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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 [email protected]

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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

[email protected]

University of León / Spain

Electrical and Electronical Engineering


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


- 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


- 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

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


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


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:



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









… improves with increasing

number of (non-normal)


… depends only weakly on the

considered number of


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


- determines favorable positions of the prototypes

- adapts the corresponding distance measure

81.4 % (4.0)

81.6 % (4.5)


76.4 % (3.8)

75.6 % (4.1)



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


(LVQ1 prototypes)


GRLVQ: resulting relevances

  • only very few pixels are sufficient for successful classification

  • test error: (all) 82.75%, (69) 82.75%, (15) 81.87%


- improve LVQ system, algorithms, relevance schemes

- training data, objective classification (staining method)

- classification based on contour information (gradient profile)


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)


very few relevant pixels, robust performance

noisy labels / insufficient resolution?