Efficient Similarity Search in Scientific Databases with Feature Signatures

Transcription

1 DATA MANAGEMENT AND DATA EXPLORATION GROUP Prof. Dr. rer. nat. Thomas Seidl DATA MANAGEMENT AND DATA EXPLORATION GROUP Prof. Dr. rer. nat. Thomas Seidl Efficient Similarity Search in Scientific Databases with Feature Signatures Merih Seran Uysal Christian Beecks Jochen Schmücking Thomas Seidl RWTH Aachen University, Germany 27th International Conference on Scientific and Statistical Database Management July 1, 2015 San Diego, California

2 Similarity Search How to determine the similarity between two data objects in scientific databases? similar? Requirements Feature representation Similarity measure Efficient query processing Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 2 / 18

3 Similarity Search How to determine the similarity between two data objects in scientific databases? similar? Requirements Feature representation use feature signatures Similarity measure use Earth Mover s Distance Efficient query processing new lower-bounding techniques Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 2 / 18

4 Overview 1 Preliminaries 2 Reduced Signatures Filter Approximations 4 Experimental Evaluation 5 Conclusion and Outlook Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures / 18

5 Feature Representation similar? data object feature signature Feature Signature Represent the data object by features in a feature space F Aggregate features to obtain a compact feature representation Finite number of features with non-zero weights (representatives) Formally; X : F R subject to R X < with R X = {f F X(f ) 0} F Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 4 / 18

6 Intuition: Earth Mover s Distance Earth Mover s Distance (EMD) [1] Emd:,2 tested with java transforms each feature signature to another one denotes a transportation problem (linear optimization problem) chooses the minimum-cost flow among all flows exhibits high computational time complexity [1] Y. Rubner, C. Tomasi, and L. J. Guibas. The earth mover s distance as a metric for image retrieval. Int. Journal of Computer Vision, 40(2):99-121, Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 5 / 18

7 Earth Mover s Distance Given feature signatures X, Y S + over a feature space (F, δ) with a distance function δ : F F R, EMD : S + S + R between X and Y is defined as a minimum-cost flow of all possible flows F = {f f : F F R} = R F F by: subject to constraints: EMD(X, Y ) = min f F Non-negativity: x, y F : f (x, y) 0 Source: x F : f (x, y) X(x) Target: y F : y F f (x, y) Y (y) x F Total flow: m = x F y F 1 δ(x, y) f (x, y) m x F y F f (x, y) = min{ X(x), Y (y)} x F y F Emd:,2 tested with java Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 6 / 18

8 Efficient Query Processing High computational time complexity of the EMD Bottleneck! How to perform query processing with the EMD on signatures efficiently? Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 7 / 18

9 Efficient Query Processing High computational time complexity of the EMD Bottleneck! How to perform query processing with the EMD on signatures efficiently? Approach: Filter: Utilize reduced signatures via some heuristics Lower-bounding filter distance functions on reduced signatures Filter-and-refine architecture Completeness (no false dismissal) lower bound property Selectivity a small candidate set Efficiency database query object filter candidates EMD result database Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 7 / 18

10 Efficient Query Processing High computational time complexity of the EMD Bottleneck! How to perform query processing with the EMD on signatures efficiently? Approach: Filter: Utilize reduced signatures via some heuristics Lower-bounding filter distance functions on reduced signatures Filter-and-refine architecture Completeness (no false dismissal) lower bound property Selectivity a small candidate set Efficiency database query object filter candidates EMD result database query object filter candidates EMD result Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 7 / 18

11 Reduced Signature Definition (Reduced Signature) Let X, X r S 0 be two feature signatures. X r is a reduced feature signature with respect to X if it holds: x F : X(x) X r (x). Dimensionality reduction is a special case of signature reduction (a) (b) (a) EMD flow between Beforetwo dimred: signatures Emd:,2 EMD(X,Y Emd:,71 )=.2 tested tested with java with java (b) Removing a representative and EMD flow EMD(X r,y )=.71 Discarding representatives in a signature leads to a higher EMD value Completeness not preserved! Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 8 / 18

12 λ-im-sig Lower Bound Definition (λ-independent Minimization for Signatures) Let (F, δ) be a feature space with a distance function δ, X, Y S 0 be feature signatures, and λ R +. λ-im-sig : S 0 S 0 R 0 between X and Y is defined as: subject to λ-im-sig(x, Y ) = min f F 1 f (x, y) δ(x, y) λ x F y F non-negativity constraint: x, y F : f (x, y) 0, source constraint: x F : f (x, y) X(x), and λ-im-sig y F target constraint: x, y F : f (x, y) Y (y), and total flow constraint: f (x, y) = min{ X(x), Y (y)} x F y F x F y F Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 9 / 18

13 λ-im-sig Lower Bound Constraint relaxation with respect to the target constraint Greater solution space than that for the EMD Adaptable independent normalization factor λ The optimal factor λ = min{ X(x), Y (y)} (shown in the paper) x F y F Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 10 / 18

14 λ-im-sig Lower Bound λ-im-sig lower-bounds EMD on reduced signatures Given feature signatures X, Y S 0 with total weights m X = X(x) Y (y) = m Y, a reduced feature signature X r S 0 with x F y F respect to X, and λ R + with λ = m X, it holds: λ-im-sig(x r, Y ) EMD(X, Y ). (Proved in the paper) λ-emd can be defined in a similar way As experiments will show later, λ-im-sig lower bound is more efficient than λ-emd Different signature reduction heuristics possible, such as earth-based (ER) or centroid-based (CR) dimensionality reduction heuristics Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 11 / 18

