Brainstorm for a metric for the "interestingness" of a hit

[Nerzhul]

Good ideas so far. Keep them coming. I'll try to contribute a bit, but I'm currently travelling through Laos with unreliable internet connections.

IMO we should start from scratch and first identify the factors which make a hit interesting or not. Then we should see how we can mathematically combine these attributes, normalize them and maybe simplify them.

So, what have we got:

1) Number of entries. A quintuple hit is much more uncommon than a "normal" hit (2 entries) and thus much more interesting.

2) Distance. The bigger, the better?

3) Time distance. Same.

4) Hit ratios of users / cities / countries involved. A hit involving France is much rarer than a hit involving Finland.

Anything else? Internationality? Hits involving different cities? I think 4) already covers this. However, I'm not really content factoring in the hit ratio (it will probably complicate things a lot so that the final score won't be transparent), but it really is a good indicator for interestingness / commonness, so let's work with it.

Now, how do we weigh the factors against each other? A 100days/100km is probably more interesting than a 99days/100km hit and could be considered equal to 99days/101km, but does this scale linearly? Probably not since the max travel time is currently around 2800 days, but max distance is much higher than that.

Should we apply the number of entries as a factor, i.e. a triple be 1.5 times as interesting as a normal hit, a quintuple 2.5 times? Intuitively I wouldn't want this to scale linearly but prefer the really uncommon combinations over more common ones (actually a quadruple is about 30 times more common than a quintuple, a tiple ~1800 times).

So what do you think about normalizing the factors to their commonness? Basically the same approach you already took with the hit ratio, but more global. We (EBT) can easily provide these numbers, e.g. average / median travel distance (of all hits). Likewise with total time difference and probability for being entered N times.

Basically, the more uncommon each factor, the higher it is weighed. If the probability for a specific event is extremely low, the specific attribute should be weighed very high, thus having a big impact on the interestingness score.

Of course the reverse should also be true. If the probability for an event is high (e.g. a Vienna - Vienna hit), the score should be lowered significantly.

Let's say the average hit is 100km, 100 days. The more a hit differs from these averages, the more interesting / less interesting it becomes. A 200 days / 100 km hit would then get factors of 2 and 1 (if scaled linearly).

The probability for the number of entries could be normalized ("how many times more likely than a normal hit is this N?") and simply factored into the score.

So a crude formula could be:

P(N) * max(days/avg days, km/avg km) * avg (hitratio between all involved cities)

P(2) = 1, P(3) = 59 etc.

Just some food for thought. What do you think?

[doiknow]

I thought a bit over our attempts and faced two problems we should discuss or agree to ignore for now:
1. If we take average values - which average do we take? The average of the time the hit happened or the average of now? Let's assume place A in country B is really untracked for the moment. At this time a hit happens and due to its rareness it gets scaled 'very interesting'. The local press then writes about EBT and our Place gets tracked like Vienna or Finland. Surely hits like that will occur much more often and decreasing the hits interestingness. Resulting in one and the same hit-data having 2 different ratings. Should we rank down the first hit or shouldn't we? Why is the first hit still as interesting as it was at that time it happened? Why isn't it? Or think backwards. What if a hit happens in a tracked place that gets untracked? This leads us to some kind of 'average paradoxon'
Every answer will seem unlogic in one of those situations - so what to do?

2.The independent factor problem:
Up to now we talked of hits being interesting if they fulfill some criteria (large distance, long travelling time....). At least some of those criteria are not independent: For example: the hitratio has influence on the number of hits that have happened between two or more users/cities etc. Second the distance interferes with the number of involved countries as well as the number of times the note was entered does. If we take those factors into account we could overestimate some hits as others are underestimated which results in some 'unfairness'. How can we get rid of non-independent factors?

[Jes]

Why is the first hit still as interesting as it was at that time it happened? Why isn't it? Or think backwards. What if a hit happens in a tracked place that gets untracked? This leads us to some kind of 'average paradoxon'

Well, the first hit ever, is interesting because it was the first one. The first Hit ever in a city, is somehow more interesting than the comming ones, because it was the first and it brought us attention, at least more than the second hit; right?

