Generate random samples at a certain point in Matlab - matlab

Question

I have the following two data set:
A= (1,1) 1.9643
(2,1) 2.2753
(3,1) 2.9781
(4,1) 2.9320
(5,1) 3.5772
(6,1) 4.0150
(7,1) 3.3814
(8,1) 3.9113
(9,1) 2.7822
(10,1) 2.5518
(11,1) 3.3698
(12,1) 3.1048
(13,1) 1.9182
(14,1) 2.2638
(15,1) 2.6555
(16,1) 3.1855
(17,1) 3.6579
(18,1) 3.9113
(19,1) 3.6002
(20,1) 3.0357
(21,1) 1.5841
(22,1) 2.0103
(23,1) 1.9527
(24,1) 2.2753
(25,1) 2.3099
(26,1) 2.8283
(27,1) 3.0473
(28,1) 2.4827
(29,1) 2.5057
(30,1) 1.8721
(31,1) 2.0103
(32,1) 1.2269
(33,1) 1.8951
(34,1) 1.5610
(35,1) 1.5495
(36,1) 1.6878
(37,1) 1.4919
(38,1) 0.9620
(39,1) 1.1693
(40,1) 0.8122
(41,1) 0.9735
(42,1) 1.2500
(43,1) 1.3191
(44,1) 2.2292
(45,1) 2.4482
(46,1) 2.7938
(47,1) 2.0910
(48,1) 2.5403
(49,1) 0.9044
(50,1) 0.7662
(1,2) 4.5957
(2,2) 3.8589
(3,2) 4.5651
(4,2) 3.5519
(5,2) 2.8560
(6,2) 3.1937
(7,2) 3.4291
(8,2) 4.1761
(9,2) 4.0431
(10,2) 4.6162
(11,2) 3.9101
(12,2) 3.0709
(13,2) 4.0534
(14,2) 4.3706
(15,2) 3.5008
(16,2) 4.2888
(17,2) 3.8692
(18,2) 3.4291
(19,2) 3.1221
(20,2) 3.3165
(21,2) 3.3575
(22,2) 3.2039
(23,2) 2.7843
(24,2) 2.7127
(25,2) 2.9584
(26,2) 2.6309
(27,2) 2.2931
(28,2) 2.0373
(29,2) 2.3853
(30,2) 2.0577
(31,2) 2.3546
(32,2) 2.3239
(33,2) 2.9174
(34,2) 3.0709
(35,2) 2.6923
(36,2) 2.4057
(37,2) 2.0271
(38,2) 2.6820
(39,2) 2.9276
(40,2) 2.9992
(41,2) 3.3881
(42,2) 3.1937
(43,2) 3.5109
(44,2) 2.2010
(45,2) 2.6411
(46,2) 1.9656
(47,2) 1.6177
(48,2) 2.8867
(49,2) 3.0198
(50,2) 2.5899
Here, A is two dimensional sparse matrix where (i,i).
And B is (50,1) matrix, where the first 20 values are +1 and last 30 values are -1.
So the data point is look like this:
Now, I want to choose the (40,50) position of A and then want to generate 1000 random points within +/- 2 regions of the points.
So, the graph should be something like this:
Please let me know, how can I do it in matlab.

Answer 1

Since you don't mention a programming language, here is the general solution:
Assuming you want the data to be centered around (x,y), spread s, and label l.
Then you would for each object generatw two random Gaussians, scale them by the desired spread s, add the center vector (x,y), and append this vector to your data with the desired label.
Here, your center would be something like (45,45) and spread maybe 5 or just 1.

Answer 2

This generates and plots 1000 uniformly distributed random points within a +/- 2 region of position (40,50):
plot (40+4*rand(1000,1)-2, 50+4*rand(1000,1)-2,'o')
I know I ignored the "choosing a position from sparse matrix A"-part of your question. I hope that part is not crucial, and this will help you along anyway.
When you want other random distributions, check out randn (for gaussian) or other rand* functions.