorithm that uses dynamic time warping on daily demand patterns. The approach is tested on simulated and measured single family home datasets. We show that the novel algorithm performs better compared to commonly used clustering methods, both, in finding the right number of clusters as well as assigning patterns correctly. Additionally, the methodology can be used to identify outliers within clusters of demand patterns. Furthermore, this study investigates which socio-economic characteristics (e.g. employment status, number of residents) are prevalent within single clusters and, consequently, can be linked to the shape of the cluster's barycenters. In future, the proposed methods in combination with stochastic demand models can be used to fill data-gaps in hydraulic models.

Stylianos Paraschiakos, Cláudio Rebelo de Sá, Jeremiah Okai et al.

Through the quantification of physical activity energy expenditure (PAEE), health care monitoring has the potential to stimulate vital and healthy ageing, inducing behavioural changes in older people and linking these to personal health gains. To be able to measure PAEE in a monitoring environment, methods from wearable accelerometers have been developed, however, mainly targeted towards younger people. Since elderly subjects differ in energy requirements and range of physical activities, the current models may not be suitable for estimating PAEE among the elderly. Because past activities influence present PAEE, we propose a modeling approach known for its ability to model sequential data, the Recurrent Neural Network (RNN). To train the RNN for an elderly population, we used the GOTOV dataset with 34 healthy participants of 60 years and older (mean 65 years old), performing 16 different activities. We used accelerometers placed on wrist and ankle, and measurements of energy counts by means of indirect calorimetry. After optimization, we propose an architecture consisting of an RNN with 3 GRU layers and a feedforward network combining both accelerometer and participant-level data. In this paper, we describe our efforts to go beyond the standard facilities of a GRU-based RNN, with the aim of achieving accuracy surpassing the state of the art. These efforts include switching aggregation function from mean to dispersion measures (SD, IQR, ...), combining temporal and static data (person-specific details such as age, weight, BMI) and adding symbolic activity data as predicted by a previously trained ML model. The resulting architecture manages to increase its performance by approximatelly 10% while decreasing training input by a factor of 10. It can thus be employed to investigate associations of PAEE with vitality parameters related to metabolic and cognitive health and mental well-being.

Dylan te Lindert, Cláudio Rebelo de Sá, Carlos Soares et al.

The costs associated with refrigerator equipment often represent more than half of the total energy costs in supermarkets. This presents a good motivation for running these systems efficiently. In this study, we investigate different ways to construct a reference behavior, which can serve as a baseline for judging the performance of energy consumption. We used 3 distinct learning models: Multiple Linear Regression, Random Forests, and Artificial Neural Networks. During our experiments we used a variation of the sliding window method in combination with learning curves. We applied this approach on five different supermarkets, across Portugal. We are able to create baselines using off-the-shelf data mining techniques. Moreover, we found a way to create them based on short term historical data. We believe that our research will serve as a base for future studies, for which we provide interesting directions.