RE: Collaborative filtering item-based in mahout - without isolating users
Mario, I think in terms of correctness. In similarities like Euclidean, Pearson correlation or Cosine Similarity better results are if we consider only common users (users who rated both compared items). This assumption let to find similar item for those which are unpopular, otherwise we recommend only very popular items. For my data it is unacceptable. But if you take, for example, the cosine similarity, you shouldn't throw away the data. - you should, it result in dimension reduction and it is good. Everything is still in the same space but for each pair the space is reduced. My question is why someone who wrote this code ignored this so important assumption? It was by accident or due to some important reasons like effectiveness or computational complexity? Natalia -Original Message- From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] Sent: Wednesday, December 10, 2014 7:05 PM To: user@mahout.apache.org Subject: Re: Collaborative filtering item-based in mahout - without isolating users Hi Natalia Regarding example 1, if you think in terms of likelihood that the two products have been bought together because they are similar (opposed to by chance), the similarity is undefined. As everyone buys 12, of course the person who bought 11 bough also 12, right? This if you compute the similarity through a co-occurence matrix (and loglikelihood ratio) But you say In the theory, similarity between two items should be calculated only for users who ranked both items. I guess you mean: Users [1,2,4] don't know about item 11, therefore they do not collaborate in building the similarity between the two items. User [3], on the contrary, does, and gives the same rating to the two products, therefore the similarity is 1. But if you take, for example, the cosine similarity, you shouldn't throw away the data. Here, you build a space with four dimensions -the ratings of four users. You can't say product 11 is on another space when it relates with user 1,2,4 because hasn't been rated by those users. They all are there. They are dimensions, like in physics. Therefore you must use this information too. Items are in the user-space... all. Even intuitively, items 11 and 12 are not similar at all -one has been bought by every customer, the other by just one customer. How could you tell the next customer who buys 12 (everyone does...) that she would really like 11...? Mario On Wed, Dec 10, 2014 at 4:40 PM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Hi All, In mahout there is implemented method for item based Collaborative filtering called itemsimilarity, which returns the similarity between each two items. In the theory, similarity between two items should be calculated only for users who ranked both items. During testing I realized that in mahout it works different. Below two examples. Example 1. items are 11-12 In below example the similarity between item 11 and 12 should be equal 1, but mahout output is 0.36. It looks like mahout treats null as 0. Similarity between items: 101 102 0.36602540378443865 Matrix with preferences: 11 12 1 1 2 1 3 1 1 4 1 Example 2. items are 101-103. Similarity between items 101 and 102 should be calculated using only ranks for users 4 and 5, and the same for items 101 and 103 (that should be based on theory). Here (101,103) is more similar than (101,102), and it shouldn't be. Similarity between items: 101 102 0.2612038749637414 101 103 0.4340578302732228 102 103 0.2600070276638468 Matrix with preferences: 101 102103 1 1 0.1 2 1 0.1 3 1 0.1 4 1 1 0.1 5 1 1 0.1 6 1 0.1 7 1 0.1 8 1 0.1 9 1 0.1 101 0.1 Both examples were run without any additional parameters. Is this problem solved somewhere, somehow? Any ideas? Why null is treated as 0? Source: http://files.grouplens.org/papers/www10_sarwar.pdf Kind regards, Natalia Gruszowska
Re: Collaborative filtering item-based in mahout - without isolating users
otherwise we recommend only very popular items this is why you have loglikelihood ratio, right? m On Thu, Dec 11, 2014 at 11:51 AM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Mario, I think in terms of correctness. In similarities like Euclidean, Pearson correlation or Cosine Similarity better results are if we consider only common users (users who rated both compared items). This assumption let to find similar item for those which are unpopular, otherwise we recommend only very popular items. For my data it is unacceptable. But if you take, for example, the cosine similarity, you shouldn't throw away the data. - you should, it result in dimension reduction and it is good. Everything is still in the same space but for each pair the space is reduced. My question is why someone who wrote this code ignored this so important assumption? It was by accident or due to some important reasons like effectiveness or computational complexity? Natalia -Original