ML20M Data Description – LensKit Codex

Rating Statistics

This section describes the distribution of various item statistics from the data set.

What is the distribution of popularity?

Let’s also look at this as a Lorenz curve, for clarity:

What is the distribution of average ratings?

We now turn to the distribution of various user statistics.

How are user averages distributed?

And what is the distribution of user activity levels (# of ratings)?

The MovieLens ratings have timestamps, so we’ll also look at a temporal view of the data.

How did the data grow over time?

How many ratings are we getting each month through the life of the data set?

Monthly unique users is a good measure of user activity.

How long do users usually stick around?

Some downstream uses benefit from parametric distributions of user/item activity levels.

This section models the item popularity distribution with various parametric distributions.

Distribution	Params	Location	Scale	D(KL)	Δ(JS)
Log-normal	`s`=13.357	1	0.104	1.013	0.434
Pareto	`b`=0.250	0.597	0.393	0.334	0.249
Power law	`a`=0.219	0.233	999.955	inf	0.299
Geometric	`p`=0.001	0		2.226	0.533

Now the same, for user activity distributions.

Distribution	Params	Location	Scale	D(KL)	Δ(JS)
Log-normal	`s`=1.609	19.078	43.087	0.036	0.095
Pareto	`b`=0.716	0.172	19.624	0.093	0.151
Power law	`a`=0.297	19.967	999.214	inf	0.273
NegBinom	`n`=1.000, `p`=0.008	20		0.203	0.189
BetaNegBinom	`n`=161.000, `a`=1.891, `b`=0.766	20		0.017	0.068