Dear Bernhard,
in out1 and out2, the data set a is first projected by scaling pipeline s, creating a temporary data set to which w is applied. In out3 and out4, the two-stage pipeline is first created applied to a data set in one step. The concatenation with brackets in out4 is deprecated, use the functionally identical concatenation by multiplication (as in out3).
Now to the differences. Redoing your example, I found out that the reason lies in the empty offset you’re passing in to sdp_affine (turning empty offset to zero vector is not a documented behaviour).
>> rand('state',42); a=sddata(rand(3,2))
3 by 2 sddata, class: 'unknown'
>> +a
ans =
0.1591 0.4966
0.3710 0.0149
0.9005 0.4225
Lets define two sdp_affine pipelines, once with offset specified, once empty.
>> p1=sdp_affine([2.3 4; -7 5],[0 0],sdlab('out'))
Affine pipeline 2x2 (sdp_affine)
>> p2=sdp_affine([2.3 4; -7 5],[],sdlab('out'))
Affine pipeline 2x2 (sdp_affine)
>> p=a*sdparzen % just to have some 2nd stage
Parzen pipeline 2x1 one class, 3 prototypes (sdp_parzen)
Applying scaling with offset set to zero:
>> out1=a*p1*p
3 by 1 sddata, class: 'unknown'
>> out2=(a*p1)*p
3 by 1 sddata, class: 'unknown'
>> out3=a*(p1*p)
3 by 1 sddata, class: 'unknown'
>> out4=a*[p1 p]
3 by 1 sddata, class: 'unknown'
>> [+out1 +out2 +out3 +out4]
ans =
0.0006 0.0006 0.0006 0.0006
0.2175 0.2175 0.2175 0.2175
0.0004 0.0004 0.0004 0.0004
>> [+out1 - +out3]
ans =
0
0
0
Applying the scaling with empty offset:
>> out1=a*p2*p
3 by 1 sddata, class: 'unknown'
>> out2=(a*p2)*p
3 by 1 sddata, class: 'unknown'
>> out3=a*(p2*p)
3 by 1 sddata, class: 'unknown'
>> out4=a*[p2 p]
3 by 1 sddata, class: 'unknown'
>>
>> [+out1 +out2 +out3 +out4]
ans =
0.0006 0.0006 0 0
0.2175 0.2175 0 0
0.0004 0.0004 0 0
We will add the conversion of empty offset to zero in the next release.
For some commonly-used scaling approaches, look at sdscale (http://perclass.com/doc/ref/sdscale.html)
Kind Regards,
Pavel