Message- From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] Sent: Wednesday, December 10, 2014 7:05 PM To: user@mahout.apache.org Subject: Re: Collaborative filtering item-based in mahout - without isolating users Hi Natalia Regarding example 1, if you think in terms of likelihood that the two products have been bought together because they are similar (opposed to by chance), the similarity is undefined. As everyone buys 12, of course the person who bought 11 bough also 12, right? This if you compute the similarity through a co-occurence matrix (and loglikelihood ratio) But you say In the theory, similarity between two items should be calculated only for users who ranked both items. I guess you mean: Users [1,2,4] don't know about item 11, therefore they do not collaborate in building the similarity between the two items. User [3], on the contrary, does, and gives the same rating to the two products, therefore the similarity is 1. But if you take, for example, the cosine similarity, you shouldn't throw away the data. Here, you build a space with four dimensions -the ratings of four users. You can't say product 11 is on another space when it relates with user 1,2,4 because hasn't been rated by those users. They all are there. They are dimensions, like in physics. Therefore you must use this information too. Items are in the user-space... all. Even intuitively, items 11 and 12 are not similar at all -one has been bought by every customer, the other by just one customer. How could you tell the next customer who buys 12 (everyone does...) that she would really like 11...? Mario On Wed, Dec 10, 2014 at 4:40 PM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Hi All, In mahout there is implemented method for item based Collaborative filtering called itemsimilarity, which returns the similarity between each two items. In the theory, similarity between two items should be calculated only for users who ranked both items. During testing I realized that in mahout it works different. Below two examples. Example 1. items are 11-12 In below example the similarity between item 11 and 12 should be equal 1, but mahout output is 0.36. It looks like mahout treats null as 0. Similarity between items: 101 102 0.36602540378443865 Matrix with preferences: 11 12 1 1 2 1 3 1 1 4 1 Example 2. items are 101-103. Similarity between items 101 and 102 should be calculated using only ranks for users 4 and 5, and the same for items 101 and 103 (that should be based on theory). Here (101,103) is more similar than (101,102), and it shouldn't be. Similarity between items: 101 102 0.2612038749637414 101 103 0.4340578302732228 102 103 0.2600070276638468 Matrix with preferences: 101 102103 1 1 0.1 2 1 0.1 3 1 0.1 4 1 1 0.1 5 1 1 0.1 6 1 0.1 7 1 0.1 8 1 0.1 9 1 0.1 101 0.1 Both examples were run without any additional parameters. Is this problem solved somewhere, somehow? Any ideas? Why null is treated as 0? Source: http://files.grouplens.org/papers/www10_sarwar.pdf Kind regards, Natalia Gruszowska
RE: Collaborative filtering item-based in mahout - without isolating users
To be honest I haven't seen the code of this similarity (do you have?). But then as I see it, it ignore other side - this time popular items and additional it looks like it ignore value of ratig - has only 1 or 0. N. -Original Message- From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] Sent: Thursday, December 11, 2014 12:00 PM To: user@mahout.apache.org Subject: Re: Collaborative filtering item-based in mahout - without isolating users otherwise we recommend only very popular items this is why you have loglikelihood ratio, right? m On Thu, Dec 11, 2014 at 11:51 AM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Mario, I think in terms of correctness. In similarities like Euclidean, Pearson correlation or Cosine Similarity better results are if we consider only common users (users who rated both compared items). This assumption let to find similar item for those which are unpopular, otherwise we recommend only very popular items. For my data it is unacceptable. But if you take, for example, the cosine similarity, you shouldn't throw away the data. - you should, it result in dimension reduction and it is good. Everything is still in the same space but for each pair the space is reduced. My question is why someone who wrote this code ignored this so important assumption? It was by accident or due to some important reasons like effectiveness or computational complexity? Natalia -Original Message- From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] Sent: Wednesday, December 10, 2014 7:05 PM To: user@mahout.apache.org Subject: Re: Collaborative filtering item-based in mahout - without isolating users Hi Natalia Regarding example 1, if you think in terms of likelihood that the two products have been bought together because they are similar (opposed to by chance), the similarity is undefined. As