Yes, that's pretty much it. Sparse linear classifiers aren't as simplistic as your googling led you to believe; look at figure 4, where they carved out pixels of the image that led to the three classifications they got for it. Their algorithm could also use some other easily comprehensible model than sparse linear classifiers, just like all learning algorithms you have to decide in advance the sort of model you're going to learn.
Copy copy. Thanks. I saw the dog and his guitar and learned what a superpixel was but the math was too rigorous for me to follow along without a spotter. Last question: what is it about their approach that's novel, and why hasn't an approach like this been attempted before? "Parzen windows", whatever they are, appear to be like 50 years old so I have to assume attempts at doing stuff like this has to have been around for as long as AI itself... but again, I'm a plebian.
There have been a lot of symbolic AI programs that could explain themselves, because it's relatively easy to explain what your program is thinking when your program does its thinking by constructing a proof. I'm not aware of many attempts to do it with learning algorithms, and the authors only cite three.
If you're looking at machine learning as modeling a kind of thinking instead of just computational statistics (always a thing to be cautious about), it's modeling the kind of unconscious thinking you have a hard time explaining yourself. How do you know that's your friend standing in the crowd over there? You just recognize them, that's all. How do you walk without falling down? You just do it. How do you interpret a bunch of sounds as words? ...