Over the past few years, the scale of sensor networks has greatly expanded. This generates extended spatiotemporal datasets, which form a crucial information resource in numerous fields, ranging from sports and healthcare to environmental science and surveillance. Unfortunately, these datasets often contain missing values due to systematic or inadvertent sensor misoperation. This incompleteness hampers the subsequent data analysis, yet addressing these missing observations forms a challenging problem. This is especially the case when both the temporal correlation of timestamps within a single sensor and the spatial correlation between sensors are important. Here, we apply and evaluate 12 imputation methods to complete the missing values in a dataset originating from large-scale environmental monitoring. As part of a large citizen science project, IoT-based microclimate sensors were deployed for six months in 4400 gardens across the region of Flanders, generating 15-min recordings of temperature and soil moisture. Methods based on spatial recovery as well as time-based imputation were evaluated, including Spline Interpolation, MissForest, MICE, MCMC, M-RNN, BRITS, and others. The performance of these imputation methods was evaluated for different proportions of missing data (ranging from 10% to 50%), as well as a realistic missing value scenario. Techniques leveraging the spatial features of the data tend to outperform the time-based methods, with matrix completion techniques providing the best performance. Our results therefore provide a tool to maximize the benefit from costly, large-scale environmental monitoring efforts.

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image noise, and quantify the loss of performance in classifying the MNIST handwritten digits when noise is added to the data. The results show that the sensitivity to noise of PH is influenced by the choice of filtrations and persistence signatures (respectively the input and output of PH), and in particular, that PH features are often not robust to noise in a classification task.