emis 8381 – spring 2012 1 netflix and your next movie night nonlinear programming ron andrews emis...
TRANSCRIPT
EMIS 8381 – Spring 20121
Netflix and Your Next Movie Night
Nonlinear Programming
Ron Andrews
EMIS 8381
EMIS 8381 – Spring 20122
Elevator Pitch:
Situation:
Problem: You have finished your NLP homework, have some downtime but don’t know what movie to watch…
Solution: Netflix’s collaborative filter (cf) based movie recommendation engine that utilizes NLP methods.
Relevancy:
Customer: – The algorithm makes more relevant movie recommendations than nonlinear methods– Better movie choices
Company:– Decreased resource utilization (program complexity) – Increased customer retention.
EMIS 8381 – Spring 2012
Agenda:
• Netflix - Business of movie recommendation• Collaborative filtering• Linear Aspects• Nonlinear Aspects• Performance Improvement
3
EMIS 8381 – Spring 2012
Netflix - Business of movie recommendation
4
- Movie recommendation system: System that seeks to predict or anticipate a user’s preference for a film that has not been viewed by utilizing an algorithm that takes into consideration the collaborative nature of the website (user ratings via collaborative based filtering) -Utilizes linear, nonlinear and statistical methods
EMIS 8381 – Spring 2012
Collaborative filtering
5
•Collaborative filtering is a process to make automated recommendations based upon crowd sourced information such as preference, taste and patterns.
•Two advantages:Wisdom of crowdsLarge Numbers
•Netflix collects four pieces of information from its users:
User Movie Date of grade Grade
Group unity
EMIS 8381 – Spring 2012
Linear Approach:
6
• Computes a prediction for an item (i) using the weighted sum of items similar to i.• Corresponding similarity si,j
• Captures how users rate similar items
EMIS 8381 – Spring 2012
Linear Approach Cont.:
7
Traditionally:
NxM modeled by NxC N= users M= movies Rows= user feature columns are movie feature vectors
•Low rank approximations can be found•Data Sets are sparse•Result:
• difficult non-convex problem •approximation of gradient is difficult to approximate
•Need: nonlinear aspects.
EMIS 8381 – Spring 2012
Nonlinear approaches to movie recommendation:
• Nonlinear Principal Component Analysis (h-NLPCA)• PCA – Principal Component Analysis
– Well established data analysis technique
– Transformation of recorded observations to produce independent score variables
– Captures linear relationships well
– Not sufficient to capture nonlinear patterns
• Introducing ANN: Artificial Neural Network (models defining a function f: X-> Y) Function approximated.
8
NonlinearComponent,Associative network
EMIS 8381 – Spring 2012
Nonlinear Approach: NLPCA
• ANN allows for mappings onto a reduced dimensional space.• Relies on the SVD: Singular value decomposition (factorization of matrix
– first step for CF) Example:
9
Variable ofprincipal components
Uniquely determinedsingle value variances
Conjugate transpose
• Hidden layer enables the function to perform nonlinear mapping functions from extraction : X -> Z to generate: Z -> ^X
• Associative network performs identify mapping, reducing the squared reconstruction error: ½||x^-x||^2
EMIS 8381 – Spring 2012
Nonlinear Approach: NLPCA Cont.
• Nonlinear principal component analysis provides:– Optimal nonlinear subspace spanned by components (different groups formed) – Constrains nonlinear hierarchical order of linear components – A minimum error between groups using conjugate gradient descent algorithm– N components explain the maximal variance– Tries to search for a k-dimensional subspace of minimal mean square error
10
Application to class:• Is used to find a local minimum (not global)• Works when function is quadratic (twice differentiable)
= step size
Update iterationPi = nonlinear
EMIS 8381 – Spring 2012
Nonlinear Approach: NLPCA Algorithm
• Step 1: Data representation– Figure out missing values in original user item matrix (we know how to do
this)
• Step 2: Low rank representation– Use conjugate gradient descent algorithm– Hierarchical error minimized
• Step 3: Neighborhood Formation– Calculate similarity between each user and his closest neighbors.– A = reconstructed matrix, rij = rating of user ui on item ij. – Summations of l are calculated when both users (ua and ui) have rated a
movie
11
EMIS 8381 – Spring 2012
Nonlinear Approach: NLPCA Algorithm Cont.
• Step 4: Prediction Generation – Matching of neighborhood to user
12
Neighborhood formation
User ratings
Original itemaverage
EMIS 8381 – Spring 2012
Nonlinear effectiveness
13
Dimensions
Acc
urac
y Nonlinear can account for more variance.
True accuracy:.7843
EMIS 8381 – Spring 2012
Nonlinear effectiveness: Conclusions
• Faster convergence• Less resources • For small data sets, i.e. not many film ratings, nonlinear provides better
suggestions faster:
• More difficult to implement from a programming stand point
14
EMIS 8381 – Spring 2012
•Questions?
15