ML1M 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`=1.782	0	89.664	0.337	0.28
Pareto	`b`=0.231	0.001	0.997	0.877	0.394
Power law	`a`=0.589	0.492	998.567	inf	0.344
Geometric	`p`=0.004	0		0.416	0.298

Now the same, for user activity distributions.

Distribution	Params	Location	Scale	D(KL)	Δ(JS)
Log-normal	`s`=1.387	17.714	67.252	0.134	0.185
Pareto	`b`=0.574	0.016	18.952	0.292	0.245
Power law	`a`=0.378	19.991	999.949	inf	0.303
NegBinom	`n`=1.000, `p`=0.007	19		0.169	0.195
BetaNegBinom	`n`=1.000, `a`=3.574, `b`=378.749	19		0.125	0.179