Uncovering Population Patterns in Volcanic Areas with PCA(Principal Component Analysis of Population Pattern in Volcanic Areas

In this paper, we have applied PCA(principal component analysis) to a dataset related to volcanic eruptions, focusing on those variables connected with population density at several distances from volcanic areas. There are 2662 observations in the dataset and four numerical features: population within 5 $\mathrm{km}, 10 \mathrm{~km}, 30 \mathrm{~km}$, and 100 km from volcanoes. PCA is a powerful method of dimensionality reduction and very often applied in the analysis of large datasets to reveal the major trends hidden in initial high-dimensional data. First of all, we are going to standardize the variables in order to make them comparable and not biased due to different scales. Then, from the standardized data, we will derive a covariance matrix that contains the correlations between the variables. Finally, the eigenvalue decomposition of the covariance matrix will yield principal components used to project. We have plotted various graphs to analyze the hidden trends.