Question about implementing item-based collaborative filtering algorithms

[Guohua Hao <ha...@gmail.com>]

Hello All,

In item-based CF algorithms, when we predict the rating P_{u, i} of some
user 'u' for some item 'i', shall we consider all available items j, whose
similarities with item 'i' are not zero, or shall we only consider those
items whose have been both rated by user u and their similarities with item
i are not zero. This will affect the normalization part as we need to sum up
all those considered similarity scores.

I am reading the following paper,

Item-Based Collaborative Filtering Recommendation Algorithms (
www.grouplens.org/papers/pdf/www10_sarwar.pdf)

The normalization part is in the middle left of page 5.

Thank you very much,
Guohua

Re: Question about implementing item-based collaborative filtering algorithms

[Ted Dunning <te...@gmail.com>]

This makes clear the real problem with considering ratings as numerical
values.  In my experience, a reasonable ordering of similarities between two
ratings from different users on the same item is like this:

     both rated the item high
     both rated it low
     one rated high, the other low
     one rated the item, the other did not

I would content that having opposite ratings is actually a sign of
similarity between the users tastes rather than a sign of dis-similarity.
It is a weaker sign of similarity than an identical rating, but it is still
an indication of similarity.  This is because users rate items low if they
are close to what they like, but the item somehow pissed them off by
violating their expectations.  Items that are far from their tastes, they
simply don't rate.

Moreover, since negative ratings are relatively rare (typically 5-10% of the
number of high ratings), the both-low condition is rarer still.  You
therefore actually get more mileage out of the high-low discordance.

My conclusion from this is that viable strategies include:

a) use only high ratings and do binary recommendations

b) use any rating at all as a binary recommendation

c) do both (a) and (b) and blend the results with more emphasis on (a).

On Thu, Feb 11, 2010 at 12:41 PM, Sean Owen <sr...@gmail.com> wrote:

> Yes, you are right. It seems counter-intuitive, at first. I might
> argue it is not so counter-intuitive, however.
>
> A similarity of -1 is low, as low as possible. But the fact that the
> two items have any similarity at all is significant. It means there
> are a number of users who have rated both items, although they have
> rated them quite differently. Note that most pairs of items have no
> similarity whatsoever.
>
> So a similarity of -1 is still in a way significant. The result is
> less counter-intuitive when you think of it this way.
>
> On Thu, Feb 11, 2010 at 8:35 PM, Guohua Hao <ha...@gmail.com> wrote:
> > Hello Sean,
> >
> > First, I like your tweaks there.
> >
> > Based on your example, I came up with a new extreme case, which may cause
> > some trouble. Suppose the user u has rated several items (e.g., 10 items)
> > all with rating 5, and we want to predict user u's rating for item i,
> P_{u,
> > i}. If item i 's similarities with all those already rated items are the
> > same, which are very close to -1, we are still going to get P_{u,i} = 5,
> > because those similarities factors will be canceled out. However, there
> is
> > still counter-intuitive, since we expect P_{u, i} to be very close to 1 (
> in
> > the 1-5 rating range) with more confidence.
> >
> > Shall we consider this case in the code?
> >
> > Thanks,
> > Guohua
> >
> > On Wed, Feb 10, 2010 at 6:13 PM, Sean Owen <sr...@gmail.com> wrote:
> >
> >> Yes, great point. It's bad if there's only one item that the user has
> >> rated that has any similarity to the item being predicted. According
> >> to even the 'corrected' formula, the similarity value doesn't even
> >> matter. It cancels out. That leads to the counter-intuitive
> >> possibility you highlight.
> >>
> >> For that reason GenericItemBasedRecommender won't make a prediction in
> >> this situation. You could argue it's a hack but I feel it should be
> >> undefined in this situation.
> >>
> >> You could certainly throw out 3.2.1 entirely and think up something
> >> better, though I think with the two tweaks I've described here, its
> >> core logic is simple and remains sound.
> >>
> >> Sean
> >>
> >>
> >> On Thu, Feb 11, 2010 at 12:04 AM, Guohua Hao <ha...@gmail.com>
> wrote:
> >> > I think you brought up a good point as to dealing with negative
> >> > similarities, which I have not realized before. Here is my other
> thought.
> >> > Based on your example and the proposed method, we will get a predicted
> >> > rating of 5 in such case after normalization. This seems
> >> counter-intuitive
> >> > to me, since we know that these two items are very dissimilar
> (actually
> >> > opposite correlated), a predicted rating close to 1 will be more
> >> intuitive
> >> > to me. Maybe we need to think more about the expression in section
> 3.2.1
> >> of
> >> > that paper.
> >>
> >
>



-- 
Ted Dunning, CTO
DeepDyve

Re: Question about implementing item-based collaborative filtering algorithms

[Sean Owen <sr...@gmail.com>]

Yes, you are right. It seems counter-intuitive, at first. I might
argue it is not so counter-intuitive, however.

