# can we have different features for different hyperplanes in SVM?

is it possible if we have different features for different classes of svm?

For example one of the hyperplane:

$$w_1\cdot \text{age}+ w_2 \cdot \text{ trip duration} +w_3 \cdot \text{ income}$$

and the other hyperplane be

$$w_1\cdot \text{cost}+ w_2 \cdot \text{trip duration} +w_3 \cdot \text{purpose of trip}$$

the other one

$$w_1\cdot \text{distance}+ w_2 \cdot \text{trip duration} +w_3 \cdot 0?$$

Does it make sense?

It is possible.

All of these hyperplanes live in the space of

$$\text{(age, trip duration, income, cost, purpose of trip, distace)}$$

even though some of the coefficients are $$0$$.

Remark: For the last hyperplane $$w_3\cdot 0 = 0$$.

• no I mean if my data is in 3 dimension Commented Aug 4, 2019 at 3:42
• and what are those $3$ dimensions? You can only use features from your data. Commented Aug 4, 2019 at 3:48
• I can make my data with 3 columns, for some row the first column is age and for some of them cost and some of them distance. same for other columns Commented Aug 4, 2019 at 4:10
• Hence, you are partitioning your data set into $3$ subdata set? Why do you want to do that? Is it due to difficulty in data collections? Commented Aug 4, 2019 at 4:16
• reducing the dimension of problem Commented Aug 4, 2019 at 5:58

It is common in multi-class systems to have several different models. These models could conceivably rely on very different feature sets.

One model could rely on features {A,B,C,D} for separating out A from BC. Then another model could be found and tuned with features {D,E,F,G} such that model #2 separates separate B from C.

It is also common to have an "Ensemble" approach to working with multi-class systems, datasets and predictors.