count the circles of numbers

lr_circles.m

X = [
    1,0,3,0,0,0,0,0,1,0,0; % 7111
    1,1,0,0,0,0,0,0,0,2,1; % 8809
    1,0,1,2,0,0,0,0,1,0,0; % 2172
    1,0,0,0,0,0,0,4,0,0,0; % 6666
    1,0,4,0,0,0,0,0,0,0,0; % 1111
    1,0,0,4,0,0,0,0,0,0,0; % 2222
    1,0,0,1,0,0,0,2,1,0,0; % 7662
    1,0,1,0,2,0,0,0,0,0,1; % 9313
    1,4,0,0,0,0,0,0,0,0,0; % 0000
    1,0,0,0,0,0,4,0,0,0,0; % 5555
    1,0,1,0,1,0,0,0,0,1,1; % 8193
    1,1,0,0,0,0,0,1,0,1,1; % 8096
    1,0,0,0,1,1,0,0,0,1,1; % 4398
    1,0,0,0,0,1,1,0,1,0,1; % 9475
    1,1,0,0,1,0,0,0,0,1,1; % 9038
    1,0,1,0,1,1,0,0,0,1,0; % 3148
];

y = [
    0;
    6;
    0;
    4;
    0;
    0;
    2;
    1;
    4;
    0;
    3;
    5;
    3;
    1;
    4;
    2;
];

theta = pinv (X' * X) * X' * y;

x = [
    1,0,0,1,0,0,0,0,0,2,1; % 2889
    1,0,0,1,0,1,0,1,1,0,0; % 2467
];

x * theta