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Unsupervised anomaly detection aims to identify anomalous samples from highly complex and unstructured data, which is pervasive in both fundamental research and industrial applications. However, most existing methods neglect the complex correlation among data samples, which is important for capturing normal patterns from which the abnormal ones deviate. In this paper, we propose a method of Correlation aware unsupervised Anomaly detection via Deep Gaussian Mixture Model (CADGMM), which captures the complex correlation among data points for high-quality low-dimensional representation learning. Specifically, the relations among data samples are correlated firstly in forms of a graph structure, in which, the node denotes the sample and the edge denotes the correlation between two samples from the feature space. Then, a dual-encoder that consists of a graph encoder and a feature encoder, is employed to encode both the feature and correlation information of samples into the low-dimensional latent space jointly, followed by a decoder for data reconstruction. Finally, a separate estimation network as a Gaussian Mixture Model is utilized to estimate the density of the learned latent vector, and the anomalies can be detected by measuring the energy of the samples. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed method.