In the age of big data, services in the pervasive edge environment are expected to offer end-users better Quality-of-Experience (QoE) than that in a normal edge environment. However, the combined impact of the storage, delivery, and sensors used in various types of edge devices in this environment is producing volumes of high-dimensional big data that are increasingly pervasive and redundant. Therefore, enhancing the QoE has become a major challenge in high-dimensional big data in the pervasive edge computing environment. In this paper, to achieve high QoE, we propose a QoE model for evaluating the qualities of services in the pervasive edge computing environment. The QoE is related to the accuracy of high-dimensional big data and the transmission rate of this accurate data. To realize high accuracy of high-dimensional big data and the transmission of accurate data through out the pervasive edge computing environment, in this study we focused on the following two aspects. First, we formulate the issue as a high-dimensional big data management problem and test different transmission rates to acquire the best QoE. Then, with respect to accuracy, we propose a Tensor-Fast Convolutional Neural Network (TF-CNN) algorithm based on deep learning, which is suitable for high-dimensional big data analysis in the pervasive edge computing environment. Our simulation results reveal that our proposed algorithm can achieve high QoE performance.