Recommendation Systems

Transcription

1 Recommendation Systems Collaborative Filtering Finding somebody or something similar by looking at recommendation systems Recommendation systems are found everywhere example: Amazon Recommendation systems are collaborative since recommendations are made based on other people or things Here s a table showing 3 users who rated 2 books: Homeword Bound Jill 5 5 John 2 5 Tyler 1 4 Down and Dirty Try to represent this table in 2D

2 Distance Measure Manhattan Distance Use Distance Measure techniques for computation Say you have a fourth person who rates both books: Mr.X rates Homeword Bound 4 stars and Down and Dirty 2 stars How do you find the person who is most similar or closest Manhattan Distance Easiest distance measure (fast to compute) Use the 2D representation (person is represented by an (x,y) point) Formula: Uses absolute value of the difference Recommend another book liked by Jill to Mr.X? Jill 4 John 5 Tyler 5 Distance from Mr.X

3 Distance Measure Euclidean Distance Manhattan Distance is fast to compute, but not very accurate Euclidean Distance More accurate Uses Pythagorean theorem Computes the hypotenuse of the triangle for better results Formula: Distance from Mr.X Jill 3.16 John 3.61 Tyler 3.61

4 2-Dimensional to N-Dimensional Example: Users can rate music service bands on a star system (1 to 5 including half star rating) Compute the distance based on the number of bands any 2 people reviewed

5 2-Dimensional to N-Dimensional Manhattan distance between Angelica and Bill

6 2-Dimensional to N-Dimensional Euclidean distance between Angelica and Bill

7 Flaw with Distance Measure Consider Euclidean distance between Hailey and Veronica Only 2 bands in common between the two! Compare this 2-D computation with another pair who might have 5 bands in common making it 5-dimensional Doesn t make the distance measure very accurate if data set is incomplete

8 Generalizing Distance Measure Minkowski Distance Metric: When r = 1, the formula is Manhattan distance When r = 2, the formula is Euclidean distance (The greater the r value, the more a large difference in one dimension will influence the total difference)

9 Represent Data in Python

10 Manhattan distance Algorithm to compute Manhattan distance For any two user ratings For every band rated by one user If second user has rated same band then Get the distance and add it to total distance

11 Compute Nearest Neighbor Algorithm to compute nearest neighbor Use the Manhattan distance function for each person and get the distances to everybody else Based on the distances, you can get any person s nearest neighbor

12 Recommendations Making Recommendations Say that we wanted to make recommendations to Hailey We find her nearest neighbor (using computenearestneighbor) Find bands that Veronica has rated but Hailey has not

13 Recommendations Problems with Recommendations For Angelica we get back an empty set, to indicate no recommendations!

14 Implement Minkowski Distance Use Minkowski distance formula to be able to compute either Manhattan or Euclidean Make appropriate changes to computenearestneighbor to use Minkowski distance Chart out Recommendations for a few users for both distance measures

15 Rating Behavior Users rating behavior can be quite different Bill avoids extremes Jordyn likes everything or hesitant to rate anything below 4 Hailey gives either a 1 or a 4 So how does Hailey s 4 compare to Jordyn s 4? Hailey may really like it but Jordyn might find it just ok so a score of 4 can be relative in the mind of the user Jordyn s scoring can also be termed as grade inflation One solution to the problem is to find a correlation coefficient called the Pearson Correlation Coefficient

16 Pearson Correlation Coefficient In statistics, the Pearson product-moment correlation coefficient (sometimes referred to Pearson's r) is a measure of the linear dependence between two variables X and Y Gives a value between +1 and 1 inclusive 1 is total positive linear correlation 0 is no linear correlation 1 is total negative linear correlation

17 Pearson Correlation Coefficient Graph showing the above chart indicates a Straight Line which means it s Perfect Agreement If Clara and Robert agree less, the less the data points reside on a straight line Pearson Correlation Coefficient is a measure of correlation between two variables Ranges between -1 and 1 inclusive, 1 indicates perfect agreement, -1 indicates perfect disagreement

18 Pearson Correlation Coefficient Formula is: Alternative approximation of Pearson (slightly simplified): (If you plug in the ratings for Clara & Robert, r will be 1!)

19 Cosine Similarity Need to avoid shared-zero values Example: Track number of times a song was played Is Sally more similar in listening habits to Ann than Ben? Problem? There are over 15 million tracks in itunes and one may only have a few thousand Out of these number of tracks played might be even less; and there are more zero attributes (not played) Compare this with another person s play list and zero attributes and it s likely that shared zeros are more common

20 Cosine Similarity Formula to ignore 0-0 matches: Where x. y is the dot product and x indicates the length of the vector x which is: For the example which had perfect agreement: Vector x = (4.75, 4.5, 5, 4.25, 4) Vector y = (4, 3, 5, 2, 1) Cosine similarity:

21 Similarity Selection If data is subject to grade-inflation (different scales for different users) use Pearson If data is dense with almost all attributes having non-zero values, use Manhattan or Euclidean If data is sparse, use Cosine Similarity If data is not dense equally across the spectrum there are oddities that present themselves Example: 3 users with 25, 26 and 150 ratings who all share 25 non-zero tracks with similar ratings It s a mistake to rely on a single most similar person since any quirk with the person is passed on as a recommendation!

22 K-nearest neighbor Problems arise when we rely on a single most similar person Any quirk that person has gets passed on as a recommendation Instead if we use k most similar people it filters out some of these anomalies called the K-nearest neighbor approach Value for k depends on application

23 K-nearest neighbor Example using k=3 Each person is going to influence the recommendation but by how much? Sally s share is 0.8/2 or 40% Eric s share is 0.7/2 or 35% Amanda s share is 0.5/2 or 25% Projected rating = (4.5 x 0.25) + (5 x 0.35) + (3.5 x 0.4) = 4.2