15 Efficiency vs. Dimensionality: λ-im-sig Real world data: ImageNet [1] ,000 data objects ; 100 nn 100,000 data objects ; 100 nn query time [sec] nr. of EMD computations λ IM Sig CR 50% λ IM Sig CR 70% λ IM Sig CR 90% λ IM Sig ER 50% λ IM Sig ER 70% λ IM Sig ER 90% signature size (a) signature size (b) [1] J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei. ImageNet: A Large-Scale Hierarchical Image Database. In CVPR09, p , Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 12 / 18

16 Efficiency vs. Dimensionality (Imagenet) Real world data: ImageNet [1] Imagenet all :: Save two images as pdfs for subfigure OPT1 VALID 100K Existing lower bounds on feature signatures: Rubner [2] and IM-Sig [] query time [sec] Imagenet ; 100,000 data objects ; 100 nn signature size λ EMD ER 90% λ IM Sig CR 90% λ IM Sig CR 90% and IM Sig λ IM Sig and λ EMD Sig CR 90% Rubner and λ EMD ER 90% Rubner and λ IM Sig CR 90% IM Sig Rubner [1] J. Deng et al. ImageNet: A Large-Scale Hierarchical Image Database. In CVPR09, p , [2] Y. Rubner et al. The earth mover s distance as a metric for image retrieval. Int. Journal of Computer Vision, 40(2):99-121, number of EMD computations Imagenet ; 100, λ EMD ER 90% λ IM Sig CR 90% and IM Rubner and λ EMD ER 9 IM Sig [] M.S. Uysal et al. Efficient Filter Approximation Using the EMD in Very Large Multimedia Databases with Feature Signatures. In CIKM, p , Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 1 / 18

17 VALID 100K Preliminaries Reduced Signatures Filter Approximations Experimental Evaluation Conclusion Efficiency vs. Dimensionality (Imagenet) query time [sec] Imagenet ; 100,000 data objects ; 100 nn signature size λ EMD ER 90% λ IM Sig CR 90% λ IM Sig CR 90% and IM Sig λ IM Sig and λ EMD Sig CR 90% Rubner and λ EMD ER 90% Rubner and λ IM Sig CR 90% IM Sig Rubner number of EMD computations Imagenet ; 100, λ EMD ER 90% λ IM Sig CR 90% and IM Rubner and λ EMD ER 9 IM Sig Less query time than for the competitive methods The combination of Rubner and λ-im-sig outperforms other combinations or existing methods regarding efficiency and signature size Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 14 / 18

18 Selectivity vs. Dimensionality (Imagenet) ta objects ; 100 nn ure size λ IM Sig CR 90% λ IM Sig and λ EMD Sig CR 90% Rubner and λ IM Sig CR 90% Rubner number of EMD computations Imagenet ; 100,000 data objects ; 100 nn signature size λ EMD ER 90% λ IM Sig CR 90% λ IM Sig CR 90% and IM Sig λ IM Sig and λ EMD Sig CR 90% Rubner and λ EMD ER 90% Rubner and λ IM Sig CR 90% IM Sig Rubner Smaller candidate set than for the existing methods The combination of Rubner and λ-im-sig shows better selectivity than for existing methods w.r.t signature size Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 15 / 18

19 Ukbench all :: Save two images as pdfs for subfigure OPT1 Efficiency vs. Dimensionality VALID ER and CR are(ukbench) changed Real world data: UKBench [4] query time [sec] Ukbench ; 10,200 data objects ; 100 nn signature size λ EMD ER 90% λ IM Sig CR 90% λ IM Sig CR 90% and IM Sig λ IM Sig and λ EMD ER 90% Rubner and λ EMD ER 90% Rubner and λ IM Sig CR 90% IM Sig Rubner number of EMD computations Ukbench ; 10, λ EMD ER 90% λ IM Sig CR 90% and Rubner and λ EMD ER IM Sig Less query time than for the competitive methods The combination of Rubner and λ-im-sig outperforms other combinations or existing methods regarding efficiency and signature size [4] D. Nister and H. Stewenius. Scalable recognition with a vocabulary tree. In CVPR, pages , Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 16 / 18

20 wo images as pdfs for subfigure OPT1 changed Selectivity vs. Dimensionality (UKBench) objects ; 100 nn Real world data: UKBench [4] e size λ IM Sig CR 90% λ IM Sig and λ EMD ER 90% Rubner and λ IM Sig CR 90% Rubner number of EMD computations Ukbench ; 10,200 data objects ; 100 nn signature size λ EMD ER 90% λ IM Sig CR 90% λ IM Sig CR 90% and IM Sig λ IM Sig and λ EMD ER 90% Rubner and λ EMD ER 90% Rubner and λ IM Sig CR 90% IM Sig Rubner Smaller candidate set than for the existing methods The combination of Rubner and λ-im-sig shows better selectivity than for existing methods w.r.t signature size [4] D. Nister and H. Stewenius. Scalable recognition with a vocabulary tree. In CVPR, pages , Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 17 / 18

21 Conclusion and Outlook Feature signature as feature representation model for scientific data High computational time complexity of the Earth Mover s Distance Novel lower-bounding filter approximations λ-im-sig and λ-emd High efficiency and selectivity providing time cost reduction How to extend this work for other domains? e.g. probabilistic data, uncertain data Further minimization of the candidate set Investigation of the constraint relaxation Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 18 / 18

22 Conclusion and Outlook Feature signature as feature representation model for scientific data High computational time complexity of the Earth Mover s Distance Novel lower-bounding filter approximations λ-im-sig and λ-emd High efficiency and selectivity providing time cost reduction How to extend this work for other domains? e.g. probabilistic data, uncertain data Further minimization of the candidate set Investigation of the constraint relaxation Thank you for your attention! Any questions? Merih Seran Uysal et al. Efficient Similarity Search in Scientific Databases with Feature Signatures 18 / 18