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• This paper proposes a new feature selection method called SLMEA. • The sparse transformation and pseudo label matrix are combined to optimize. • The pseudo label matrix is used to guide the learning of low-dimensional space. • The similarity matrix is constructed adaptively. • The constraint of ℓ 2 , 1 / 2 -norm is applied to the matrix. • The SLMEA can have higher clustering accuracy and normalized mutual information. Traditional feature selection algorithms usually explore the relationship between data and cluster structure in a single space, so the internal relationship obtained is not very rich, and it is not enough to select more valuable features. To solve the above problems, in order to fully mine the intrinsic correlation information in different spaces, so that the relationship between data, features and clustering structure can be explored at the same time, this paper proposes a feature selection method based on sparse and low-dimensional representation with maximum entropy adaptive graph (SLMEA). Firstly, the SLMEA combines the sparse transform representation with pseudo-label matrix learning to optimize, and uses the pseudo-label matrix to guide the learning of sparse low-dimensional space. It can not only explore the relationship between data and pseudo-labels in data space, but also mine the association between features and pseudo-labels in feature space, so as to select more discriminative features. Secondly, based on the maximum entropy theory, the similarity matrix is constructed adaptively, so that the two different manifold structures corresponding to sparse transform representation and pseudo label matrix learning can be adaptively learned and retained in the iterative process. In addition, in order to ensure the sparsity of the transformation matrix, the constraint of ℓ 2 , 1 / 2 -norm is applied to the matrix, which can better deal with the redundant features and obtain more sparse solutions. Finally, the SLMEA uses an alternate iterative update method to optimize the objective function, and carries out extensive experiments on eight mainstream datasets. Compared with seven state-of-the-art algorithms, SLMEA can have higher clustering accuracy and normalized mutual information. [ABSTRACT FROM AUTHOR]