What is the difference between attribute reduction and dimensional reduction?
What methods are considered attribute reduction techniques as opposed to dimensional reduction?
I am not aware of the term 'attribute reduction' in machine learning. Can you provide a link to what this refers to?
On the other hand, some papers use the term 'attribute selection' to refer to feature selection.
Feature selection is a special type of dimensionality reduction in which the set of features produced must be a subset of the original features. Importantly, it means the features have not been transformed or altered in any way other than inclusion or exclusion.
General dimensionality reduction usually works by first transforming the input features into a new representation, such as by using the coordinate transformation that corresponds to the PCA dimensions, or by first projecting the data into a new space (of possibly higher dimensionality) via a kernel function, and then using some measure of informativeness to prune away features in that new space.
Dimensionality reduction could also involve simpler transformation, such as averaging together multiple components of the input feature vector due to observed collinearity. Even though the transformation is simplistic (taking an average), it still differs from feature selection in that the new feature is not a subset of the original.
In summary, the main difference is that feature selection does not change anything apart from dropping some of the less informative features of the original input. It keeps the remaining features without change. Dimensionality reduction transforms the data, and the final representation may be quite different (even apart from dimensionality) from the original input features.