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Ultra accurate personalized recommendation via eliminating redundant correlations

Tao Zhou, Riqi Su, Runran Liu, Luoluo Jiang, Bing-Hong Wang, Yi-Cheng Zhang

arXiv:0805.4127v2physics.soc-phphysics.data-an

TL;DR

Information overload makes relevant items hard to find, and recommendations can count correlations from the same attribute repeatedly. The paper uses higher-order correlations to modify NBI; on MovieLens and Netflix, it reports lower ranking scores and improvements across accuracy, diversity, and popularity measures.

  • Problem

    NBI may repeatedly count correlations arising from the same attribute, which the paper says depresses its accuracy.

    Source: §3 · p. 8

  • Method

    The paper modifies NBI by considering higher-order correlations, including W^2, to reduce redundant correlations in a weighted projection of the user-object network.

    Source: §2 · p. 4, §5 · p. 19

  • Results

    Ranking score falls by 23% for MovieLens and 22% for Netflix versus standard NBI; the improved method also outperforms standard NBI and Heter-NBI on all five reported criteria.

    Source: §4 · p. 17, §5 · p. 19

  • Takeaways & Limitations

    The results support considering accuracy, diversity, and popularity together: the reported method improves across all five criteria compared with standard NBI and Heter-NBI.

    Source: §4 · p. 17, §5 · p. 19

    For huge systems, finding optimal parameters may take a very long time, and algorithms using three or higher orders of the weighted matrix may not be applicable in real systems.

    Source: §3 · p. 13

Abstract

from arXiv · show

In this paper, based on a weighted projection of bipartite user-object network, we introduce a personalized recommendation algorithm, called the \emph{network-based inference} (NBI), which has higher accuracy than the classical algorithm, namely \emph{collaborative filtering}. In the NBI, the correlation resulting from a specific attribute may be repeatedly counted in the cumulative recommendations from different objects. By considering the higher order correlations, we design an improved algorithm that can, to some extent, eliminate the redundant correlations. We test our algorithm on two benchmark data sets, \emph{MovieLens} and \emph{Netflix}. Compared with the NBI, the algorithmic accuracy, measured by the ranking score, can be further improved by 23% for \emph{MovieLens} and 22% for \emph{Netflix}, respectively. The present algorithm can even outperform the \emph{Latent Dirichlet Allocation} algorithm, which requires much longer computational time. Furthermore, most of the previous studies considered the algorithmic accuracy only, in this paper, we argue that the diversity and popularity, as two significant criteria of algorithmic performance, should also be taken into account. With more or less the same accuracy, an algorithm giving higher diversity and lower popularity is more favorable. Numerical results show that the present algorithm can outperform the standard one simultaneously in all five adopted metrics: lower ranking score and higher precision for accuracy, larger Hamming distance and lower intra-similarity for diversity, as well as smaller average degree for popularity.

1. Introduction

Information overload makes it difficult to find relevant items, while tag-based search does not personalize results and misses tastes that cannot be expressed as tags. The paper introduces NBI and an improved approach intended to reduce redundant correlations and improve recommendation accuracy, diversity, and popularity.

1. Introduction

  • Tag-based search returns the same results for users with different habits and cannot capture tastes that are difficult to express through tags or language.Source: §1 · p. 2
  • Personalized recommendations use users’ activity histories to identify habits and address information overload that makes relevant items difficult to find.The passage gives purchase, reading, and viewing histories as examples of information used for recommendations.Source: §1 · p. 2
  • Recommendation research includes collaborative filtering, content-based analysis, spectral analysis, iterative refinement, and principal component analysis.Source: §1 · p. 2
  • The paper presents NBI and an improved algorithm that uses higher-order correlations to reduce redundant correlations, reporting greater accuracy and more diverse, less popular recommendations.The introduction describes NBI as more accurate than collaborative filtering.Source: §1 · p. 2

2. Network-Based Inference for Personal Recommendation

NBI represents a user–object system as a bipartite network, projects it onto an object network through resource allocation, and recommends uncollected objects with the highest final resource. It is evaluated on MovieLens and Netflix against global ranking and collaborative-filtering methods.

2. Network-Based Inference for Personal Recommendation

  • A recommendation system is represented as a bipartite user–object network, with an object-object network connecting objects collected together by at least one user.The weight from object oj to oi represents the proportion of oj’s resource distributed to oi.Source: §2 · p. 3
  • Resource allocation transfers each object’s resource equally to its collecting users and then back equally to the objects they collected, yielding a weighted object projection independent of initial resources.Source: §2 · p. 4
  • For a target user, NBI assigns unit initial resource to collected objects and recommends uncollected objects ranked by their final resource.The method is called network-based inference because it uses the weighted object-object network.Source: §2 · p. 4
  • MovieLens and Netflix are evaluated using a random 90% training split and 10% probe, retaining ratings of at least 3 as collected links.Source: §2 · p. 5
  • Ranking score averages the probe items’ positions in recommendation lists, while precision measures the share of top-L recommendations that are probe items.Lower ranking score indicates higher accuracy; precision is averaged across users.Source: §2 · pp. 6–7
  • NBI performs better than global ranking and collaborative filtering for recommendation accuracy; it substantially outperforms user-based collaborative filtering and is better than object-based collaborative filtering on ranking score, with competitive precision.Source: §2 · p. 7

3. Improved Algorithm by Eliminating Redundant Correlations

The section proposes subtracting higher-order correlations to reduce redundant attribute-based recommendations in NBI. On MovieLens and Netflix, the modified algorithm improves ranking score over standard NBI, with precision also improving at negative parameter values.

