Generating two classes of points

Hi,

I want to create a 100x2 feature vector set, with roughly half in class '1' and the rest in class '-1'. (As in, when I make a scatter plot of the x-y coordinates, the points should be almost linearly separable). I suppose rand or randn wouldn't help much here.

Thanks for your inputs.

Answer 1

[John D'Errico]

Why would rand or randn NOT be of use here?

For example, what do you know about a bivariate random sample? How far out can you expect points to deviate from the mean, if you know the variances? In the case of using randn, the default covariance matrix would be an identity matrix. So you would expect almost the entire distribution to lie within 3*sigma.

So if you adjust the mean of the two set of samples to be separate by a sufficient amount, they will be distinct. You even know how much to offset the two distributions, based on those variances. Adding a constant value to normally distributed samples just adjusts the mean. So WTP?

Likewise, had you used rand, it produces uniformly distributed samples. In 2-dimensions, they will thus live in a unit square. Again, WTP? add a constant to one set.

[Deepayan Bhadra]

The idea is that the 100x2 matrix I am manually generating will reflect a real-world data set. Some of these 100 points will lie on one side of a line and the rest on the other. The problem will assign to each point a 'class' of +1 or -1, accordingly. Also, when a new 'point' is generated, we can classify which side of the line to assign it to. The 'random' data-generation with such strict separation is the focal issue here.

Answer 2

[Image Analyst]

No, but randperm() can help. Try this:

m = zeros(100, 2); % Initialize to all zero.
indexes = randperm(numel(m), numel(m)/2) % Get half of the indexes to change to 1.
m(indexes) = 1 % Change them to 1.

[Deepayan Bhadra]

I ran this but it didn't really relate well. As I mentioned above, the idea is that the 100x2 matrix I am manually generating will reflect a real-world data set. Some of these 100 points will lie on one side of a line and the rest on the other.

The problem will assign to each point a 'class' of +1 or -1, accordingly. Also, when a new 'point' is generated, we can classify which side of the line to assign it to. The 'random' data-generation with such strict separation is the focal issue here.