With the development of Web 2.0

social websites centered on user-generated content are arising. Therefore

tag-based image retrieval becomes more and more important. However

the image tags that users upload are incomplete because users label images freely and arbitrarily and thus decrease the performance of image retrieval. To solve the problem of image tag incompletion

this paper proposes an algorithm based on regularized non-negative matrix factorization to enrich the tags of social images and make these tags complete. This proposed algorithm casts the original tag-image matrix to a latent low-rank space and discovers the correlations between tags with the matrix factorization technique. The relationships among tags are utilized to enrich tags for social images. Meanwhile

the overall visual diversity as a regularization term is utilized to restrict the impact of content-irrelevant tags and enrich image tags. This paper constructs comparison experiments on images downloaded from sharing website Flickr. Accuracy is used to evaluate these comparison experiments. These experiments demonstrate the effectiveness of our proposed algorithm for enriching image tags. Compared with state-of-the-art approaches

our approach could improve average accuracy by 12.3%. This paper proposes a regularized non-negative matrix factorization framework with overall visual diversity as the regularization term and enriches the tags of images effectively. Our proposed algorithm can solve the problem of incomplete tags.