K-Nearest Neighbors: dangerously simple
I spend my time at work nowadays thinking about how to start a company in data science. Since there are tons of companies now collecting tons of data, and they don’t know what do to do with it, nor who to ask, part of me wants to design (yet another) dumbed-down “analytics platform” so that business people can import their data onto the platform, and then perform simple algorithms themselves, without even having a data scientist to supervise.
After all, a good data scientist is hard to find. Sometimes you don’t even know if you want to invest in this whole big data thing, you’re not sure the data you’re collecting is all that great or whether the whole thing is just a bunch of hype. It’s tempting to bypass professional data scientists altogether and try to replace them with software.
I’m here to say, it’s not clear that’s possible. Even the simplest algorithm, like k-Nearest Neighbor (k-NN), can be naively misused by someone who doesn’t understand it well. Let me explain.
Say you have a bunch of data points, maybe corresponding to users on your website. They have a bunch of attributes, and you want to categorize them based on their attributes. For example, they might be customers that have spent various amounts of money on your product, and you can put them into “big spender”, “medium spender”, “small spender”, and “will never buy anything” categories.
What you really want, of course, is a way of anticipating the category of a new user before they’ve bought anything, based on what you know about them when they arrive, namely their attributes. So the problem is, given a user’s attributes, what’s your best guess for that user’s category?
Let’s use k-Nearest Neighbors. Let k be 5 and say there’s a new customer named Monica. Then the algorithm searches for the 5 customers closest to Monica, i.e. most similar to Monica in terms of attributes, and sees what categories those 5 customers were in. If 4 of them were “medium spenders” and 1 was “small spender”, then your best guess for Monica is “medium spender”.
Holy shit, that was simple! Mathbabe, what’s your problem?
The devil is all in the detail of what you mean by close. And to make things trickier, as in easier to be deceptively easy, there are default choices you could make (and which you would make) which would probably be totally stupid. Namely, the raw numbers, and Euclidean distance.
So, for example, say your customer attributes were: age, salary, and number of previous visits to your website. Don’t ask me how you know your customer’s salary, maybe you bought info from Acxiom.
So in terms of attribute vectors, Monica’s might look like:
And the nearest neighbor to Monica might look like:
In other words, because you’re including the raw salary numbers, you are thinking of Monica, who is 22 and new to the site, as close to a 75-year old who comes to the site a lot. The salary, being of a much larger scale, is totally dominating the distance calculation. You might as well have only that one attribute and scrap the others.
Note: you would not necessarily think about this problem if you were just pressing a big button on a dashboard called “k-NN me!”
Of course, it gets trickier. Even if you measured salary in thousands (so Monica would now be given the attribution vector ) you still don’t know if that’s the right scaling. In fact, if you think about it, the algorithm’s results completely depends on how you scale these numbers, and there’s almost no way to reasonably visualize it even, to do it by hand, if you have more than 4 attributes.
Another problem is redundancy – if you have a bunch of attributes that are essentially redundant, i.e. that are highly correlated to each other, then including them all is tantamount to multiplying the scale of that factor.
Another problem is not all your attributes are even numbers, so you have string attributes. You might think you can solve this by using 0’s and 1’s, but in the case of k-NN, that becomes just another scaling problem.
One way around this might be to first use some kind of dimension-reducing algorithm, like PCA, to figure out what attribute combinations to actually use from the get-go. That’s probably what I’d do.
But that means you’re using a fancy algorithm in order to use a completely stupid algorithm. Not that there’s anything wrong with that, but it indicates the basic problem, which is that doing data analysis carefully is actually pretty hard and maybe should be done by professionals, or at least under the supervision of a one.