A similarity of -1 is low, as low as possible. But the fact that the
two items have any similarity at all is significant. It means there
are a number of users who have rated both items, although they have
rated them quite differently. Note that most pairs of items have no
similarity whatsoever.

So a similarity of -1 is still in a way significant. The result is
less counter-intuitive when you think of it this way.

On Thu, Feb 11, 2010 at 8:35 PM, Guohua Hao <ha...@gmail.com> wrote:
> Hello Sean,
>
> First, I like your tweaks there.
>
> Based on your example, I came up with a new extreme case, which may cause
> some trouble. Suppose the user u has rated several items (e.g., 10 items)
> all with rating 5, and we want to predict user u's rating for item i, P_{u,
> i}. If item i 's similarities with all those already rated items are the
> same, which are very close to -1, we are still going to get P_{u,i} = 5,
> because those similarities factors will be canceled out. However, there is
> still counter-intuitive, since we expect P_{u, i} to be very close to 1 ( in
> the 1-5 rating range) with more confidence.
>
> Shall we consider this case in the code?
>
> Thanks,
> Guohua
>
> On Wed, Feb 10, 2010 at 6:13 PM, Sean Owen <sr...@gmail.com> wrote:
>
>> Yes, great point. It's bad if there's only one item that the user has
>> rated that has any similarity to the item being predicted. According
>> to even the 'corrected' formula, the similarity value doesn't even
>> matter. It cancels out. That leads to the counter-intuitive
>> possibility you highlight.
>>
>> For that reason GenericItemBasedRecommender won't make a prediction in
>> this situation. You could argue it's a hack but I feel it should be
>> undefined in this situation.
>>
>> You could certainly throw out 3.2.1 entirely and think up something
>> better, though I think with the two tweaks I've described here, its
>> core logic is simple and remains sound.
>>
>> Sean
>>
>>
>> On Thu, Feb 11, 2010 at 12:04 AM, Guohua Hao <ha...@gmail.com> wrote:
>> > I think you brought up a good point as to dealing with negative
>> > similarities, which I have not realized before. Here is my other thought.
>> > Based on your example and the proposed method, we will get a predicted
>> > rating of 5 in such case after normalization. This seems
>> counter-intuitive
>> > to me, since we know that these two items are very dissimilar (actually
>> > opposite correlated), a predicted rating close to 1 will be more
>> intuitive
>> > to me. Maybe we need to think more about the expression in section 3.2.1
>> of
>> > that paper.
>>
>

Re: Question about implementing item-based collaborative filtering algorithms

[Guohua Hao <ha...@gmail.com>]

Hello Sean,

First, I like your tweaks there.

Based on your example, I came up with a new extreme case, which may cause
some trouble. Suppose the user u has rated several items (e.g., 10 items)
all with rating 5, and we want to predict user u's rating for item i, P_{u,
i}. If item i 's similarities with all those already rated items are the
same, which are very close to -1, we are still going to get P_{u,i} = 5,
because those similarities factors will be canceled out. However, there is
still counter-intuitive, since we expect P_{u, i} to be very close to 1 ( in
the 1-5 rating range) with more confidence.

Shall we consider this case in the code?

Thanks,
Guohua

On Wed, Feb 10, 2010 at 6:13 PM, Sean Owen <sr...@gmail.com> wrote:

> Yes, great point. It's bad if there's only one item that the user has
> rated that has any similarity to the item being predicted. According
> to even the 'corrected' formula, the similarity value doesn't even
> matter. It cancels out. That leads to the counter-intuitive
> possibility you highlight.
>
> For that reason GenericItemBasedRecommender won't make a prediction in
> this situation. You could argue it's a hack but I feel it should be
> undefined in this situation.
>
> You could certainly throw out 3.2.1 entirely and think up something
> better, though I think with the two tweaks I've described here, its
> core logic is simple and remains sound.
>
> Sean
>
>
> On Thu, Feb 11, 2010 at 12:04 AM, Guohua Hao <ha...@gmail.com> wrote:
> > I think you brought up a good point as to dealing with negative
> > similarities, which I have not realized before. Here is my other thought.
> > Based on your example and the proposed method, we will get a predicted
> > rating of 5 in such case after normalization. This seems
> counter-intuitive
> > to me, since we know that these two items are very dissimilar (actually
> > opposite correlated), a predicted rating close to 1 will be more
> intuitive
> > to me. Maybe we need to think more about the expression in section 3.2.1
> of
> > that paper.
>

Re: Question about implementing item-based collaborative filtering algorithms

[Sean Owen <sr...@gmail.com>]

Yes, great point. It's bad if there's only one item that the user has
rated that has any similarity to the item being predicted. According
to even the 'corrected' formula, the similarity value doesn't even
matter. It cancels out. That leads to the counter-intuitive
possibility you highlight.

For that reason GenericItemBasedRecommender won't make a prediction in
this situation. You could argue it's a hack but I feel it should be
undefined in this situation.

