I encountered following problem in one of the paper:
Consider 2-class PR problems with n Boolean features. Consider two specific classification tasks specified by the following: (i) a feature vector X should be in Class-I if the integer represented by it is divisible by 4, otherwise it should be in Class-II; (ii) a feature vector X should be in Class-I if it has odd number of 1’s in it, otherwise it is in Class-II. In each of these two cases, state whether the classifier can be represented by a Perceptron; and, if so, show the Perceptron corresponding to it; if not, give reasons why it cannot be represented by a Perceptron.
If I understand correctly, none of these looks like a linearly separable dataset. I give following reasoning:
Case 1: Since given data is 1-D, we can plot it on X-axis and there is no point on that axis which can define the boundary between two classes.
Case 2: If I understand that correctly, it puts number with odd 1s like 1, 21, 31 in one class and other numbers like 211, 11, in different class. Same problem exists here as well. If we plot them on X-axis, there is no point which can separate the two classes.
Is this reasoning correct or I am totally out of way? Any help will be much appreciated?