everyone buys 12, of course the person who bought 11 bough also 12, right? This if you compute the similarity through a co-occurence matrix (and loglikelihood ratio) But you say In the theory, similarity between two items should be calculated only for users who ranked both items. I guess you mean: Users [1,2,4] don't know about item 11, therefore they do not collaborate in building the similarity between the two items. User [3], on the contrary, does, and gives the same rating to the two products, therefore the similarity is 1. But if you take, for example, the cosine similarity, you shouldn't throw away the data. Here, you build a space with four dimensions -the ratings of four users. You can't say product 11 is on another space when it relates with user 1,2,4 because hasn't been rated by those users. They all are there. They are dimensions, like in physics. Therefore you must use this information too. Items are in the user-space... all. Even intuitively, items 11 and 12 are not similar at all -one has been bought by every customer, the other by just one customer. How could you tell the next customer who buys 12 (everyone does...) that she would really like 11...? Mario On Wed, Dec 10, 2014 at 4:40 PM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Hi All, In mahout there is implemented method for item based Collaborative filtering called itemsimilarity, which returns the similarity between each two items. In the theory, similarity between two items should be calculated only for users who ranked both items. During testing I realized that in mahout it works different. Below two examples. Example 1. items are 11-12 In below example the similarity between item 11 and 12 should be equal 1, but mahout output is 0.36. It looks like mahout treats null as 0. Similarity between items: 101 102 0.36602540378443865 Matrix with preferences: 11 12 1 1 2 1 3 1 1 4 1 Example 2. items are 101-103. Similarity between items 101 and 102 should be calculated using only ranks for users 4 and 5, and the same for items 101 and 103 (that should be based on theory). Here (101,103) is more similar than (101,102), and it shouldn't be. Similarity between items: 101 102 0.2612038749637414 101 103 0.4340578302732228 102 103 0.2600070276638468 Matrix with preferences: 101 102103 1 1 0.1 2 1 0.1 3 1 0.1 4 1 1 0.1 5 1 1 0.1 6 1 0.1 7 1 0.1 8 1 0.1 9 1 0.1 101 0.1 Both examples were run without any additional parameters. Is this problem solved somewhere, somehow? Any ideas
Re: Collaborative filtering item-based in mahout - without isolating users
Using LLR ratings are ignored. It is only interested in whether there was an interaction between the user and the item. LLR calculates its own weights based on a probabilistic measure of cooccurrence importance. Cooccurrences are all it looks at so 0 is ignored, it does not indicate a negative preference it mean any preference is undefined or non-existant. In fact those implied 0s in a particular user’s history are exactly where recommendations will come from since we don’t want to recommend something the user already know about. The root of your question is a bit hard to explain since it requires a knowledge of cooccurrence recommenders and the LLR calculation itself. So you can read these for more explanation: A short ebook here that talks about LLR: https://www.mapr.com/practical-machine-learning a blog post here: http://tdunning.blogspot.com/2008/03/surprise-and-coincidence.html wikipedia: http://en.wikipedia.org/wiki/Likelihood_function The spark version “spark-itemsimilarity” can take in multiple actions/events, calculate a cross-cooccurrence with the primary action to determine the strength of correlation, and use the secondary data to improve recs. This is a better way to handle thumbs up/thumbs down or other user actions in a recommender since it automatically determines correlation strength, not relying on user or developer supplied weights. Ratings are often problematic, people rate on different scales at different times on different subjects. There have been many algorithms proposed to deal with this but most new research deals with optimizing the ranking order of recommendations which is usually more important in the application. On Dec 11, 2014, at 4:23 AM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: To be honest I haven't seen the code of this similarity (do you have?). But then as I see it, it ignore other side - this time popular items and additional it looks like it ignore value of ratig - has only 1 or 0. N. -Original Message- From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] Sent: Thursday, December 11, 2014 12:00 PM To: user@mahout.apache.org Subject: Re: Collaborative filtering item-based in mahout - without isolating users otherwise we recommend only very popular items this is why you have loglikelihood ratio, right? m On Thu, Dec 11, 2014 at 11:51 AM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Mario, I