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**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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**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)

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**RF for EMD Relevance Feedback Earth Mover’s Distance RF EMD**

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

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**Overview Introduction Adaptive Similarity Model**

Feature Signatures The Earth Mover’s Distance Relevance Feedback for the Earth Mover’s Distance Experimental Evaluation Conclusion

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**Similarity Model – Feature Signatures**

color x

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**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 Q P x y x y

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**Feature Transformation**

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**EMD – Formal Definition**

Modeled as linear optimization (transportation problem)

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**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

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**? The Feedback Loop no yes exit start get query retrieve results**

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

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**Query Adaptation Input: signatures from relevant objects**

satisfied? retrieve results exit start get query query distance feedback display results 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

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**Heuristic EMD Adaptation 1**

satisfied? retrieve results exit start get query query distance feedback display results 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 ci(Q). Define gd: c(Q) x FS → R ( )

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**Heuristic EMD Adaptation 2**

satisfied? retrieve results exit start get query query distance feedback display results Heuristic EMD Adaptation 2 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

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**Optimization-Based EMD Adaptation 1**

satisfied? retrieve results exit start get query query distance feedback display results 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 Ranking Avg. Precision 1.000 0.854 0.365

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**Optimization-Based EMD Adaptation 2**

satisfied? retrieve results exit start get query query distance feedback display results Optimization-Based EMD Adaptation 2 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

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**Optimization-Based EMD Adaptation 3**

satisfied? retrieve results exit start get query query distance feedback display results 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(EMDgd , q, Feedback) Results for EMDgd on DB?

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**Overview Introduction Adaptive Similarity Model**

Relevance Feedback for the Earth Mover’s Distance Experimental Evaluation Conclusion

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**Experimental Evaluation: Databases**

72,000 images in ALOI DB ~60,000 images in COREL DB

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**Experimental Evaluation: ALOI**

Query-by-Refinement Heuristic Adaptation Optimization-based

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**Experimental Evaluation: COREL**

Query-by-Refinement Heuristic Adaptation Optimization-based

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**Experimental Evaluation**

After 5 iterations of looking for doors in COREL: (a) Query-by-Refinement (b) Heuristic (c) Optimization-Based pos

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**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

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