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Many graph construction methods cannot consider both local and global data structures in the construction of initial graph. Meanwhile, redundant features or even outliers and data with important characteristics are addressed equally in the graph optimization process. These lead to the learned representation graph may not capture the optimal structure. This paper proposes a novel graph learning method, called ACLWN, to overcome these problems. ACLWN is composed of an adaptive representation graph construction model named ARG, and an adaptive weighted sparse representation graph learning model named AWSG. In ARG, manifold learning and sparse representation are employed to capture the local structure of data. In AWSG, an adaptive weighted matrix is proposed to strengthen the important features and improve the robustness of the low-dimensional representation graph. Moreover, constraints such as non-negative low-rank, sparsity and distance regularization terms are imposed to capture the local and global structures of data. Comprehensive experimental results show that our method outperforms the compared state-of-the-art methods. The low-dimensional representation graph constructed by ACLWN is more suitable for clustering. INDEX TERMSadaptive initial graph construction, adaptive weighted matrix, graph learning, low-rank constraint. I. INTRODUCTION C LUSTERING as an unsupervised learning method has long been favored by researchers in machine learning, data mining and pattern recognition. A cluster is a set of data points that are the same as one another within the same cluster and are disparate from the points in other clusters [1]-[3]. Spectral clustering [4]-[6], the most typical graph learning clustering method, has good performance when dealing with complex high-dimensional data. It first constructs an initial graph to describe the similar relationships among data, then develops a low-dimensional representation matrix based on the initial graph, and eventually obtains the final clusters by k-Means [7]. Spectral clustering can be more accurate and robust only when the initial graph is well constructed. Similarly, the other clustering of graph representation is also done. The existing graph construction strategies can be roughly categorized into three groups: (1) Capture the similarity between data points by distance metric. Jurusan et al. utilized the straight-line distance between data points to assess similarity [8]; Yin et al. used the cosine function to construct the similarity matrix in the original space [9]; and Ding et 22 al. proposed a random compact Gaussian (RCG) kernel, and 23 used it to measure similarity between data points [10]. But 24 these methods are unable to automatically collect structural 25 information of points suitable for graph learning clustering. 26 (2) Obtain similarity between data points based on global 27 self-representation. Each point is encoded as a weighted 28 combination of all other points, i.e., data point could be rep-29 resented by its adjacent and reachable indirect neighbors....