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.

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Abstract
Background and Objective: Convolutional neural networks are widely used to detect radiological findings in chest radiographs. Standard architectures are optimized for images of relatively small size (for exam-ple, 224 x 224 pixels), which suffices for most application domains. However, in medical imaging, larger inputs are often necessary to analyze disease patterns. A single scan can display multiple types of radi-ological findings varying greatly in size, and most models do not explicitly account for this. For a given network, whose layers have fixed-size receptive fields, smaller input images result in coarser features, which better characterize larger objects in an image. In contrast, larger inputs result in finer grained features, beneficial for the analysis of smaller objects. By compromising to a single resolution, existing frameworks fail to acknowledge that the ideal input size will not necessarily be the same for classifying every pathology of a scan. The goal of our work is to address this shortcoming by proposing a lightweight framework for multi-scale classification of chest radiographs, where finer and coarser features are com-bined in a parameter-efficient fashion. Methods: We experiment on CheXpert, a large chest X-ray database. A lightweight multi-resolution (224 x 224, 4 48 x 4 48 and 896 x 896 pixels) network is developed based on a Densenet-121 model where batch normalization layers are replaced with the proposed size-specific batch normalization. Each input size undergoes batch normalization with dedicated scale and shift parameters, while the remaining parameters are shared across sizes. Additional external validation of the proposed approach is performed on the VinDr-CXR data set. Results: The proposed approach (AUC 83 . 27 +/- 0 . 17 , 7.1M parameters) outperforms standard single-scale models (AUC 81 . 76 +/- 0 . 18 , 82 . 62 +/- 0 . 11 and 82 . 39 +/- 0 . 13 for input sizes 224 x 224, 4 48 x 4 48 and 896 x 896, respectively, 6.9M parameters). It also achieves a performance similar to an ensemble of one individual model per scale (AUC 83 . 27 +/- 0 . 11 , 20.9M parameters), while relying on significantly fewer parameters. The model leverages features of different granularities, resulting in a more accurate classifi-cation of all findings, regardless of their size, highlighting the advantages of this approach. Conclusions: Different chest X-ray findings are better classified at different scales. Our study shows that multi-scale features can be obtained with nearly no additional parameters, boosting performance. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Abstract
Artificial Intelligence (AI) is one of the big hopes for the future of a positive revolution in the use of medical data to improve clinical routine and personalized medicine [...]

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Abstract