# How to use Principal Components Analysis (PCA) to find overall orientation of polygons collectively?

I was advised to use the Principal Component Analysis (PCA) to find first eigenvector which gives the direction of the first principal direction.

Principal Component Analysis (PCA) is a new concept to me.

I have polygons as in the following image:

Both visually and as illustrated by the Rose Diagram (in the image below) using Line Histogram Tool QGIS plugin available from the following link: https://plugins.qgis.org/plugins/LineDirectionHistogram/, it can be deduced that the overall orientation of the polygons is around 30 degrees, confirmed by calculating the mean of angle of orientation of all polygons.

I am looking for a Mathematical Tool to validate the mean angle. I was advised to use the Principal Component Analysis (PCA) to find first eigenvector which gives the direction of the first principal direction.

CSV file with angle and height (i.e. length of longest segment) of each polygon is available from the following link: https://drive.google.com/drive/folders/1Y98gwDXWooKksfQjl0vpl6j8DC52k7fc?usp=sharing

The shapefile of the polygons is available from the following link: https://drive.google.com/drive/folders/1BKp5VbR1aMAzCObGprvqeL0WSMqpTX32?usp=sharing

Since I am new to Principal Components Analysis (PCA). Can I have suggestions of software and procedures to follow to carry out the Principal Components Analysis (PCA) and find first eigenvector.

I used XLSTAT to use Principal Component Analysis but did not achieve conculsive results. Computed results and report is accessible from following link: https://drive.google.com/drive/folders/1CHDfJ9poD8tk-KQLmRV8NbilZCyGtTs5?usp=sharing

• I don't necessarily see how PCA would help, although a circular version does exist. You say you wish to validate the mean direction. Then, make sure you deal with your data being axial data (ie. take 2*the angles). You can then just test the mean direction with any standard circular test; but to be honest the test is not that interesting as the data is almost entirely in the direction you expect. – Kees Mulder Jan 25 at 9:08