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Relevance Feedback for the Earth Mover‘s Distance / 21 I9 CHAIR OF COMPUTER SCIENCE 9 DATA MANAGEMENT AND EXPLORATION Relevance Feedback for the Earth Mover‘s Distance Marc Wichterich, Christian Beecks, Martin Sundermeyer, Thomas Seidl Data Management and Data Exploration Group RWTH Aachen University, Germany

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Relevance Feedback for the Earth Mover‘s Distance / 21 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) 1

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Relevance Feedback for the Earth Mover‘s Distance / 21 2 Relevance Feedback user DB query, feedback results feedback system similarity model Photo: Flickr / Caro WallisCaro Wallis Earth Mover’s Distance RF for EMD RF EMD

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Relevance Feedback for the Earth Mover‘s Distance / 21 Overview Introduction Adaptive Similarity Model Feature Signatures The Earth Mover’s Distance Relevance Feedback for the Earth Mover’s Distance Experimental Evaluation Conclusion 3

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Relevance Feedback for the Earth Mover‘s Distance / 21 Similarity Model – Feature Signatures 4 x y color

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Relevance Feedback for the Earth Mover‘s Distance / 21 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 5 Q P x y x y

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Relevance Feedback for the Earth Mover‘s Distance / 21 Feature Transformation 6

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Relevance Feedback for the Earth Mover‘s Distance / 21 EMD – Formal Definition Modeled as linear optimization (transportation problem) 7

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Relevance Feedback for the Earth Mover‘s Distance / 21 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 8

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Relevance Feedback for the Earth Mover‘s Distance / 21 The Feedback Loop 9 user DB query, feedback results feedback system similarity model yes exit start get query adapt distance no get feedback adapt query retrieve results display results satisfied?

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Relevance Feedback for the Earth Mover‘s Distance / 21 Query Adaptation 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 signature accordingly 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 10 satisfie d? retrieve results exit start get query query distance feedback display results

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Relevance Feedback for the Earth Mover‘s Distance / 21 Heuristic EMD Adaptation 1 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 c i (Q). Define gd: c (Q) x FS → R ( ) 11 satisfie d? retrieve results exit start get query query distance feedback display results

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Relevance Feedback for the Earth Mover‘s Distance / 21 Heuristic EMD Adaptation 2 Not 1 but m distance functions: gd i (c i (Q),y) = ((c i (Q) - y) V i (c i (Q) - y) T ) ½ Weighted Euclidean Distances (weights on diagonal of V i ) V i : inverted variance for c i (Q) per feature space dimension 12 satisfie d? retrieve results exit start get query query distance feedback display results

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Relevance Feedback for the Earth Mover‘s Distance / 21 Optimization-Based EMD Adaptation 1 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 13 satisfie d? retrieve results exit start get query query distance feedback display results RankingAvg. Precision

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Relevance Feedback for the Earth Mover‘s Distance / 21 Optimization-Based EMD Adaptation 2 Optimization: Optimization variable: gd Objective function: avgPrec(EMD gd, 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 14 satisfie d? retrieve results exit start get query query distance feedback display results

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Relevance Feedback for the Earth Mover‘s Distance / 21 Optimization-Based EMD Adaptation 3 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(EMD gd, q, Feedback) Results for EMD gd on DB? 15 satisfie d? retrieve results exit start get query query distance feedback display results

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Relevance Feedback for the Earth Mover‘s Distance / 21 Overview Introduction Adaptive Similarity Model Relevance Feedback for the Earth Mover’s Distance Experimental Evaluation Conclusion 16

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Relevance Feedback for the Earth Mover‘s Distance / 21 Experimental Evaluation: Databases 17 72,000 images in ALOI DB~60,000 images in COREL DB

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Relevance Feedback for the Earth Mover‘s Distance / 21 Experimental Evaluation: ALOI 18 Heuristic Adaptation Optimization-based Query-by-Refinement

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Relevance Feedback for the Earth Mover‘s Distance / 21 Experimental Evaluation: COREL 19 Heuristic Adaptation Optimization-based Query-by-Refinement

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Relevance Feedback for the Earth Mover‘s Distance / 21 Experimental Evaluation 20 After 5 iterations of looking for doors in COREL: (a) Query-by-Refinement (b) Heuristic (c) Optimization-Based pos

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Relevance Feedback for the Earth Mover‘s Distance / 21 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 21

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