Abstract

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Abstract
We investigate the fuzzy clustering of interval time series using wavelet variances and covariances; in particular, we use a fuzzy c-medoids clustering algorithm. Traditional hierarchical and non-hierarchical clustering methods lead to the identification of mutually exclusive clusters whereas fuzzy clustering methods enable the identification of overlapping clusters, implying that one or more series could belong to more than one cluster simultaneously. An interval time series (ITS) which arises when interval-valued observa-tions are recorded over time is able to capture the variability of values within each interval at each time point. This is in contrast to single-point information available in a classical time series. Our main contribution is that by combining wavelet analysis, interval data analysis and fuzzy clustering, we are able to capture information which would otherwise have not been contemplated by the use of traditional crisp clustering methods on classical time series for which just a single value is recorded at each time point. Through simulation studies, we show that under some circumstances fuzzy c-medoids clustering performs better when applied to ITS than when it is applied to the corresponding traditional time series. Applications to exchange rates ITS and sea-level ITS show that the fuzzy clustering method reveals different and more meaningful results than when applied to associated single-point time series.

Abstract

Abstract
[No abstract available]

Abstract
Concerns with the interpretability of ML models are growing as the technology is used in increasingly sensitive domains (e.g., health and public administration). Synthetic data can be used to understand models better, for instance, if the examples are generated close to the frontier between classes. However, data augmentation techniques, such as Generative Adversarial Networks (GAN), have been mostly used to generate training data that leads to better models. We propose a variation of GANs that, given a model, generates realistic data that is classified with low confidence by a given classifier. The generated examples can be used in order to gain insights on the frontier between classes. We empirically evaluate our approach on two well-known image classification benchmark datasets, MNIST and Fashion MNIST. Results show that the approach is able to generate images that are closer to the frontier when compared to the original ones, but still realistic. Manual inspection confirms that some of those images are confusing even for humans.