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Classification of boar sperm head images using Learning Vector Quantization. Michael Biehl, Piter Pasma, Marten Pijl, Nicolai Petkov. Lidia S á nchez. Rijksuniversiteit Groningen/ NL Mathematics and Computing Science http://www.cs.rug.nl/~biehl m.biehl@rug.nl.

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## Classification of boar sperm head images using Learning Vector Quantization

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**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**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**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**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**• 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**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)**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**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)**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)**- 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**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**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%**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?

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