Exploring one of the many applications of PCA in finance – stock price prediction.
In a recent post, we covered one of the most widely used data clustering algorithms K-means.
Here, we’ll shed some light on a bedrock technique for dimensionality reduction (applied extensively in probability and statistics) – principal component analysis (PCA).
What’s curious about PCA is that it’s not a dimensionality reduction method per se, despite mostly being advertised as such. Actually, it transforms data in a certain way to make it amenable to reduction later.
The algorithm finds new views (axes) for datasets in which it’s easy to separate out data instances and consequently cluster them.
By default, it creates as many axes as there are dimensions to a given dataset but it ranks these directions, called principal components (PCs), in the order of importance: the first PC always captures the most amount of data variance possible, the second one shows the second-largest amount of variance, and so forth.
After the data has been projected into this new subspace, we might drop out some of the axes and thus reduce dimensionality without losing much important information.
Let’s dig a bit deeper into this.
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