[pymvpa] help understanding 1-dimension classification differences

[Yaroslav Halchenko]

;-) 1d space could be non-linear as well.

imagine such 2-class problem in 1d:

x o x o x o x o x o

;-) depending on the actual data and how you slice the cake you would be
getting different results with linear/non-linear classifiers.
Question about difference in SVM and logistic is of related nature (e.g.
in SVM margin will tradeoff where to place the decision "value", thus
differing where logistic regression would place it)

or I misunderstood the question?

On Fri, 27 Jan 2012, David V. Smith wrote:

> As a simple test, I was curious to see how much better a multivariate classification test (2 or more dimensions/features) would be compared to a univariate classification test (1 dimension/feature). In the univariate case, can someone help me understand why LinearNuSVMC would differ from RbfNuSVMC?

> CV: 79.28% (RbfNuSVMC)
> CV: 66.42% (LinearNuSVMC)

> We know from a logistic regression that this particular feature can predict our two conditions with ~80% accuracy. If the SVM classifier only has a single dimension to work with, should linear and RBF differ this much? I was under the impression that, given a single dimension, both methods would only find the best point on that dimension that discriminates the classes.

> Details on the dataset are printed below:
> Dataset / float64 140 x 1
> uniq: 140 chunks 2 labels
> stats: mean=0.256292 std=0.231866 var=0.0537616 min=0 max=1
> No details due to large number of labels or chunks. Increase maxc and maxl if desired
> Summary per label across chunks
>   label  mean  std  min max #chunks
>    0    0.443 0.497  0   1     62
>    1    0.557 0.497  0   1     78

> To account for the unbalanced labels, I'm using nperlabel='equal' in my splitter.
> cv = CrossValidatedTransferError(
> 	TransferError(clf),
> 	NFoldSplitter(nperlabel='equal'),
> 	enable_states=['confusion'])

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