It depends on what is understood as noise, since a noise source can be interpreted as any way of corrupting/altering the data.
Technically, if you want to add noise to your dataset you can proceed as follows:
- Add noise to the raw data, i.e, corrupt the raw data with some noise distribution and with certain signal to noise ratio,
- Add noise to the feature space, but keeping its dimension.
Adding noise is not the same as changing the dimension of the feature space. If the data is linearly separable in the original feature space, it will be also separable although you add an extra random feature. Take a look at figure 1 and figure 2. Figure depicts the scatter plot (var1_1 vs var1_1) of a linear separable data in a one dimensional feature space. Figure 2 depicts the scatter plot of the same feature space with an extra random feature, now the dimension is 2, but the data is still linearly separable. You only have to look at the projection of the data in the var1_1 axis.
Figure 1: Scatter plot of separable data in a 1-D feature space
Figure 2:Scatter plot of separable data in a 2-D feature space, which is the same as the previous space plus an extra random feature
If you want to evaluate the robustness of your prediction model against noise, I will take option 1, since it not straightforward to derive what kind of noise to apply in the feature space. If you are working with images, you can blur them or if you are dealing with audio files, you can add white gaussian noise, or another kind of noise source, for example another mixing the original audio files with other sound sources.