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Top1. Introduction
Latent semantic indexing (LSI) was initially proposed to cluster the text documents (Deerwester et al, 1990). The LSI finds the best subspace which approximates an original document space onto a smaller subspace by minimizing the global reconstruction error. Initially the LSI was used for text clustering / classification and later it has been explored for other applications such as indexing of audio documents (Kurimo, 1990), retrieval of images (Zhao & Grosky, 2000) and modeling of video content (Souvannavong et al, 2003). Kurimo (1999) developed a method to enhance the indexing of spoken documents with the help of LSI and a self organizing map. Zhao and Grosky (2000) extracted global color histogram from images and latent semantic analysis was performed to learn those extracted features to develop an image retrieval system. Souvannavong et al. (2003) used latent semantic indexing for modeling video content with Gaussian mixture model. Although LSI finds an appropriate subspace to obtain lower dimensional representation of original space, it is found that LSI seeks to uncover the most representative features rather than the most discriminative features for representation (He et al, 2004).
Hence, Locality Preserving Indexing (LPI) was developed for document representation (He et al, 2004) on the basis of Locality Preserving Projection (He and Niyogi, 2003) which preserves local structure of the given high dimensional space in a lower dimensional space using spectral clustering. Later, it was modified by introducing an additional step of singular value decomposition in (Cai et al, 2007) in order to ensure that the transformed matrix is of full order. The modified LPI (Cai et al, 2007) tries to ascertain both geometric and discriminating structure of the document space by discovering the local geometrical structures (Cai et al, 2007). In order to project images onto the LPI subspace, images need to be transformed into a one dimensional vector thereby requiring more memory and high computational time. In general all one-dimensional projection methods may not work efficiently, since they usually demand computing a very high dimensional covariance matrix and eigen-decomposition. However, a number of works are reported in the literature where vector based projection techniques are successfully extended to image based projection techniques (Yang, 2004; Li & Yuan, 2005; Chen, 2007). The image based projection techniques project images directly onto lower dimensional space rather than transforming them into a one dimensional vector (Chen, 2007), thereby working directly on matrices (images) and hence requiring less memory and less computational time in computing the eigen decomposition. Guru and Suraj (2007) designed a method of fusing the covariance matrices of PCA and FLD for recognition of finger spellings. A review on various subspace methods for face recognition can be found in (Ashok & Noushath, 2010)
Motivated by the works of (Yang, 2004; Li & Yuan, 2005; Chen, 2007), Manjunath et al, (2009) extended the conventional LPI (Cai et al, 2007) to two dimensional LPI, which can be applied directly on images to project them onto lower dimensions by preserving both representative as well as discriminative features of images. Two dimensional LPI (Manjunath et al, 2009) was successfully applied for applications such as video summarization, face recognition and finger spelling recognition. However, the above mentioned image based approaches work by reducing the dimensionality in the row direction of an image. Alternatively, methods were proposed to reduce the dimension of the image matrices in column direction also.