As a fundamental task in modern data mining, time series classification is powering mission-critical tasks including stock price prediction and network traffic analysis. Due to the non-linear structure of deep neural networks (DNN), deep learning has established as a promising solution to time series classification. However, the excessive learning capacity of DNNs may make them prone to threats of backdoor attacks, where an attacker embeds hidden functionalities (i.e., backdoor) to DNNs and activates the backdoor by specially-designed inputs (i.e., triggers). Despite extensive studies concerning backdoor attacks on image and text domains, there is little known about the vulnerability of DNN based time series classifiers against backdoor attacks. Due to the unique characteristics of time series data, most existing backdoor attack techniques fail to threaten time series classifiers. In this paper, through analyzing the key factors which influence the effectiveness of a backdoor, we systematize a list of practical principles for designing triggers on time series data. In this light, we propose a novel framework called TimeTrojan, which aims to learn to form the trigger pattern through a constrained multi-objective optimization. To solve the hereafter challenging optimization issue, we further design an iterative learning algorithm. Remarkably, the proposed framework is agnostic to a wide range of DNN classifiers. Extensive empirical results on 6 representative DNN classifiers and 6 real-world datasets validate the effectiveness of the proposed attack framework. In most cases, TimeTrojan successfully injects backdoors with 100% attack success rate without affecting the model accuracy on clean samples, which implies the complete control of the behavior of the DNN classifiers by the adversary.

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