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k-Separability Presentation
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Transcript of k-Separability Presentation
An Efficient Collaborative Recommender Systembased on k -separability
Georgios Alexandridis Georgios Siolas Andreas Stafylopatis
Department of Electrical and Computer EngineeringNational Technical University of Athens
20th International Conference on Artificial Neural Networks(ICANN 2010)
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 1 / 16
Outline
1 Current Trends in Recommender SystemsRecommender SystemsDesign Issues
2 Theoretical & Practical Aspects of our Contributionk-SeparabilitySystem Architecture
3 Evaluating our SystemExperimentResultsConclusions
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 2 / 16
What are the Recommender Systems?
Recommender Systems attempt to present information items (e.g.movies, music, books, news stories) that are likely to be of interestto the user.
Some implementations
I AmazonF "Customers Who Bought This Item Also Bought"
I Google NewsF "Recommended Stories"
I Online Audio BroadcastersF last.fmF Pandora
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 3 / 16
What are the Recommender Systems?
Recommender Systems attempt to present information items (e.g.movies, music, books, news stories) that are likely to be of interestto the user.Some implementations
I AmazonF "Customers Who Bought This Item Also Bought"
I Google NewsF "Recommended Stories"
I Online Audio BroadcastersF last.fmF Pandora
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 3 / 16
Taxonomy of Recommender Systems
Criterion: How are the predictions made?I Content-Based Recommenders
F Locate "similar" itemsI Collaborative Recommenders
F Find "like-minded" usersI Hybrid Recommenders
F Combination of the two
Which method is the best?
I Open academic subjectI Highly dependent on the application domainI We followed the Collaborative Recommender approach
F Computationally simpler than the Hybrid approachF A user rating is more than a mere number; it is an aggregation of
various characteristics
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 4 / 16
Taxonomy of Recommender Systems
Criterion: How are the predictions made?I Content-Based Recommenders
F Locate "similar" itemsI Collaborative Recommenders
F Find "like-minded" usersI Hybrid Recommenders
F Combination of the two
Which method is the best?I Open academic subjectI Highly dependent on the application domainI We followed the Collaborative Recommender approach
F Computationally simpler than the Hybrid approachF A user rating is more than a mere number; it is an aggregation of
various characteristics
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 4 / 16
Collaborative Recommender Systems
Key Component: The User Ratings’ Matrix
Ratings
I Indicate how much a user likes an item
F "like" \"dislike"F 1-star up to 5-stars
I1 I2 I3 I4U1 5 3 2U2 3 5 2U3 1 2U4 2 3
Users become each other’s predictor
I By locating positive and negative correlations among them.
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 5 / 16
Collaborative Recommender Systems
Key Component: The User Ratings’ MatrixRatings
I Indicate how much a user likes an itemF "like" \"dislike"F 1-star up to 5-stars
I1 I2 I3 I4U1 5 3 2U2 3 5 2U3 1 2U4 2 3
Users become each other’s predictor
I By locating positive and negative correlations among them.
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 5 / 16
Collaborative Recommender Systems
Key Component: The User Ratings’ MatrixRatings
I Indicate how much a user likes an itemF "like" \"dislike"F 1-star up to 5-stars
I1 I2 I3 I4U1 5 3 2U2 3 5 2U3 1 2U4 2 3
Users become each other’s predictor
I By locating positive and negative correlations among them.
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 5 / 16
Collaborative Recommender Systems
Key Component: The User Ratings’ MatrixRatings
I Indicate how much a user likes an itemF "like" \"dislike"F 1-star up to 5-stars
I1 I2 I3 I4U1 5 3 2U2 3 5 2U3 1 2U4 2 3
Users become each other’s predictorI By locating positive and negative correlations among them.
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 5 / 16
Challanges in Collaborative Recommender SystemDesign
1 The cold-start problem
I Recommendations cannot be made unless a user has providedsome ratings
I Solutions:
F Recommend the most popular itemsF Explicity ask the user to rate some items prior to making
recommendations
2 The sparsity problem
I The ratings matrix is sparse
F Empty elements: More than 90%
I Solution: Dimensionality Reduction techniques
F Singular Value Decomposition (SVD) yields good results
I Pros: The resultant matrix is substantially smaller & densierI Cons: The dataset becomes very "noisy"
F Most elements assume values that are marginally larger than zero
I Conclusion: We are in need of techniques that can "learn" noisydatasets!
