# Sparsity problem in KNN

There is something wrong with the following explanation regarding this figure:

The data densities are 6.3%, 4.19%, 1.39% respectively, so that the degrees of sparsity are 93.7%, 95.81%, 98.61%.

Quote:

“ we can see the MAE value will gradually increase when the degree of sparsity of the data gradually increases. This shows that the lower the degree of sparsity, more abundant the rating information, more accurate the item similarity computation, eventually leading to smaller error between predicted score and actual score; when the degree of sparsity of the data gradually increases, the speed of reaching the smallest MAE value becomes slower, slower, that is $$K$$ value becomes bigger. This is because that the higher the degree of sparsity, item similarity computation needs more abundant rating information, resulting in bigger neighborhood set; when the degree of sparsity of the data increases, the rate of decline of MAE becomes faster. “

I have put in bold what I think is not correct, meaning: “when the degree of sparsity of the data gradually increases, the speed of reaching the smallest MAE value becomes slower” and “when the degree of sparsity of the data increases, the rate of decline of MAE becomes faster.” .

Both phrases either say the same or they are contradicting themselves.

• From the graph, what do you think the relationship must be? – BruceET Oct 6 '19 at 2:45
• You tell me, Professor! What the relationship must be? – Delan Oct 6 '19 at 4:32
• Maybe the word “gradually” is making the whole difference – Delan Oct 6 '19 at 4:43