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This paper presents a novel technique for learning the underlying structure that links visual observations with semantics. The technique, inspired by a text-retrieval technique known as cross-language latent semantic indexing uses linear algebra to learn the semantic structure linking image features and keywords from a training set of annotated images. This structure can then be applied to unannotated images, thus providing the ability to search the unannotated images based on keyword. This factorisation approach is shown to perform well, even when using only simple global image features.