Relevance Feedback for the Earth Mover‘s Distance

Relevance Feedback for theEarth Mover‘s Distance Marc Wichterich, Christian Beecks, Martin Sundermeyer, Thomas Seidl Data Management and Data Exploration GroupRWTH Aachen University, Germany

Introduction • Distance-based Adaptable Similarity Search • Similarity of objects defined by distance function • Small distance → similar, large distance → dissimilar • Query by example: user-given object, find similar ones • Query and distance only approximate descriptions of user’s desired result • If delivered result does not meet expectations: • Bad query? Bad distance? Bad database? • How to do it better? • Relevance Feedback attempts to adapt query/similarity model based on simple user input (result relevancy)

Relevance Feedback Earth Mover’s Distance • EMD • RF query, feedback feedback system similarity model user Photo: Flickr / Caro Wallis results DB • RF for EMD

Overview • Introduction • Adaptive Similarity Model • Feature Signatures • The Earth Mover’s Distance • Relevance Feedback for the Earth Mover’s Distance • Experimental Evaluation • Conclusion

Similarity Model – Feature Signatures y color x

Similarity Model – Earth Mover’s Distance • Introduced in Computer Vision by Rubner et al. • Used in many differing application domains • Idea: transform features of Q into features of P • EMD: minimum of transformation cost P y y Q x x

Feature Transformation

EMD – Formal Definition • Modeled as linear optimization (transportation problem)

Overview • Introduction • Adaptive Similarity Model • Relevance Feedback for the Earth Mover’s Distance • The Feedback Loop • Query Adaptation • Heuristic EMD Adaptation • Optimization-based EMD Adaptation • Experimental Evaluation • Conclusion

The Feedback Loop start query, feedback get query feedback system retrieve results adapt distance similarity model ? user display results adapt query results DB no satisfied? get feedback yes exit

Query Adaptation start • Input: signatures from relevant objects • Output: new query signature • Idea: cluster signature elements • Refinements by Rubner: • Only keep clusters with elements from majority of signatures • Reweight resulting signatureaccordingly • Combine with fixed gd L2 and call it „Query-by-Refinement“ • „Query-by-Refinement“ is baseline for our evaluation • We adapt EMD via ground distance getquery retrieveresults distance displayresults query satisfied? feedback exit

Heuristic EMD Adaptation 1 start • Approach: pick gd based on feedback • gd should reflect user preferences: • Don’t care if blue cluster at upper half of image is moved left/right • Do care if it is moved vertically • Use variance information in relevant feedback • Low variance → assume user cares • High variance → assume user does not care • Measure variance in feedback locally around query signature elements ci(Q). • Define gd: c(Q) x FS → R ( ) getquery retrieveresults distance displayresults query satisfied? feedback exit

Heuristic EMD Adaptation 2 start • Not 1 but m distance functions: • gdi(ci(Q),y) = ((ci(Q)- y) Vi (ci(Q)- y)T)½ • Weighted Euclidean Distances (weights on diagonal of Vi) • Vi : inverted variance for ci(Q) per feature space dimension getquery retrieveresults distance displayresults query satisfied? feedback exit

Optimization-Based EMD Adaptation 1 start • Aim: Pick best possible gd. • Failback: Find a good one. • Q: When is gd good? A: If ranking it produces is good. • New Q: When is a ranking of DB good? • Given ground truth, a number of measures exist • We used “average precision at relevant positions” • We have ground truth for part of the DB: feedback • Idea: test candidates for gd on feedback getquery retrieveresults distance displayresults query satisfied? feedback exit

Optimization-Based EMD Adaptation 2 start • Optimization: • Optimization variable: gd • Objective function: avgPrec(EMDgd, q, Feedback) • Constraints: m weighted Euclidean distances • Analytic optimization with closed form for weights infeasible (ranking/sorting, EMDs in objective function) • Probabilistic optimization via Simulated Annealing • Start with some initial solution • Move in solution space • Compute objective function • Adopt solution with certain probability • Iterate & turn more greedy getquery retrieveresults distance displayresults query satisfied? feedback exit

Optimization-Based EMD Adaptation 3 start • Optimization for EMD based on Feedback: • Solution: weights for m weighted Euclidean distances • Initial solution: given by heuristic • Moving: redistribute weights per Euclidean distance • Objective function: avgPrec(EMDgd, q, Feedback) • Results for EMDgd on DB? getquery retrieveresults distance displayresults query satisfied? feedback exit

Overview • Introduction • Adaptive Similarity Model • Relevance Feedback for the Earth Mover’s Distance • Experimental Evaluation • Conclusion

Experimental Evaluation: Databases 72,000 images in ALOI DB ~60,000 images in COREL DB

Experimental Evaluation: ALOI Query-by-Refinement Heuristic Adaptation Optimization-based

Experimental Evaluation: COREL Query-by-Refinement Heuristic Adaptation Optimization-based

Experimental Evaluation • After 5 iterations of looking for doors in COREL: (a) Query-by-Refinement (b) Heuristic (c) Optimization-Based pos 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Conclusion • Exploited adaptability of the EMD in RF framework • Goal: Improve similarity search results • Techniques: • Baseline: fixed ground distance • Statistics-based heuristic adaptation • Optimization-based adaptation • Evaluation: • Experiments on two image datasets • More relevant objects in fewer iterations • Techniques extensible to other adaptable distance functions

Relevance Feedback for the Earth Mover‘s Distance