You could certainly throw out 3.2.1 entirely and think up something
better, though I think with the two tweaks I've described here, its
core logic is simple and remains sound.

Sean


On Thu, Feb 11, 2010 at 12:04 AM, Guohua Hao <ha...@gmail.com> wrote:
> I think you brought up a good point as to dealing with negative
> similarities, which I have not realized before. Here is my other thought.
> Based on your example and the proposed method, we will get a predicted
> rating of 5 in such case after normalization. This seems counter-intuitive
> to me, since we know that these two items are very dissimilar (actually
> opposite correlated), a predicted rating close to 1 will be more intuitive
> to me. Maybe we need to think more about the expression in section 3.2.1 of
> that paper.

Re: Question about implementing item-based collaborative filtering algorithms

[Guohua Hao <ha...@gmail.com>]

Hello Sean,

Thank you very much for your explanation. I agree with you as to which items
should be considered when compute P_{u,i}. They need to be both rated by
user u and similar (non-zero similarity) to item i.

I think you brought up a good point as to dealing with negative
similarities, which I have not realized before. Here is my other thought.
Based on your example and the proposed method, we will get a predicted
rating of 5 in such case after normalization. This seems counter-intuitive
to me, since we know that these two items are very dissimilar (actually
opposite correlated), a predicted rating close to 1 will be more intuitive
to me. Maybe we need to think more about the expression in section 3.2.1 of
that paper.

Any thoughts or comments?

Thank you,
Guohua


On Wed, Feb 10, 2010 at 5:16 PM, Sean Owen <sr...@gmail.com> wrote:

> You would only consider those items j that user u has rated. That is
> how I understand the expression in 3.2.1, and happens to be what
> GenericItemBasedRecommender does too.
>
>
> For the expression in 3.2.1, you are right that similarities of 0
> could be ignored, since they would not affect the calculation.
>
> However I am not sure I agree with this expression (or else I
> misunderstand it). It suggests using similarities as weights, and
> normalizing by the absolute values of weights. Similarities can be
> negative though. Say that only one item enters into this expression,
> and its rating is 5 on a scale of 1 to 5, and the item similarity is
> -1. This says the prediction is (-1*5)/1 = -5. Oops.
>
> For this reason I did something different in
> GenericItemBasedRecommender. I weight with 1+similarity. These weights
> are nonnegative then. The sense of the expression is preserved.
>
>
> Sean
>
>
> On Wed, Feb 10, 2010 at 10:59 PM, Guohua Hao <ha...@gmail.com> wrote:
> > Hello All,
> >
> > In item-based CF algorithms, when we predict the rating P_{u, i} of some
> > user 'u' for some item 'i', shall we consider all available items j,
> whose
> > similarities with item 'i' are not zero, or shall we only consider those
> > items whose have been both rated by user u and their similarities with
> item
> > i are not zero. This will affect the normalization part as we need to sum
> up
> > all those considered similarity scores.
> >
> > I am reading the following paper,
> >
> > Item-Based Collaborative Filtering Recommendation Algorithms (
> > www.grouplens.org/papers/pdf/www10_sarwar.pdf)
> >
> > The normalization part is in the middle left of page 5.
> >
> > Thank you very much,
> > Guohua
> >
>

Re: Question about implementing item-based collaborative filtering algorithms

[Sean Owen <sr...@gmail.com>]

You would only consider those items j that user u has rated. That is
how I understand the expression in 3.2.1, and happens to be what
GenericItemBasedRecommender does too.


For the expression in 3.2.1, you are right that similarities of 0
could be ignored, since they would not affect the calculation.

However I am not sure I agree with this expression (or else I
misunderstand it). It suggests using similarities as weights, and
normalizing by the absolute values of weights. Similarities can be
negative though. Say that only one item enters into this expression,
and its rating is 5 on a scale of 1 to 5, and the item similarity is
-1. This says the prediction is (-1*5)/1 = -5. Oops.

For this reason I did something different in
GenericItemBasedRecommender. I weight with 1+similarity. These weights
are nonnegative then. The sense of the expression is preserved.


Sean


On Wed, Feb 10, 2010 at 10:59 PM, Guohua Hao <ha...@gmail.com> wrote:
> Hello All,
>
> In item-based CF algorithms, when we predict the rating P_{u, i} of some
> user 'u' for some item 'i', shall we consider all available items j, whose
> similarities with item 'i' are not zero, or shall we only consider those
> items whose have been both rated by user u and their similarities with item
> i are not zero. This will affect the normalization part as we need to sum up
> all those considered similarity scores.
>
> I am reading the following paper,
>
> Item-Based Collaborative Filtering Recommendation Algorithms (
> www.grouplens.org/papers/pdf/www10_sarwar.pdf)
>
> The normalization part is in the middle left of page 5.
>
> Thank you very much,
> Guohua
>