There will not be much difference (in interestingness means) between the 1st and 2nd hit in the same place, but when there are 100 hits involving that city, the 1st one would be regarded as "the pioner"... well... maybe. it is just an opinion.

[claudio vda]

With the algorithms that are going to be developed, the index of interest is something that can change in the time.

If the index is calculated using hit ratio of towns and users, those ratios change in the time, so also the index will: the first hit Barcelona - Kosice, for example, may have idex 100, when a second hit will born between Barcellona and Kosice, the first hit will decrease to 75.

[Jes]

With the algorithms that are going to be developed, the index of interest is something that can change in the time.

If the index is calculated using hit ratio of towns and users, those ratios change in the time, so also the index will: the first hit Barcelona - Kosice, for example, may have idex 100, when a second hit will born between Barcellona and Kosice, the first hit will decrease to 75.

I think that's a very smart aproach. Although it would be difficult to "change" all the hits' "interestingness factor" When a new hit does appear

[doiknow]

What I want to say is: We need to recalculate the interestingness in a continius way. Otherwise the hitscore will decrease over the years and our whole rating system would be wrong...
Maybe we shouldn't take into account the 'hitratio of a city' but the 'hitratio of the city in the last 12 months' or whatever? Nonetheless I like claudios approach to decrease a factor with the number of hits that happened between two special places...

[-STAR-]

What I want to say is: We need to recalculate the interestingness in a continius way. Otherwise the hitscore will decrease over the years and our whole rating system would be wrong...

What's wrong with this approach? Personally, I don't like the idea of leveraging the "interestingness" of a hit over time or dynamically adjust it with current factors.
I'd suggest to calculate the "interestingness" of a hit the moment it happens and store it somewhere with the hit data (seperate database table for example).
Otherwise the results we achieve would not be comparable, because even a single hit can change the whole outcome of the formula.
The only exception would be the "upgrade" of a hit, i.e. when a double becomes a triple, a triple becomes a quadruple and so on.

Rgds, Franz

[claudio vda]

So, you propose to froze all the parameters at the instant when a hit it is done.

Although it would be difficult to "change" all the hits' "interestingness factor"

I thought it was the opposite: the more easy algoritm is the dinamic one

Dinamic
01 Look for parameters
02 Calculate formula
03 Show result
04 End

Static
01 Have this hit an index?
If "yes" go to 100, if "no" go to 02
02 Look for parameters
03 Calculate the formula
04 Write index
05 Show result
06 End
100 Read index
101 Show result
102 End

But let's find a good formula, then we will discuss about static or dinamic: tomorrow morning I have got my exam, see you just after!

[De-Ker]

wow nice suggestions here...

First question.. Will a dynamic ranking system not to demanding for the server. I mean if the server has to calculate them every now and then it might be to slow??

We could control the deceasing of the ranking system by using the total hitratio of a city + the last years city ratio /2
Also we could calculate this when we constantly use the average hitratio of all notes/hits in whole ebt. not sure how to do this exactly tho

Also, shouldn't we include the direction of a hit. For instance a note from Greece, taken by a finish user to Finland, is in my opinion less interesting then visa versa.

Lastly. We should find something to exclude the belgium/dutch hits, which are the most common i guess. These are international, but less intresting then a france/spain hit or italy/greece, however they got the same value as a belgium/dutch hit in the county's involved. Maybe we can also include some sort of hits between county's and not only between the two city's. Not sure how to work this out with national hits.

[claudio vda]

Not sure how to work this out with national hits.

Calculating only kilometers and not the number of borders?

By the way, I am working...

[claudio vda]

I am working to an index that resumes many of the ideas showed in the precedents post


I = m log(d t) : log((n+e) c)

m=multeplicity: 2 for normal hits, 3 for triples, 4 for quadruples...
d=distance in km in d>=1 ; d=1 if the distance is 0 km
t= time in days

n= number of hit involving the users
c= number of hit involving the locations
e= little number because log(1) = 0
in my calculations , e is for the moment 0,1 , but we will see later about that number

log = decimal logarithm (because is more easy do calculations, we can change the base)

About the numerator. Usually the kilometres are something about 10, 100, 500, 1000 if you are very lucky 2000 or 3000, but hit of 15 000 km are extremely unusual. Usually the days are 10, 100, 500, more than 1000 they became unusual. So the product is something between 1 and about 3 millions: with the log it becomes something between 1 and 6.

