Classification of boar sperm head images using Learning Vector Quantization

1. Classification of boar sperm head images using Learning Vector Quantization Michael Biehl, Piter Pasma, Marten Pijl, Nicolai Petkov Lidia Sánchez Rijksuniversiteit Groningen/ NL Mathematics and Computing Science http://www.cs.rug.nl/~biehl m.biehl@rug.nl University of León / Spain Electrical and Electronical Engineering

2. Motivation semen fertility assessment: important problem in human / veterinary medicine medical diagnosis: - sophisticated techniques, e.g. staining methods - high accurracy determination of fertility evaluation of sample quality for animal breeding purposes - fast and cheap method of inspection here: - microscopic images of boar sperm heads (Leon/Spain) e.g. quality inspection after freezing and storage - distance-based classification, parameterized by prototypes - Learning Vector Quantization + Relevance Learning

3. preprocessing: - isolate and align head images - normalize with respect to mean grey level and corresponding variance - resize and approximate by an ellipsoidal region of 19x35 pixels • replace “missing” pixels (black) • by the overall mean grey level microscopic images of boar sperms

4. example images, classified by experts (visual inspection) normal (650) non-normal (710) application of Learning Vector Quantization: - prototypes determined from example data - parameterize a distance based classification - plausible, straightforward to interpret/discuss with experts - include adaptive metrics in relevance learning

5. • initialize prototype vectors for different classes example: basic scheme LVQ1 [Kohonen] • present a single example   • identify the closest prototype, i.ethe so-calledwinner classification:    assignment of a vector  to the class of the closest prototype w  • move the winner -closertowards the data (same class)  -away from the data (different class) Learning Vector Quantization (LVQ)  aim: generalization ability classificationof novel data after learning from examples

6. decreasing learning rate : Learning algorithms LVQ1 Euclidean distance between data ξprototype w: given ξ, update only the winner: (sign acc. to class membership) prototype initialization: class-conditional means + random displacement (∼70% correct classification)

7. example outcome: LVQ1 with 4 prototypes for each class: normal non-normal cross-validation scheme evaluation of performance - with respect to the training data, e.g. 90% of all data - with respect to test data 10% of all data average outcome over 10 realizations

8. performance w.r.t. test data performance on training data correct correct % % normal normal non-normal non-normal … improves with increasing number of (non-normal) prototypes … depends only weakly on the considered number of prototypes ten-fold cross-validation: comparison of different LVQ systems (# of prototypes)

9. perform gradient descent steps with respect to an instantaneous cost function f(z) Generalized Learning Vector Quantization (GLVQ) [A.S. Sato and K. Yamada, NIPS 7, 1995)] given a single example, update the two winning prototypes : wJ from the same class as the example (correct winner) wK from the other class (wrong winner)

10. - re-define cost function f(z) in terms of dλ: - perform gradient steps w.r.t. prototypes wJ , wK and vectorλ Generalized Relevance LVQ (GRLVQ) [B. Hammer, T. Villmann, Neural Networks 15: 1059-1068] GLVQ with modified distance measure vector of relevances, normalization GRLVQ - determines favorable positions of the prototypes - adapts the corresponding distance measure

11. 81.4 % (4.0) 81.6 % (4.5) LVQ1 76.4 % (3.8) 75.6 % (4.1) GLVQ GRLVQ 81.5 % (3.5) 81.7 % (3.7) Comparison of performance: estimated test error normal/non-normal prototypes alg.3/3 1/7 mean (stand. dev.) • - weak dependence on the number of prototypes • inferior performance of GLVQ (cost function ↮ classification error) • - recovered when including relevances

12. normal (LVQ1 prototypes) non-normal GRLVQ: resulting relevances • only very few pixels are sufficient for successful classification • test error: (all) 82.75%, (69) 82.75%, (15) 81.87%

13. Outlook - improve LVQ system, algorithms, relevance schemes - training data, objective classification (staining method) - classification based on contour information (gradient profile) Summary LVQ provides a transparent, plausible classification of microscopic boar sperm head images Performance: LVQ1 ↘GLVQ↗GRLVQ satisfactory classification error (ultimate goal: estimation of sample composition) Relevances: very few relevant pixels, robust performance noisy labels / insufficient resolution?

14. LVQ1 demo