This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deeplearning models. The method combines an autoencoder, for learning a low-dimensional representation of the data, with a density-estimation model based on random Fourier features and density matrices in an end-to-end architecture that can be trained using gradient-based optimization techniques. The method predicts a degree of normality for new samples based on the estimated density. A systematic experimental evaluation was performed on different benchmark datasets. The experimental results show that the method performs on par with or outperforms other state-of-the-art methods. Keywords anomaly detection • density matrix • random Fourier features • kernel density estimation • approximations of kernel density estimation • quantum machine learning • deep learning
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