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The tongue data

Harshman et al. performed an interesting analysis of data on tongue shapes with respect to a defined grid when uttering different English vowels. The data were generated from X-rays taken of five different speakers during their pronunciation of the vowels. Details of the experimental conditions may be found in the literature. The data array has the size 5 (speakers) ´10 (vowels) ´13 (position in cm on grid). The data were centered across vowels (Harshman & Lundy personal communication) and it was found that two components were definitely present. A possible third component could not be substantiated partly because apparently it was difficult to fit three components reliably. This in itself is an indication that too many components are extracted from the data. The raw data seem to have some problems with degeneracy.

Get the data: Use the original pdf (linked above) or run the below MATLAB code

X=[
2.45 2.40 2.40 2.50 2.45 2.05 1.65 1.00 .45 .40 .55 .55 .95
2.55 2.05 1.95 1.90 1.80 1.60 1.30 .95 .55 .65 .90 .90 1.05
2.35 1.90 1.80 1.80 1.80 1.55 1.30 .95 .65 .70 .90 .85 1.05
2.50 2.05 1.65 1.65 1.55 1.45 1.25 1.05 .70 1.05 1.20 1.15 1.10
2.05 1.50 1.35 1.50 1.55 1.45 1.30 1.15 .95 1.40 1.55 1.40 1.25
1.55 1.00 .85 1.00 1.25 1.35 1.50 2.00 2.10 2.55 2.65 2.35 2.00
1.65 .90 .65 .65 .75 .95 1.40 1.90 2.15 2.60 2.70 2.60 2.40
1.90 1.30 .95 .85 .75 .75 .95 1.30 1.65 2.15 2.30 2.25 2.30
2.40 1.60 1.45 1.25 1.00 .95 .80 .85 1.10 1.50 2.10 2.00 1.65
2.70 1.95 1.50 1.30 .90 .70 .55 .55 .95 1.45 1.80 1.90 2.00
2.95 2.70 2.75 2.75 2.70 2.60 2.25 1.00 .35 .15 .30 .60 1.15
2.40 2.20 2.25 2.20 2.25 2.15 1.85 1.25 .75 .75 .90 1.05 1.10
2.25 2.45 2.65 2.65 2.40 2.20 2.05 1.55 .95 .85 1.10 1.40 1.65
2.00 1.75 1.90 2.30 2.40 2.20 2.00 1.45 1.00 1.05 1.40 1.75 1.80
1.25 1.15 1.30 1.65 1.95 1.90 1.80 1.65 1.40 1.70 2.15 2.45 2.60
.45 .25 .30 .40 1.15 1.70 1.95 2.30 2.60 2.95 3.30 3.15 2.60
.40 .20 .20 .30 .60 1.05 1.35 1.65 2.60 3.05 3.45 3.60 3.40
1.00 .55 .55 .45 .65 .80 1.15 1.55 2.25 2.75 3.20 3.35 3.25
1.30 .70 .65 .45 .65 .90 1.20 1.45 1.90 2.40 2.85 2.80 2.45
2.15 1.80 1.50 1.05 .65 .55 .65 .80 .95 1.55 2.10 2.35 2.60
2.10 2.00 2.15 2.05 1.95 1.80 1.45 1.10 .75 .65 .75 .80 .90
2.00 1.70 1.90 1.95 1.90 1.75 1.35 1.15 .95 1.00 1.10 .90 .65
1.95 1.80 1.80 1.95 1.95 1.95 1.65 1.25 .90 .85 1.05 .95 .90
1.55 1.40 1.50 1.70 1.85 1.80 1.90 1.80 1.75 1.70 1.70 1.40 1.10
1.65 1.25 1.40 1.70 1.90 1.95 2.05 2.10 1.95 1.95 2.15 2.10 1.70
.95 .55 .70 1.15 1.65 2.20 2.65 2.95 3.05 3.20 3.35 2.95 1.90
1.20 .65 .45 .65 .75 1.00 1.45 2.10 2.40 2.65 2.80 2.55 1.95
1.55 1.45 1.05 1.15 1.05 1.00 1.15 1.45 1.90 2.40 2.70 2.65 1.85
1.80 1.05 1.05 1.05 1.00 1.00 1.15 1.40 1.65 1.95 2.15 1.85 1.50
2.00 1.70 1.40 1.20 1.00 .85 .95 1.00 1.10 1.55 1.80 1.70 1.25
2.70 2.60 2.55 2.50 2.45 2.40 1.80 1.35 .70 .55 .75 .85 1.85
2.25 1.90 1.85 1.90 2.15 2.05 1.85 1.65 1.35 1.40 1.50 1.90 1.80
2.25 2.20 2.30 2.25 2.30 2.20 1.70 1.45 .90 .90 1.10 1.25 1.85
1.90 1.50 1.40 1.40 1.65 1.75 1.75 1.85 1.60 1.80 1.90 1.65 1.50
1.70 1.20 1.05 1.05 1.55 1.70 1.80 1.90 1.85 2.10 2.35 2.40 2.25
1.05 .90 .45 .60 1.45 2.05 2.90 2.90 3.00 3.20 3.35 2.95 2.15
.90 .40 .45 .55 1.30 1.80 2.30 2.80 3.10 3.40 3.45 3.00 2.40
2.00 1.30 1.05 .90 .95 .90 1.25 1.65 1.80 2.30 2.60 2.60 1.90
2.15 1.70 1.45 1.30 1.30 1.25 1.20 1.35 1.45 1.95 2.20 2.25 1.95
2.95 2.30 2.05 1.80 1.70 1.45 1.00 .80 .80 1.15 1.55 1.90 1.40
3.00 2.45 2.30 2.20 2.10 1.45 1.15 .80 .40 .60 .45 .40 .85
2.40 2.10 1.95 1.90 1.80 1.45 1.10 .90 .70 .95 .95 .75 1.10
2.50 2.40 2.20 2.05 2.05 1.70 1.30 .95 .65 .95 1.00 .85 1.20
2.25 2.10 1.95 1.90 1.90 1.55 1.15 1.00 .90 1.10 1.05 .90 1.25
1.70 1.95 2.05 2.10 1.95 1.50 1.15 1.15 1.10 1.30 1.30 1.20 1.45
1.40 .85 1.05 1.30 1.55 1.55 1.65 2.00 2.40 2.75 2.80 2.60 2.35
1.10 .70 .70 .90 1.15 1.00 1.20 1.80 2.40 2.75 2.80 2.35 2.05
1.80 1.05 .75 .70 .70 .55 .60 1.20 1.85 2.40 2.45 2.25 2.40
1.90 1.25 1.05 .90 .95 .65 .65 1.25 1.85 2.35 2.35 2.05 2.30
2.70 2.05 1.65 1.40 1.15 .60 .40 .50 .60 1.15 1.40 1.60 1.65];
X=X';
DimX=[13 10 5];
X = reshape(X,DimX);


Please make reference to the data by this publication:

R. A. Harshman, P. Ladefoged, and L. Goldstein. Factor analysis of tongue shapes. J Acoust Soc Am 62:693-707, 1977.

We used the data in the publication:

R. Bro and H. A. L. Kiers. A new efficient method for determining the number of components in PARAFAC models. J.Chemom. 17:274-286, 2003.