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 6 / 16
Challanges in Collaborative Recommender SystemDesign
1 The cold-start problemI Recommendations cannot be made unless a user has provided
some ratingsI Solutions:
F Recommend the most popular itemsF Explicity ask the user to rate some items prior to making
recommendations2 The sparsity problem
I The ratings matrix is sparse
F Empty elements: More than 90%
I Solution: Dimensionality Reduction techniques
F Singular Value Decomposition (SVD) yields good results
I Pros: The resultant matrix is substantially smaller & densierI Cons: The dataset becomes very "noisy"
F Most elements assume values that are marginally larger than zero
I Conclusion: We are in need of techniques that can "learn" noisydatasets!
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 6 / 16
Challanges in Collaborative Recommender SystemDesign
1 The cold-start problemI Recommendations cannot be made unless a user has provided
some ratingsI Solutions:
F Recommend the most popular itemsF Explicity ask the user to rate some items prior to making
recommendations2 The sparsity problem
I The ratings matrix is sparseF Empty elements: More than 90%
I Solution: Dimensionality Reduction techniquesF Singular Value Decomposition (SVD) yields good results
I Pros: The resultant matrix is substantially smaller & densierI Cons: The dataset becomes very "noisy"
F Most elements assume values that are marginally larger than zeroI Conclusion: We are in need of techniques that can "learn" noisy
datasets!
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 6 / 16
"Noisy" Datasets
The added noise in the dataset hinders the discovery of patternsin data
I Data clusters become difficult to separate
Machine Learning techniques for highly non-separable datasets
I Support Vector Machines, Radial Basis Functions
F Computing the support vector (or estimating the surface . . . ) can be acomputationally intensive task
I Evolutionary Algorithms
F Meaningful Recommendations are not always guaranteed(evolutionary dead-ends)
I Our approach: Use k -separability!
F Originally proposed by W. Duch1
F Special case of the more general method of Projection PursuitF Application to Feed-Forward ANNsF Extends linear separability of data clusters into k > 2 segments on
the discriminating hyperplane
1W. Duch, K-separability. Lecture Notes in Computer Science 4131 (2006) 188-197
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 7 / 16
"Noisy" Datasets
The added noise in the dataset hinders the discovery of patternsin data
I Data clusters become difficult to separateMachine Learning techniques for highly non-separable datasets
I Support Vector Machines, Radial Basis Functions
F Computing the support vector (or estimating the surface . . . ) can be acomputationally intensive task
I Evolutionary Algorithms
F Meaningful Recommendations are not always guaranteed(evolutionary dead-ends)
I Our approach: Use k -separability!
F Originally proposed by W. Duch1
F Special case of the more general method of Projection PursuitF Application to Feed-Forward ANNsF Extends linear separability of data clusters into k > 2 segments on
the discriminating hyperplane
1W. Duch, K-separability. Lecture Notes in Computer Science 4131 (2006) 188-197
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 7 / 16
"Noisy" Datasets
The added noise in the dataset hinders the discovery of patternsin data
I Data clusters become difficult to separateMachine Learning techniques for highly non-separable datasets
I Support Vector Machines, Radial Basis FunctionsF Computing the support vector (or estimating the surface . . . ) can be a
computationally intensive taskI Evolutionary Algorithms
F Meaningful Recommendations are not always guaranteed(evolutionary dead-ends)
I Our approach: Use k -separability!
F Originally proposed by W. Duch1
F Special case of the more general method of Projection PursuitF Application to Feed-Forward ANNsF Extends linear separability of data clusters into k > 2 segments on
the discriminating hyperplane
1W. Duch, K-separability. Lecture Notes in Computer Science 4131 (2006) 188-197
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 7 / 16
"Noisy" Datasets
The added noise in the dataset hinders the discovery of patternsin data
I Data clusters become difficult to separateMachine Learning techniques for highly non-separable datasets
I Support Vector Machines, Radial Basis FunctionsF Computing the support vector (or estimating the surface . . . ) can be a
computationally intensive taskI Evolutionary Algorithms
F Meaningful Recommendations are not always guaranteed(evolutionary dead-ends)
I Our approach: Use k -separability!F Originally proposed by W. Duch1
F Special case of the more general method of Projection PursuitF Application to Feed-Forward ANNsF Extends linear separability of data clusters into k > 2 segments on
the discriminating hyperplane
1W. Duch, K-separability. Lecture Notes in Computer Science 4131 (2006) 188-197
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 7 / 16
Extending linear separability to 3-separabilityThe 2-bit XOR problem
A highly non-separable datasetIt can be learned by a 2-layered perceptron, or ......by a single layer percpetron that implements k -separability!
