Respuesta :
Answer: I would say.
Step-by-step explanation: Principal Component Analysis (PCA) is a useful technique for exploratory data analysis, allowing you to better visualize the variation present in a dataset with many variables. It is particularly helpful in the case of "wide" datasets, where you have many variables for each sample. In this tutorial, you'll discover PCA in R. More specifically, you'll tackle the following topics:
You'll first go through an introduction to PCA: you'll learn about principal components and how they relate to eigenvalues and eigenvectors.
Then, you'll try a simple PCA with a simple and easy-to-understand data set.
Next, you'll use the results of the previous section to plot your first PCA - Visualization is very important!
You'll also see how you can get started on interpreting the results of these visualizations and
How to set the graphical parameters of your plots with the ggbiplot package!
Of course, you want your visualizations to be as customized as possible, and that's why you'll also cover some ways of doing additional customizations to your plots!
You'll also see how you can add a new sample to your plot and you'll end up projecting a new sample onto the original PCA.
Wrap-up
Introduction to PCA
As you already read in the introduction, PCA is particularly handy when you're working with "wide" data sets. But why is that? Well, in such cases, where many variables are present, you cannot easily plot the data in its raw format, making it difficult to get a sense of the trends present within. PCA allows you to see the overall "shape" of the data, identifying which samples are similar to one another and which are very different. This can enable us to identify groups of samples that are similar and work out which variables make one group different from another. The mathematics underlying it are somewhat complex, so I won't go into too much detail, but the basics of PCA are as follows: you take a dataset with many variables, and you simplify that dataset by turning your original variables into a smaller number of "Principal Components". But what are these exactly? Principal Components are the underlying structure in the data. They are the directions where there is the most variance, the directions where the data is most spread out. This means that we try to find the straight line that best spreads the data out when it is projected along it. This is the first principal component, the straight line that shows the most substantial variance in the data. PCA is a type of linear transformation on a given data set that has values for a certain number of variables (coordinates) for a certain amount of spaces. This linear transformation fits this dataset to a new coordinate system in such a way that the most significant variance is found on the first coordinate, and each subsequent coordinate is orthogonal to the last and has a lesser variance. In this way, you transform a set of x correlated variables over y samples to a set of p uncorrelated principal components over the same samples. Where many variables correlate with one another, they will all contribute strongly to the same principal component. Each principal component sums up a certain percentage of the total variation in the dataset. Where your initial variables are strongly correlated with one another, you will be able to approximate most of the complexity in your dataset with just a few principal components. As you add more principal components, you summarize more and more of the original dataset. Adding additional components makes your estimate of the total dataset more accurate, but also more unwieldy.
