Non-intrusive load monitoring (NILM) is performed to realize intelligent power consumption. A load identification algorithm which is flexible for various households is required to realize automatic NILM. An approach of NILM proposed in this paper is general for most types of loads and exclusive for different users. In this paper, inspired by the knowledge graph holding strong power for knowledge representing, a load feature graph that preserves sufficient information is constructed. The graph provides a net relation between load types and features, which is the basis of load knowledge reasoning. After transforming current and voltage into structured images and data according to the net relation, the convolutional neural networks and combined Support Vector Machines are used to classify images and data respectively. Furthermore, to minimize running time, a customized load identity library focusing on the individual user is proposed. Considering requirements of different computing power resources, above processes are deployed on the architecture of end-cloud collaboration. The experimental results on NILM datasets demonstrate that the proposed method outperforms most of the existing methods in the recognition accuracy and supports for different types of users.