The activation function must partition the input space into 3distinct areas
I Soft-Windowed Activation Functions
−0.2 0 0.2 0.4 0.6 0.8 1 1.2−0.2
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(a) Input Space Partitioning
−2 −1 0 1 2 3 40
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Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 8 / 16
Extending linear separability to 3-separabilityThe 2-bit XOR problem
A highly non-separable datasetIt can be learned by a 2-layered perceptron, or ......by a single layer percpetron that implements k -separability!The activation function must partition the input space into 3distinct areas
I Soft-Windowed Activation Functions
−0.2 0 0.2 0.4 0.6 0.8 1 1.2−0.2
0
0.2
0.4
0.6
0.8
1
1.2
(a) Input Space Partitioning
−2 −1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
(b) Soft-Windowed ActivationFunction
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 8 / 16
Extending linear separability to 3-separabilityThe 2-bit XOR problem
A highly non-separable datasetIt can be learned by a 2-layered perceptron, or ......by a single layer percpetron that implements k -separability!The activation function must partition the input space into 3distinct areas
I Soft-Windowed Activation Functions
−0.2 0 0.2 0.4 0.6 0.8 1 1.2−0.2
0
0.2
0.4
0.6
0.8
1
1.2
(a) Input Space Partitioning
−2 −1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
(b) Soft-Windowed ActivationFunction
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 8 / 16
Generalizing to k -separability
Complex DatasetsI Combine the output of two neurons (or more . . . )
I e.g. A 5-separable dataset can be learned by the combined outputof 2 neurons
Generalization by Induction
I m-neuron output ⇒ 2m + 1 regions on the discriminating line⇒ k = 2m + 1-separable dataset
Use in a Recommendation Engine
I Create a 2-layered perceptron
F n-sized input vector, m-sized hidden layer, single output layerF Overall, an n → m → 1 projection
I Build a model (NN) for each user
F Input: The ratings of the n "neighbors" of the target user on an itemhe hasn’t evaluated
F Output: A "score" for the unseen item
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 9 / 16
Generalizing to k -separability
Complex DatasetsI Combine the output of two neurons (or more . . . )
I e.g. A 5-separable dataset can be learned by the combined outputof 2 neurons
Generalization by InductionI m-neuron output ⇒ 2m + 1 regions on the discriminating line
⇒ k = 2m + 1-separable dataset
Use in a Recommendation Engine
I Create a 2-layered perceptronF n-sized input vector, m-sized hidden layer, single output layerF Overall, an n → m → 1 projection
I Build a model (NN) for each user
F Input: The ratings of the n "neighbors" of the target user on an itemhe hasn’t evaluated
F Output: A "score" for the unseen item
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 9 / 16
Generalizing to k -separability
Complex DatasetsI Combine the output of two neurons (or more . . . )
I e.g. A 5-separable dataset can be learned by the combined outputof 2 neurons
Generalization by InductionI m-neuron output ⇒ 2m + 1 regions on the discriminating line
⇒ k = 2m + 1-separable datasetUse in a Recommendation Engine
I Create a 2-layered perceptronF n-sized input vector, m-sized hidden layer, single output layerF Overall, an n → m → 1 projection
I Build a model (NN) for each userF Input: The ratings of the n "neighbors" of the target user on an item
he hasn’t evaluatedF Output: A "score" for the unseen item
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 9 / 16
Implementation Details
The index of separability (k ) is not known a-prioriI Setting k to a fixed value is of little helpI It can lead to either overspecialization or to large training errors
Therefore, k is a problem parameter: it has to be estimatedDynamic Network ArchitectureSparse user ratings’ matrix ⇒ small overall network size ⇒Constructive Network AlgorithmOur constructive network algorithm was derived from the NewConstructive Algorithm2
2Islam MM et al. A new constructive algorithm for architectural and functional adaptation of artificial neural
networks.
IEEE Trans Syst Man Cybern B Cybern. 2009 Dec;39(6):1590-605
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 10 / 16
Implementation Details
The index of separability (k ) is not known a-prioriI Setting k to a fixed value is of little helpI It can lead to either overspecialization or to large training errors
Therefore, k is a problem parameter: it has to be estimated
Dynamic Network ArchitectureSparse user ratings’ matrix ⇒ small overall network size ⇒Constructive Network AlgorithmOur constructive network algorithm was derived from the NewConstructive Algorithm2
2Islam MM et al. A new constructive algorithm for architectural and functional adaptation of artificial neural
networks.
IEEE Trans Syst Man Cybern B Cybern. 2009 Dec;39(6):1590-605
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 10 / 16
Implementation Details
The index of separability (k ) is not known a-prioriI Setting k to a fixed value is of little helpI It can lead to either overspecialization or to large training errors
Therefore, k is a problem parameter: it has to be estimatedDynamic Network Architecture
Sparse user ratings’ matrix ⇒ small overall network size ⇒Constructive Network AlgorithmOur constructive network algorithm was derived from the NewConstructive Algorithm2
2Islam MM et al. A new constructive algorithm for architectural and functional adaptation of artificial neural
networks.
