黃靖庭 || 以奇異值分解分析第十屆立法委員的投票行為 || 2023/08/09 ||
With votes on n bills of m legislators, we can put the results into a mxn matrix M. Then we apply the SVD. The SVD will have decomposed the original matrix into three matrices: a left singular vectors matrix, a singular values matrix (letting singular values o decrease when become larger), and a right singular vectors matrix.
The left singular vectors represent the contribution of each legislator to the overall variability of the voting records, while the right ones represent the contribution of each bill. And the singular values represent the amount of variability captured by each singular vector.
In this research, we take M_2 (only keep the first two singular vectors and singular values) and M_3 to make approximations to the original matrix M.