The Principal Component Analysis (PCA) is one of the procedures that have been a successful performance in signal processing and dimension reduction of the signals. However, a requirement in applying PCA to the images is converting images into a vector.This process leads to loss spatial locality information. To solve this problem, the two-dimensional PCA was proposed. Also, most recently the sparse Principal Component was introduced that not only keep the properties of standard PCA but also try to make a lot of elements of the basis vectors to zero. In this paper, inspired by the above two ideas, the two-dimensional sparse Principal Component Analysis (2-D. SPCA) is proposed.In this paper, the Least Angle Regression- Elastic Net formula, in addition, using l1 and l2 constraints is extended to two-dimensional model with a few minor changes in its input to approach 2-D. SPCA.The two-dimensional sparse Principal Component Analysis is evaluated in image compression. Before applying the algorithm, the image is divided into several blocks with resolution 8×8 and a database of these blocks is formed. Comparison the performance of 2-D. SPCA and Discrete Cosine transform, for the same number of elements that are necessary to save the image after the conversion shows the good performance of the proposed algorithm. In addition, the proposed algorithm is applied to 8×8 blocks of 60 images with different textures, and the resulted two-dimensional sparse Principal Components could be used for other test images with a suitable performance.

In this study, PC technique was used to reduce the number of spectral bands or spatial variables in a data set by finding their linear combinations. To apply the PCA for spectral/spatial data set, Landsat TM data recorded from 5 different areas in Central Iran, and 18 soil varaibales were used. The result of PCA transformation for TM bands revealed the importance of PC1 in soil studies, PC2 and or PC3 for vegetation investigations. The results of PCA for Landsat TM and soil data showed that the TM data of 7 bands and 18 soil variables v/ere mainly compressed to just three PCs that describe more than 90% and 55% of spectral and spatial information respectively. Based on the obtained results we may conclude that PCA can be applied to different sources of spectral/spatial data, for a better establishment of sampling plan and save in money and time.

It is the purpose of this paper to contribute to the discussion initiated by Wachter about the parallelism between Principal Component (PC) and a typological grade of membership (Go M) Analysis. The author tested empirically the close relationship between both Analysis in a low dimensional framework comprising up to nine dichotomous variables and two typologies.Our contribution to the subject is also empirical. It relies on a dataset from a survey which was especially designed to study the reward of skills in the banking sector in Portugal. The statistical data comprise thirty polythomous variables and were decomposed in four typologies using an optimality criterion. The empirical evidence shows a high correlation between the first PC scores and individual Go M scores. No correlation with the remaining PCs was found, however. In addtion to that, the first PC also proved effective to rank individuals by skill following the particularity of data distribution meanwhile unveiled in Go M Analysis.