3. Improved Algorithm by Eliminating Redundant Correlations

  • Repeated correlations from the same attribute can double-count support for an object and depress NBI accuracy, motivating higher-order correlations as a redundancy signal.In the illustration, D-F and E-F are redundant because both arise from the shared attribute color=black.Source: §3 · pp. 7–8, Figure 2 · p. 8
  • Subtracting higher-order correlations is proposed to reduce redundancy; the free parameter a makes a = 0 equivalent to standard NBI.The authors test whether a negative a improves accuracy over a = 0.Source: §3 · pp. 8, 10
  • At a ≈ −0.75, ranking score falls 23% on MovieLens and 22% on Netflix versus standard NBI; MovieLens also scores 0.082 versus LDA’s 0.088.LDA requires much more computational time.Source: Figure 3 · p. 9, §3 · p. 10
  • Precision improves over standard NBI at negative a values on both datasets, although its optimum differs from the value that minimizes ranking score.Figures 4 and 5 show precision versus a for typical recommendation-list lengths on MovieLens and Netflix.Source: Figure 4 · p. 10, §3 · p. 11, Figure 5 · p. 11
  • For MovieLens, including W^3 gives a minimum ranking score of about 0.0794 at (a, b) = (−1.6, 0.8), an improvement of about 3%.Figure 6 shows the ranking score across the (a, b) plane.Source: §3 · p. 12, Figure 6 · p. 12
  • Higher-order extensions increase computational complexity, and their optimal parameters may vary by system; for MovieLens, greedy tuning at a = −0.75 selects b = 0, yielding no improvement.Finding suitable parameters may take a long time for huge systems.Source: §3 · pp. 12–13

4. Popularity and Diversity of Recommendations

The section evaluates recommendations beyond accuracy, using inter-user and within-list diversity alongside popularity. At a = −0.75, the improved algorithm outperforms standard NBI and Heter-NBI across all five reported criteria.

4. Popularity and Diversity of Recommendations

  • The authors argue that accuracy alone is insufficient: popularity can fall without inter-user diversity, so they use all three diversity and popularity measures for a broader evaluation.Recommending every user the same lowest-degree objects could minimize average degree while leaving Hamming distance near zero.Source: §4 · pp. 13, 17
  • Hamming distance measures diversity between users' recommendation lists, while intra-similarity measures diversity within each user's list.The section also treats average degree across recommended objects as a measure of popularity.Source: §4 · p. 15
  • Smaller a increases Hamming distance while reducing intra-similarity and average degree, giving more inter-diverse recommendations with less popular objects.The reported trends hold for MovieLens and Netflix and for the tested recommendation-list lengths.Source: Figure 8 · p. 14, Figure 9 · p. 16, §4 · p. 17
  • At a = −0.75, the algorithm beats standard NBI and Heter-NBI on all five criteria: ranking score, precision, Hamming distance, intra-similarity, and average degree.It has lower ranking score, higher precision, larger Hamming distance, lower intra-similarity, and smaller average degree.Source: §4 · p. 17

5. Conclusion and Discussion

The paper attributes repeated counting of attribute-based correlations in NBI to reduced accuracy, and uses second-order correlations to reduce that redundancy. The resulting algorithm improves ranking score on MovieLens and Netflix, with higher-order extensions constrained by computational cost.

5. Conclusion and Discussion

  • Figure 10 plots average degree against a for MovieLens and Netflix, with a vertical line marking aopt = −0.75.The plotted results are averaged over five runs.Source: Figure 10 · p. 18
  • At a = −0.75, ranking score improves by 23% on MovieLens and 22% on Netflix versus standard NBI; the paper recommends considering W and W^2 only because higher orders take too long for real systems.The authors report that higher-order improvements beyond these are not substantial.Source: §5 · p. 19
  • Second-order correlations are used to reduce redundant counting of attribute-based correlations in NBI, which the authors say depresses accuracy.The improved algorithm can, to some extent, eliminate that redundancy.Source: §5 · p. 19
  • On Netflix ratings, considering second-order correlations in the transfer matrix also improves prediction accuracy, though the method is more complicated than for binary systems.The paper points to Ref. for details.Source: §5 · p. 19
  • The authors argue that diversity and popularity should accompany accuracy in evaluation, and report that their method outperforms standard NBI and user- and object-based collaborative filtering on all five criteria.The criteria are ranking score, precision, Hamming distance, intra-similarity, and average degree.Source: §5 · p. 19
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