ε-Differential Privacy (DP) has been popularly used for anonymizing data to protect sensitive information and for machine learning (ML) tasks. However, there is a trade-off in balancing privacy and achieving ML accuracy since ε-DP reduces the model’s accuracy for classification tasks. Moreover, not many studies have applied DP to time series from sensors and Internet-of-Things (IoT) devices. In this work, we try to achieve the accuracy of ML models trained with ε-DP data to be as close to the ML models trained with non-anonymized data for two different physiological time series. We propose to transform time series into domain-specific 2D (image) representations such as scalograms, recurrence plots (RP), and their joint representation as inputs for training classifiers. The advantages of using these image representations render our proposed approach secure by preventing data leaks since these image transformations are irreversible. These images allow us to apply state-of-the-art image classifiers to obtain accuracy comparable to classifiers trained on non-anonymized data by ex- ploiting the additional information such as textured patterns from these images. In order to achieve classifier performance with anonymized data close to non-anonymized data, it is important to identify the value of ε and the input feature. Experimental results demonstrate that the performance of the ML models with scalograms and RP was comparable to ML models trained on their non-anonymized versions. Motivated by the promising results, an end-to-end IoT ML edge-cloud architecture capable of detecting input drifts is designed that employs our technique to train ML models on ε-DP physiological data. Our classification approach ensures the privacy of individuals while processing and analyzing the data at the edge securely and efficiently.