AI for Marketing and Product Innovation

5 Identifying What Matters Most – Intuition Behind Principal Components, Factors, and Optimization

AI scientists tried to program computers to act like humans without first answering what intelligence is and what it means to understand. They left out the most important part of building intelligent machines, the intelligence! ‘Real intelligence’ makes the point that before we attempt to build intelligent machines, we have to first understand how the brain thinks, and there is nothing artificial about that. Only then can we ask how we can build intelligent machines. 

– Jeff Hawkins, On Intelligence (Times Books, 2007)

Principal Component Analysis and Its Applications

Even without Machine Learning, there are some very powerful tools to identify relationships between things, if those relationships are “linear.” Linear means what you learned in high school, such as if 10x – 7y = z, then z depends linearly on the variables x and y because a change in one of them gives a proportional change in z.

In algebra, you get to solve the equation – given a couple of points (x1, y1, z1) and (x2, y2, z2) you can solve the equations

ax1 + by1 = z1

ax2 + by2 = z2

for a and b and you’re done!

Unfortunately, real life is quite a bit messier than high school algebra. In real life, you don’t have exact relationships, you have approximate relationships, and the data is fuzzy. Even if things are related linearly, there is still a lot of “noise.”

But we can still find the “best” approximate linear ...