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.

Safeguarding the energy security is an important energy policy goal of every country. Assuring sufficient and reliable resources of energy at affordable prices is the main objective of energy security. Due to such reasons as special geopolitical position, terrorist attacks and other unrest in the Middle East, securing Iran’ s energy demand and increasing her natural gas exports have turned into a critical issue. The aim of this paper is to develop a composite index for evaluating the gas demand security. To this purpose, six individual indices (i. e. gas exports dependency, transportation cost, economic dependency, political stability of the exporting country, political stability of the importing country, and the purchasing power of the importing country) are identified and the Principle COMPONENT ANALYSIS (PCA) method is employed to weigh and combine the indices into GDSI (Gas Demand Security Index). The results show an interesting counter-intuitive phenomenon that the political stability of the importing and exporting countries have respectively the most and the least effects on the obtained composite index.