1. A similar image retrieving device for retrieval of a similar image of a query image, comprising: an image database configured for storage of sets of image data, and sets of keywords each associated with a corresponding image data; a clustering classifier configured to read the sets of image data, provide a respective one of the sets of image data with a compatibility value as an index representative of a set of compatibilities of a corresponding one of the sets of keywords, and classify the sets of image data into clusters thereof in accordance with the compatibility value; an optimum cluster extractor configured to provide the set of query image data with a compatibility value, and select one of clusters to which the query image data is to belong to minimize an error caused in a Projection onto Convex Sets using the clusters; and a similar image extractor configured to output, as a similar image, a set of image data provided a close compatibility value, among the sets of image data belonging to the cluster selected by the optimum cluster extractor.