Principal Component Analysis

Principal Component Analysis and Kriging

Introduction

Remote sensing data can be used to assist in a multitude of spatial queries. They provide both visual and statistical data that can be used to describe the area that has been remotely sensed. Landsat 8 is a satellite which carries two sensors, namely the operational land imager sensor and thermal infrared sensor.

Principal Component Analysis

Using SAGA GIS, the principal component analysis can be applied to the 7 Landsat bands. The analysis creates 7 components and shows it variance and corresponding Eigen vectors and Eigen values.

[pic 1]

Figure 1: Prinicipal Component Analysis Results

Figure 1 shows the results after performing the principal component analysis. It calculated the expected variance, explained cumulative variance, Eigen value and Eigen vectors for the seven components[pic 2]

Figure 2.2: Component 2

Figure 2.3: Component 3

Figure 2.4: Component 4

Figure 2.5: Component 5

Figure 2.6: Component 6

Figure 2.7: Component 7

Figure 2.1 to Figure 2.7 shows the visual representation of each component. This is created during the principal component analysis process in SAGA GIS.

Results of Principal Component Analysis

It can be seen that the components which represent the majority of the variance in the data is component one, which represents 66.62%, component two represents 30.42%  and component three represents 1.99% of the explained variance. The first three components cumulatively represent 99.03% of the explained variance. This is also reiterated in the visual representation of the components. It can be seen that component one and component two have the most defined images whereas the images for components four to seven become progressively less defined. This shows that components one and two represent the most variance because their images will provide the most information content compared to the rest of the bands.

From the values of the Eigen vector matrix, the bands which are predominantly represented in each of the components can be determined:

• Component 1: Band 6 (0.6921) and Band 5 (0.557)
• Component 2: Band 5(0.9401)
• Component 3: Band 4 (0.6181) and Band 6 (0.5281)
• Component 4: Band 7 (0.7301)
• Component 5:  Band 4 (0.6556)
• Component 6: Band 3 (0.7953)
• Component 7: Band 1 (0.7230) and Band 2 (0.6863)

[pic 3]

Figure 3: Natural Colour Composite Image

Figure 3 shows a colour composite image created using band 2, band 3 and band 4. Band 2 represents blue; band 3 represents green and band 4 represented. This was created using the RGB composite tools in SAGA GIS.

[pic 4]

Figure 4: False Colour Composite

Figure 4 shows a false colour composite created using the first three components. Component one represents red, component two represent green and component three represents blue.

Determining terrain features

To determine the features represented by the components, the following were used:

• A false colour composite of the first three components were used. Only the first three components were used because they cumulatively represented 99.03% of the variance in the data. This is shown in Figure 4.
• A natural colour composite image. This was used as a reference because it provided a real world depiction of what they terrain looks like in colour.
• A colour slider application to determine how much red, green and blue a colour comprised of. Where the maximum amount for red, green and blue is 255 for each. I represented the amount for each factor as a percentage.

The colour slider was used to find the amount of red, green and blue in colours from the false composite image. This indicated which component represented a type of terrain. The false colour composite was also compared to the natural colour composite to determine what types of terrain were in the area of interest.

[pic 5]

Figure 5

When comparing Figure 4 with Figure 3, it can be seen that areas with a dark pink colour in Figure 4 correlates with areas of dark green in Figure 3.

From this, it can be deduced that this pink colour in Figure 5 represents vegetation. Using the colour slider, this colour is a combination of 89% red, 0% green and 52% blue. From this colour combination, we can conclude that component 1 represents green vegetation because component one is represented by red and red is the predominant colour component in this colour representing vegetation in Figure 4.

This is representative of the fact that the major factors for component one is bands 5 and band 6 which are used to depict vegetation in remotely sensed data.