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2003 Aug 15
2
Oja median
...y <- xx[, 1] * xx[, 4] - xx[, 2] * xx[, 3]
z1 <- (xx[, 4] - xx[, 2])
z2 <- - (xx[, 3] - xx[, 1])
return(rq(y~cbind(z1, z2)-1)$coef)
}
To understand the strategy, note that the area of the triangle formed
by the points x_i = (x_i1,x_i2), x_j = (x_j1,x_j2),
and theta = (theta_1,theta_2) is given by the determinant,
| 1 1 1 |
Delta(x_i, x_j, theta) = .5 |y_i1 yj1 theta_1|.
|y_i2 yj2 theta_2|
Expanding the determinant in the unknown parameters theta gives
the l1 regression fo...