EMIS 8381 – Spring 2012 1 Netflix and Your Next Movie Night Nonlinear Programming Ron Andrews EMIS 8381.

EMIS 8381 – Spring 20121

Netflix and Your Next Movie Night

Nonlinear Programming

Ron Andrews

EMIS 8381


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.


Agenda:

• Netflix - Business of movie recommendation• Collaborative filtering• Linear Aspects• Nonlinear Aspects• Performance Improvement

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Netflix - Business of movie recommendation

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- 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


Collaborative filtering

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•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


Linear Approach:

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• 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


Linear Approach Cont.:

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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.


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.

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NonlinearComponent,Associative network


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:

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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


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

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Application to class:• Is used to find a local minimum (not global)• Works when function is quadratic (twice differentiable)

= step size

Update iterationPi = nonlinear


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

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Nonlinear Approach: NLPCA Algorithm Cont.

• Step 4: Prediction Generation – Matching of neighborhood to user

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Neighborhood formation

User ratings

Original itemaverage


Nonlinear effectiveness

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Dimensions

Acc

urac

y Nonlinear can account for more variance.

True accuracy:.7843


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

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•Questions?

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EMIS 8381 – Spring 2012 1 Netflix and Your Next Movie Night Nonlinear Programming Ron Andrews EMIS 8381.

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