This document provides an introduction to item-based collaborative filtering for building recommendation engines. It discusses how recommendation systems can help provide engaging content for websites. Item-based collaborative filtering models calculate similarities between items based on user ratings and preferences, then uses those similarities to recommend other items users may like. The key steps are collecting user-item interaction data, calculating inter-item similarities, and using those similarities to compute and rank recommendations for users.

1. A quick introduction to item-based
collaborative filtering
Pham Cong Dinh
@pcdinh
PHPDay Saigon 2012

2. Outline
● PHP popularity and challenges to produce
engaging content
● Recommendation engine at work
● How to build a item-based collaborative
filtering-based recommendation engine

3. PHP is everywhere
● W3Tech report in 2012
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4. PHP website distribution
● Reported by builtwith.com in 2012 (more than
28 millions site in PHP)
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5. You have a website. Now what?

6. Information overload
OR
no engaging
content?
From http://bethesignal.org/

7. Why recommendation system?
●

8. Recommendation engine at work

9. Recommendation engine at work

10. Build a recommendation system
● Collaborative filtering: user and item
– Filtering: automatic predictions about the interests
of a user
– Collaborative: many users (preferences or taste
information)

11. Item-based collaborative filtering
● Model-based
– The similarities between different items in the data
set are calculated
– Predict ratings for user-item pairs not present in
the data set

12. Steps to do item-based
collaborative filtering
● Data collection and representations (preferences/taste
…)
● Finding the relationships and determine the similarity
● Recommendation computations -
recommendations/suggestions/discoveries (produce
engaging content)

13. Collaborative filtering: data
collection
● Data collection and representations
(preferences/taste …) (user, item)
– Clicks X,1
✗
– Likes, favorites X,2
✗
Y,1
Watch, read
✗
–
Y,2
✗
– Survey
Z,2
✗
– Ratings Z,3
✗
– Others …
● E.x: Find the set of movies that user X likes

14. Collaborative filtering: Similarity
(1)
● Finding the relationships and determine the
similarity
– The similarity values between items are
measured by observing all the users who
have interacted (rated) both the items
● E.x: Find a group of movies that is similar to
these set of movies that we know user X likes

15. Collaborative filtering: Similarity
(2)
● Manhattan distance: |x1 – x2| + |y1 - y2|
● X Y
●
User(x, y)
Amy(5, 5)
X Bill(2, 5)
Jim(1, 4)
Item(x1, x2, x3) → Ratings
Snow Crash(5, 2, 1)
Girl with the Dragon Tattoo (5, 5, 1)
Manhattan distance
→ Amy – Bill: |5 – 2| + |5 – 5| = 3
Y → Snow Crash - Girl with the Dragon Tattoo: 3

16. Collaborative filtering: Similarity
(3)
● Cosine distance: the angle between these
vectors. Value: -1 (no related) to 1
Item(x1, x2, x3) → Ratings
Snow Crash(5, 2, 1)
Girl with the Dragon Tattoo (5, 5, 1)
Cosine distance
→ Snow Crash - Girl with the Dragon Tattoo:
(5x5 + 2x5 + 1x1) / (( 5x5 + 2x2 + 1 x 1) x ( 5x5 + 5x5 + 1x1))
PHP: https://github.com/aoiaoi/CosineSimilarity/blob/master/CosineSimilarity.php

17. Collaborative filtering: Similarity
(4)
● Pearson Correlation Coefficient: from -1 (no
related) to +1
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●
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● How much the ratings by common users for a
pair of items deviate from average ratings for
those items
● Correlation is basically the average product

18. Collaborative filtering: Similarity
(5)
● Euclidean distance: the "ordinary" distance
between two points.
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● Values: Near 0 (no related) to 1

19. Collaborative filtering: Similarity
(6)
● Spearman distance: Spearman distance is a
square of Euclidean Distance between two
rank vectors. A perfect positive correlation is
+1 and a perfect negative correlation is -1.
●
●
● Spearman Rank Correlation: The range of
Spearman Correlation is from -1 to 1 (a perfect
Spearman correlation of +1)

20. Collaborative filtering: Similarity
(6)
● Adjusted Euclidean distance: take length of
vectors into account
●

21. Collaborative filtering:
Recommendation computations
● Calculate similarity between Item A that user X
watch/buy/like with items that User X does not
watch/buy/like
● Score all the items (e.x: apply weighted
algorithms – average score by the other)
● Sorting
● Return top-N items

22. Collaborative filtering: Other
issues
● Accuracy of Predicting Ratings. To evaluate
accuracy when predicting unrated item for the active
user, use Mean Absolute Error (MAE).
● Accuracy of Recommendations. To evaluate the
accuracy of recommendations, use Mean Average
Precision (MAP), which is defined as Average of the
Average Precision (AP) value for a set of queries (a
query could be considered as a user’s asking for
recommending items in recommender systems).

23. The End
● Q&A