IEEE Trans Syst Man Cybern B Cybern. 2009 Dec;39(6):1590-605
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 10 / 16
Implementation Details
The index of separability (k ) is not known a-prioriI Setting k to a fixed value is of little helpI It can lead to either overspecialization or to large training errors
Therefore, k is a problem parameter: it has to be estimatedDynamic Network ArchitectureSparse user ratings’ matrix ⇒ small overall network size ⇒Constructive Network Algorithm
Our constructive network algorithm was derived from the NewConstructive Algorithm2
2Islam MM et al. A new constructive algorithm for architectural and functional adaptation of artificial neural
networks.
IEEE Trans Syst Man Cybern B Cybern. 2009 Dec;39(6):1590-605
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 10 / 16
Implementation Details
The index of separability (k ) is not known a-prioriI Setting k to a fixed value is of little helpI It can lead to either overspecialization or to large training errors
Therefore, k is a problem parameter: it has to be estimatedDynamic Network ArchitectureSparse user ratings’ matrix ⇒ small overall network size ⇒Constructive Network AlgorithmOur constructive network algorithm was derived from the NewConstructive Algorithm2
2Islam MM et al. A new constructive algorithm for architectural and functional adaptation of artificial neural
networks.
IEEE Trans Syst Man Cybern B Cybern. 2009 Dec;39(6):1590-605
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 10 / 16
Constructive Network Algorithm
1 Create a minimal architecture2 Train the network in two phases on the whole Training Set3 Iteratively add neurons in the hidden layer
I Create new Training Sets based on the Classification Error(Boosting Algorithm)
I Only the newly added neuron’s weights are adapted; all otherremain "frozen"
4 Stop network construction when the Classification Error stabilizes
Boosting AlgorithmInspired from AdaBoost and used in Network Training as a way ofavoiding local minimaFunctionality
I Unlearned samples ⇒ New neurons in the hidden layer ⇒ Newclusters discovered
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 11 / 16
Constructive Network Algorithm
1 Create a minimal architecture2 Train the network in two phases on the whole Training Set3 Iteratively add neurons in the hidden layer
I Create new Training Sets based on the Classification Error(Boosting Algorithm)
I Only the newly added neuron’s weights are adapted; all otherremain "frozen"
4 Stop network construction when the Classification Error stabilizes
Boosting AlgorithmInspired from AdaBoost and used in Network Training as a way ofavoiding local minimaFunctionality
I Unlearned samples ⇒ New neurons in the hidden layer ⇒ Newclusters discovered
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 11 / 16
Our Collaborative Recommender System
Input: The user ratings’ matrix and the target user
Output: A model (NN) for the target userSteps
1 Pick from the user ratings’ matrix all the co-raters of the target user2 Compute the SVD of the co-raters matrix, retaining only the
non-zero Singular Values3 Partition the resultant matrix in 3 different sets; the Training Set, the
Validation Set and the Test Set4 Train a Constructive ANN Architecture (as discussed previously...)
5 Compute the Performance Metrics on the Test Set
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 12 / 16
Our Collaborative Recommender System
Input: The user ratings’ matrix and the target userOutput: A model (NN) for the target user
Steps
1 Pick from the user ratings’ matrix all the co-raters of the target user2 Compute the SVD of the co-raters matrix, retaining only the
non-zero Singular Values3 Partition the resultant matrix in 3 different sets; the Training Set, the
Validation Set and the Test Set4 Train a Constructive ANN Architecture (as discussed previously...)
5 Compute the Performance Metrics on the Test Set
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 12 / 16
Our Collaborative Recommender System
Input: The user ratings’ matrix and the target userOutput: A model (NN) for the target userSteps
1 Pick from the user ratings’ matrix all the co-raters of the target user2 Compute the SVD of the co-raters matrix, retaining only the
non-zero Singular Values3 Partition the resultant matrix in 3 different sets; the Training Set, the
Validation Set and the Test Set4 Train a Constructive ANN Architecture (as discussed previously...)
5 Compute the Performance Metrics on the Test Set
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 12 / 16
ExperimentThe MovieLens Database
Contains the ratings of 943 users on1682 moviesSparse matrix (6.3% of non-zeroelements)Each user has rated at least 20movies (106 on average), but. . .Discrete Exponential Distribution
I 60% of all users have rated 100movies or less
I 40% of all users have rated 50movies or less
We followed a purely CollaborativeStrategy
I Taking into account only the userratings’ and not any otherdemographic information
0 100 200 300 400 500 600 700 8000
20
40
60
80
100
120
140
(a) Rated items per user
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 13 / 16
ExperimentTest Sets & Metrics
Many users rate only a few movies. How would our systemperform?