About the denominator: it's quite difficult to have "usual values" here, but in this formula, when c is locked, the increase of 10 times of the number of hits between two users may be balanced by the increase of 10 times of the distance or days, so for example

Wien-Wien 7 days between two little users = Wien-Wien 70 days between two users with 10 times hits togheter

The problem is the zero.
On the numerator: 1 or 0 km are approximatively the same thing, so we can replace the 0 with a 1; 0 days it is not possible (automatically moderated), so no problems.
On the denominator: here 1 or 2 hits between users or cities ARE different, and we have to forbid that the product will be 1 because of the logarithm, so I placed temporaneally a little number, e, for correct that. In my first calculation this number was 0,1 , but I saw that if e = 0,96478 , a hit with 10 days and 10 km, n=1, c=1, has I =100, and that is nice

I tried this index with repetite hits in the time, e=0,1

1) User A inserts some notes from a place. Those notes are found by user B at 10 km of distance, the first the day 1, the second the day 10, the third the day 20, the fourth the day 30, the fifth the day 40
I = 48,32 , then 6,418, then 4,752, then 4,078, then 3,700

2) User A inserts some notes from a place. Those notes are found by user B always on days 1,10, 20... but in different locations (user B is rotating around A)
I=48,32, then 12,41, then 9,366 , then 8,084, then 7,355

3)User A and user B are moving around Europe, but user B found many bills of A, (d t) is always 100, but locations are always virgins
I= 96,64 , then 12,41, then 8,140 , then 6,528, then 5,655

Now I have to test this algorithm with real hits, but I have got the problem of finding n and c

[Jes]

Good work!

Ok, I think it is a nice formula. Nevertheless, I think we shouldn't give that importance to the number of days. As a 100km hit in 10 days is more interesting than a 10km 100 days. (IMO!!) What do you think?

It can be easly solved by slight modification in the formula.

Btw, when I saw e, I thought e = 2.71828

Similarly, I think we should give less importance to the users themselves. What if a user has a hit when travelling with a person whith whom (s)he has previously had a hit? is the hit for that reason less interesting than if it would have occurred with a different user. Maybe... but it is not the essential part of the interest of a hit.

The same: we can slightly modify the formula; that is very easy to do.

The good thing of this formula is that it will give us a more close range of values, although I think that what we actually need is a formula which considerabely punish the non interesting hits and "rises up" the super-interesting hits.

Well, it is just my opinion, I do not know what may think the others (Math murderer or any other user )

Now I have to test this algorithm with real hits, but I have got the problem of finding n and c

Easy:

Once you are in the page of the hit. lets say: http://es.eurobilltracker.com/notes/?id=21128835" onclick="window.open(this.href);return false;

For the "c" you have to click on one of the cities: pisa and follow "Compagni di hit". In this case, you have Pisa - Torino = 1 hit.

What is for the "n" you have to be lucky: click on one of the users, and go to the page of the user. Once there, go to "Hit partners" again, and you will see (if available) the number of hits the user has with the other one.

Another reason why I do not like the "n" is that: if both users do not want to share the "hit partners" statistics... you are betrayed. I suppouse that info is stored somewhere, but the "interestingness factor" wouldn't be fully transparent. (I don't know if I explained it in a sufficently propper way )

BTW: this example gave me a hint... Should we consider the denomination of a note for this interestingness stuff?
I think a hit with a or or or are more or less within the same interestingness sphere. but and and specially are more interesting... as these notes are rather unfrequent. (At least for me)
However, this lead us into a very complicated formula, not only because we should introduce a new factor in there, but also because... Why not consider then if the note is a R/X or something more strange M/M or whatever... Ok, I'd better answer my self: not such factor is to be taken into account

[claudio vda]

Btw, when I saw e, I thought e = 2.71828

Because it was little, I started with epsilon , and I traslated in my latin keyboard, but doesn't matter

[Jes]

Btw, when I saw e, I thought e = 2.71828

Because it was little, I started with epsilon , and I traslated in my latin keyboard, but doesn't matter

and what about 1+log(whatever might be 1)

[claudio vda]

and what about 1+log(whatever might be 1)

That's a good idea!