ML32M 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`=15.011	1	0.101	0.931	0.399
Pareto	`b`=0.250	0.891	0.105	0.203	0.209
Power law	`a`=0.172	0.827	999.440	inf	0.304
Geometric	`p`=0.003	0		2.826	0.597

Now the same, for user activity distributions.

Distribution	Params	Location	Scale	D(KL)	Δ(JS)
Log-normal	`s`=1.587	18.986	48.172	0.029	0.086
Pareto	`b`=0.692	0.151	19.792	0.098	0.162
Power law	`a`=0.293	19.989	999.795	inf	0.272
NegBinom	`n`=1.000, `p`=0.007	20		0.211	0.188
BetaNegBinom	`n`=1.000, `a`=1.535, `b`=92.356	20		0.022	0.078