1. Introduction
Let’s start with a daily life example that will give us another understanding of feature variables.
I have to deal with the recipe leak issue now. You all continue reading!
From now on, I hope you can consciously think of a dataset as a recipe. This will be very helpful for your understanding of dataset.
Let’s go back to the story about the recipe. What is the essence of a recipe? Or rather, what is its main purpose? That’s right—it exists because we want to replicate or reconstruct the work of a culinary master, or perhaps a moment of your own creative inspiration. The key word here is “reconstruct”. Let’s continue looking at the slides to gain a deeper understanding of what “reconstruct” really means.
I hope you’ve learned how to use a recipe! But whatever you do, do NOT try our secret Ummus recipe—because I totally made it up.
Alright, let’s be serious and get back on track. Do you remember the analogy we made earlier between a recipe and a data matrix? When we use a recipe, we are essentially multiplying the values of variables by something related to them and then summing everything together. That is \[ \text{Individual} = X_1\text{'s value} \times X_1\text{related} + \dots + X_p\text{'s value} \times X_p\text{related} \] In other words, an individual can be reconstructed using a weighted sum of somethings associated with those variables and the weights are the variables’ values. Then, what is the thing associated with the variables? Keep this question in your mind! Next, I will use the reconstruction concept of a recipe and a concrete example to give you another perspective on understanding PCA.
