# Learning the Discriminative Power-Invariance Trade-Off

## 3. Applications

We apply our method to the UIUC
textures, Oxford flowers
and Caltech 101
and 256
object categorisation databases. Since we would like to test how
general the technique is, we assume that no prior knowledge is
available and that no descriptor is *a priori* preferable to any
other. We therefore set *σ*_{k} to be constant for
all *k* and do not make use of the constraints **Ad** ≥
**p** (unless otherwise stated). The only parameters left to be set
are *C*, the misclassification penalty, and the kernel parameters
*γ*_{k}. These parameters are not tweaked. Instead,
*C* is set to 1000 for all classifiers and databases and
*γ*_{k} is set to one over the mean of the
*k*^{th} distances over the training set for the given
pairwise classification task. Note that the kernel parameters could
instead have been learnt by creating many base kernels, each with a
different value of *γ*_{k}, and then seeing which
ones gets selected. It is also possible to analogously learn
1/*C* in an *l*_{2} SVM setting.

We compare our algorithm to the Multiple Kernel Learning Block
*l*_{1} regularisation method of [Bach *et al.* NIPS 2004] for
which code is publicly
available. All experimental results are calculated over 20 random
train/test splits of the data except for 1-vs-All results which are
calculated over 3 splits.

### 3.4 Caltech 256

**Errata Regarding the Caltech Experiments**

Please note that the results reported on the Caltech databases are not
valid. Some of the kernel matrices on which the results were based
have errors.
Thus, please disregard the Caltech results and do not cite the paper
in reference to these datasets. The results on the other two datasets,
textures and flowers, are still valid.