document: GPCA : an efficient dimension reduction scheme for image compression and retrieval Recent years have witnessed a dramatic increase in the quantity of image data collected , due to advances in fields such as medical imaging , reconnaissance , surveillance , astronomy , multimedia etc. . With this increase has come the need to be able to store , transmit , and query large volumes of image data efficiently . A common operation on image databases is the retrieval of all images that are similar to a query image . For this , the images in the database are often represented as vectors in a high-dimensional space and a query is answered by retrieving all image vectors that are proximal to the query image in this space , under a suitable similarity metric . To overcome problems associated with high dimensionality , such as high storage and retrieval times , a dimension reduction step is usually applied to the vectors to concentrate relevant information in a small number of dimensions . Principal Component Analysis ( PCA ) is a well-known dimension reduction scheme . However , since it works with vectorized representations of images , PCA does not take into account the spatial locality of pixels in images . In this paper , a new dimension reduction scheme , called Generalized Principal Component Analysis ( GPCA ) , is presented . This scheme works directly with images in their native state , as two-dimensional matrices , by projecting the images to a vector space that is the tensor product of two lower-dimensional vector spaces . Experiments on databases of face images show that , for the same amount of storage , GPCA is superior to PCA in terms of quality of the compressed images , query precision , and computational cost .
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