I Group A: The few raters user group.
F Contains all users who have rated 20-50 movies
How would our system perform on the average case?
I Group B: The moderate raters user group.
F Contains all users who have rated 51-100 moviesF May be used in comparisons to other implementations
We randomly picked 20 users from each group (40 users in total).The results were averaged for each groupMetrics
1 Precision2 Recall3 F-measure
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 14 / 16
ExperimentTest Sets & Metrics
Many users rate only a few movies. How would our systemperform?
I Group A: The few raters user group.F Contains all users who have rated 20-50 movies
How would our system perform on the average case?
I Group B: The moderate raters user group.
F Contains all users who have rated 51-100 moviesF May be used in comparisons to other implementations
We randomly picked 20 users from each group (40 users in total).The results were averaged for each groupMetrics
1 Precision2 Recall3 F-measure
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 14 / 16
ExperimentTest Sets & Metrics
Many users rate only a few movies. How would our systemperform?
I Group A: The few raters user group.F Contains all users who have rated 20-50 movies
How would our system perform on the average case?I Group B: The moderate raters user group.
F Contains all users who have rated 51-100 moviesF May be used in comparisons to other implementations
We randomly picked 20 users from each group (40 users in total).The results were averaged for each groupMetrics
1 Precision2 Recall3 F-measure
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 14 / 16
ExperimentTest Sets & Metrics
Many users rate only a few movies. How would our systemperform?
I Group A: The few raters user group.F Contains all users who have rated 20-50 movies
How would our system perform on the average case?I Group B: The moderate raters user group.
F Contains all users who have rated 51-100 moviesF May be used in comparisons to other implementations
We randomly picked 20 users from each group (40 users in total).The results were averaged for each group
Metrics
1 Precision2 Recall3 F-measure
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 14 / 16
ExperimentTest Sets & Metrics
Many users rate only a few movies. How would our systemperform?
I Group A: The few raters user group.F Contains all users who have rated 20-50 movies
How would our system perform on the average case?I Group B: The moderate raters user group.
F Contains all users who have rated 51-100 moviesF May be used in comparisons to other implementations
We randomly picked 20 users from each group (40 users in total).The results were averaged for each groupMetrics
1 Precision2 Recall3 F-measure
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 14 / 16
Results
Table: Performance Results
Methodology Precision Recall F-measureOurSystem: User Group B (moderate ratings) 75.38% 82.21% 79.37%OurSystem: User Group A (few ratings) 74.07% 88.86% 78.97%MovieMagician Clique-based 74% 73% 74%Movielens 66% 74% 70%SVD/ANN 67.9% 69.7% 68.8%MovieMagician Feature-based 61% 75% 67%MovieMagician Hybrid 73% 56% 63%Correlation 64.4% 46.8% 54.2%
Observations
I Our system achieves good results in both usergroups andoutperforms the other approaches
I Recall is higher in the few raters group because they seem to rateonly the movies they like
F Therefore, the recommender cannot generalize
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 15 / 16
Results
Table: Performance Results
Methodology Precision Recall F-measureOurSystem: User Group B (moderate ratings) 75.38% 82.21% 79.37%OurSystem: User Group A (few ratings) 74.07% 88.86% 78.97%MovieMagician Clique-based 74% 73% 74%Movielens 66% 74% 70%SVD/ANN 67.9% 69.7% 68.8%MovieMagician Feature-based 61% 75% 67%MovieMagician Hybrid 73% 56% 63%Correlation 64.4% 46.8% 54.2%
Observations
I Our system achieves good results in both usergroups andoutperforms the other approaches
I Recall is higher in the few raters group because they seem to rateonly the movies they like
F Therefore, the recommender cannot generalize
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 15 / 16
Conclusions
We have presented a complete Collaborative RecommenderSystem that is specifically fit for those cases where information islimitedOur system achieves a good trade-off between Precision andRecall, a basic requirement for RecommendersThis is due to the fact that k -separability is able to uncovercomplex statistical dependencies (positive and negative)We don’t need to filter the neighborhood of the target user as othersystems do (e.g. by using the Pearson Correlation Formula).
I All "neighbors" are consideredI Extremely useful in cases of sparse datasets
Alexandridis, Siolas, Stafylopatis (NTUA) k -separability Collaborative Recommender ICANN’10 16 / 16