think in terms of correctness. In similarities like Euclidean, Pearson correlation or Cosine Similarity better results are if we consider only common users (users who rated both compared items). This assumption let to find similar item for those which are unpopular, otherwise we recommend only very popular items. For my data it is unacceptable. But if you take, for example, the cosine similarity, you shouldn't throw away the data. - you should, it result in dimension reduction and it is good. Everything is still in the same space but for each pair the space is reduced. My question is why someone who wrote this code ignored this so important assumption? It was by accident or due to some important reasons like effectiveness or computational complexity? Natalia -Original Message- From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] Sent: Wednesday, December 10, 2014 7:05 PM To: user@mahout.apache.org Subject: Re: Collaborative filtering item-based in mahout - without isolating users Hi Natalia Regarding example 1, if you think in terms of likelihood that the two products have been bought together because they are similar (opposed to by chance), the similarity is undefined. As everyone buys 12, of course the person who bought 11 bough also 12, right? This if you compute the similarity through a co-occurence matrix (and loglikelihood ratio) But you say In the theory, similarity between two items should be calculated only for users who ranked both items. I guess you mean: Users [1,2,4] don't know about item 11, therefore they do not collaborate in building the similarity between the two items. User [3], on the contrary, does, and gives the same rating to the two products, therefore the similarity is 1. But if you take, for example, the cosine similarity, you shouldn't throw away the data. Here, you build a space with four dimensions -the ratings of four users. You can't say product 11 is on another space when it relates with user 1,2,4 because hasn't been rated by those users. They all are there. They are dimensions, like in physics. Therefore you must use this information too. Items are in the user-space... all. Even intuitively, items 11 and 12 are not similar at all -one has been bought by every customer, the other by just one customer. How could you tell the next customer who buys 12 (everyone does...) that she would really like 11...? Mario On Wed, Dec 10, 2014 at 4:40 PM, Gruszowska
Re: Collaborative filtering item-based in mahout - without isolating users
Natalia, It sounds like you are starting from the assumption that ratings are being done. This can happen, but in production recommendation settings, ratings is typically a very low value input because the meaning of a rating is very complex and because so few users actually do ratings unless forced into unnatural acts. Instead, you typically wind up using other kinds of actions. If you do use ratings, it is often better to ignore the value of the rating and use the mere fact of the rating. It is also common to assume that all users *could* have interacted with any item even if they didn't. This assumption is suspect, but it is better than assuming that lack of interaction really means lack of opportunity. Adjusting your assumptions to fit these leads, I think, to the approach used by Mahout. On Thu, Dec 11, 2014 at 2:51 AM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Mario, I think in terms of correctness. In similarities like Euclidean, Pearson correlation or Cosine Similarity better results are if we consider only common users (users who rated both compared items). This assumption let to find similar item for those which are unpopular, otherwise we recommend only very popular items. For my data it is unacceptable. But if you take, for example, the cosine similarity, you shouldn't throw away the data. - you should, it result in dimension reduction and it is good. Everything is still in the same space but for each pair the space is reduced. My question is why someone who wrote this code ignored this so important assumption? It was by accident or due to some important reasons like effectiveness or computational complexity? Natalia -Original Message- From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] Sent: Wednesday, December 10, 2014 7:05 PM To: user@mahout.apache.org Subject: Re: Collaborative filtering item-based in mahout - without isolating users Hi Natalia Regarding example 1, if you think in terms of likelihood that the two products have been bought together because they are similar (opposed to by chance), the similarity is undefined. As everyone buys 12, of course the person who bought 11 bough also 12, right? This if you compute the similarity through a co-occurence matrix (and loglikelihood ratio) But you say In the theory, similarity between two items should be calculated only for users who ranked both items. I guess you mean: Users [1,2,4] don't know about item 11, therefore they do not collaborate in building the similarity between the two items. User [3], on the contrary, does, and gives the same rating to the two products, therefore the similarity is 1. But if you take, for example, the cosine similarity, you shouldn't throw away the data. Here, you build a space with four dimensions -the ratings of four users. You can't say product 11 is on another space when it relates with user 1,2,4 because hasn't been rated by those users. They all are there. They are dimensions, like in physics. Therefore you must use this information too. Items are in the user-space... all. Even intuitively, items 11 and 12 are not similar at all -one has been bought by every customer, the other by just one customer. How could you tell the next customer who buys 12 (everyone does...) that she would really like 11...? Mario On Wed, Dec 10, 2014 at 4:40 PM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Hi All, In mahout there is implemented method for item based Collaborative filtering called itemsimilarity, which returns the similarity between each two items. In the theory, similarity between two items should be calculated only for users who ranked both items. During testing I realized that in mahout it works different. Below two examples. Example 1. items are 11-12 In below example the similarity between item 11 and 12 should be equal 1, but mahout output is 0.36. It looks like mahout treats null as 0. Similarity between items: 101 102 0.36602540378443865 Matrix with preferences: 11 12 1 1 2 1 3 1 1 4 1 Example 2. items are 101-103. Similarity between items 101 and 102 should be calculated using only ranks for users 4 and 5, and the same for items 101 and 103 (that should be based on theory). Here (101,103) is more similar than (101,102), and it shouldn't be. Similarity between items: 101 102 0.2612038749637414 101 103 0.4340578302732228 102 103 0.2600070276638468 Matrix with preferences: 101 102103 1 1 0.1 2 1 0.1 3 1 0.1 4 1 1 0.1 5 1 1 0.1 6 1 0.1 7 1 0.1 8
Re: Collaborative filtering item-based in mahout - without isolating users
Hi Natalia Regarding example 1, if you think in terms of likelihood that the two products have been bought together because they are similar (opposed to by chance), the similarity is undefined. As everyone buys 12, of course the person who bought 11 bough also 12, right? This if you compute the similarity through a co-occurence matrix (and loglikelihood ratio) But you say In the theory, similarity between two items should be calculated only for users who ranked both items. I guess you mean: Users [1,2,4] don't know about item 11, therefore they do not collaborate in building the similarity between the two items. User [3], on the contrary, does, and gives the same rating to the two products, therefore the similarity is 1. But if you take, for example, the cosine similarity, you shouldn't throw away the data. Here, you build a space with four dimensions -the ratings of four users. You can't say product 11 is on another space when it relates with user 1,2,4 because hasn't been rated by those users. They all are there. They are dimensions, like in physics. Therefore you must use this information too. Items are in the user-space... all. Even intuitively, items 11 and 12 are not similar at all -one has been bought by every customer, the other by just one customer. How could you tell the next customer who buys 12 (everyone does...) that she would really like 11...? Mario On Wed, Dec 10, 2014 at 4:40 PM, Gruszowska Natalia natalia.gruszow...@grupaonet.pl wrote: Hi All, In mahout there is implemented method for item based Collaborative filtering called itemsimilarity, which returns the similarity between each two items. In the theory, similarity between two items should be calculated only for users who ranked both items. During testing I realized that in mahout it works different. Below two examples. Example 1. items are 11-12 In below example the similarity between item 11 and 12 should be equal 1, but mahout output is 0.36. It looks like mahout treats null as 0. Similarity between items: 101 102 0.36602540378443865 Matrix with preferences: 11 12 1 1 2 1 3 1 1 4 1 Example 2. items are 101-103. Similarity between items 101 and 102 should be calculated using only ranks for users 4 and 5, and the same for items 101 and 103 (that should be based on theory). Here (101,103) is more similar than (101,102), and it shouldn't be. Similarity between items: 101 102 0.2612038749637414 101 103 0.4340578302732228 102 103 0.2600070276638468 Matrix with preferences: 101 102103 1 1 0.1 2 1 0.1 3 1 0.1 4 1 1 0.1 5 1 1 0.1 6 1 0.1 7 1 0.1 8 1 0.1 9 1 0.1 101 0.1 Both examples were run without any additional parameters. Is this problem solved somewhere, somehow? Any ideas? Why null is treated as 0? Source: http://files.grouplens.org/papers/www10_sarwar.pdf Kind regards, Natalia Gruszowska
