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Classification of boar sperm head imagesusing Learning Vector Quantization

Rijksuniversiteit Groningen/ NL

Mathematics and Computing Science

http://www.cs.rug.nl/~biehl

[email protected]

Michael Biehl, Piter Pasma,Marten Pijl, Nicolai Petkov

Lidia Sánchez

University of León / Spain

Electrical and Electronical Engineering

ESANN 2006, Classification of boar sperm head images using LVQ

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

Motivation

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


microscopic images of boar sperms

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


normal (650) non-normal (710)

1360 example images, classified by experts (visual inspection)

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


• identify the closest prototype, i.e the so-called winner

• initialize prototype vectors for different classes

• present a single example

• move the winner - closer towards the data (same class)

- away from the data (different class)

classification:

assignment of a vector to the class of the closest

prototype w

aim: generalization ability

classification of novel data

after learning from examples

Learning Vector Quantization (LVQ)

example: basic scheme LVQ1 [Kohonen]


Euclidean distance between data ξ prototype w: 2ii

N

1i

w-ξ),(d Σ

wξLVQ1

given ξ, update only the winner:

decreasing learning rate : .tfor t )t-c(t1η

tfor t η η(t)

ooo

oo

Learning algorithms

(t)w-ξ η(t))(t w 1)(t w *** (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


comparison of different LVQ systems (# of prototypes)

ten-fold cross-validation:

non-normal

normal

performance on training data

… improves with increasing number of (non-normal) prototypes

%correct

non-normal

normal

performance w.r.t. test data

… depends only weakly on the considered number of prototypes

%correct


Generalized Learning Vector Quantization (GLVQ)

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)

perform gradient descent steps with respect

to an instantaneous cost function f(z)),(d ),(d

),(d - ),(d z with

KJ

KJ

wξwξ

wξwξ

z)f(z):(here)f(η(t))(t w 1)(t wLwLL z

[A.S. Sato and K. Yamada, NIPS 7, 1995)]


Generalized Relevance LVQ (GRLVQ)

2ii

2i

N

1iλ w-ξλ),(d Σ

wξGLVQ with modified distance measure

vector of relevances, normalization i

2i 1λ

GRLVQ

- determines favorable positions of the prototypes

- adapts the corresponding distance measure

[B. Hammer, T. Villmann, Neural Networks 15: 1059-1068]

- re-define cost function f(z) in terms of dλ:

- perform gradient steps w.r.t. prototypes wJ , wK and vector λ

),(d ),(d

),(d - ),(d z

KλJλ

KλJλ

wξwξ

wξwξ


Comparison of performance: estimated test error

LVQ1 81.4 % (4.0) 81.6 % (4.5)

GLVQ 75.6 % (4.1) 76.4 % (3.8)

GRLVQ 81.5 % (3.5) 81.7 % (3.7)

alg. 3/3 1/7

normal/non-normal prototypes

- weak dependence on the number of prototypes- inferior performance of GLVQ (cost function ↮ classification error)

- recovered when including relevances

mean (stand. dev.)


- only very few pixels are sufficient for successful classification

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

GRLVQ: resulting relevances

normal non-normal(LVQ1 prototypes)


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?

Outlook

- improve LVQ system, algorithms, relevance schemes

- training data, objective classification (staining method)

- classification based on contour information (gradient profile)


LVQ1 demo

classification of boar sperm head images using learning vector quantization rijksuniversiteit...

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