SPROBID - Simplified PROBID using Top/Bottom Quartile Ideal Sets

Overview

Higher p_i = better. SPROBID is faster than PROBID: uses top/bottom ⌊m/4⌋ ideals instead of half. Best for m ≥ 4. For m < 4 falls back to trivial case.

Data

Crisp

Weights

Needs a weight source

How it works

1. 1

   Steps F1-F4 identical to PROBID: vector normalization → weighted matrix → m ideal solutions → Euclidean distances Si and Si_average.

   $$r_{ij}=\frac{x_{ij}}{\sqrt{{\sum }_k{x}_{kj}^2}};v_{ij}=w_j{r}_{ij};S_{i(k)}=\sqrt{\sum _j(v_{ij}-A_j^{(k)}{)}^2}$$

   Wang et al. 2021 §2 (SPROBID variant)

2. 2

   Step F2 (SPROBID-specific) - Use top ⌊m/4⌋ ideals for positive-ideal distance and bottom ⌊m/4⌋ for negative-ideal distance (quartile selection instead of PROBID's ⌈m/2⌉). S_pos_i = Σ_{k=1}^{⌊m/4⌋} S_i(k)/k; S_neg_i = Σ_{k=m+1-⌊m/4⌋}^{m} S_i(k)/(m-k+1). Final p_i = S_neg_i / S_pos_i. Rank descending.

   $$S_i^{pos}=\sum _{k=1}^{\lfloor m/4\rfloor }\frac{S_{i(k)}}{k};S_i^{neg}=\sum _{k=m+1-\lfloor m/4\rfloor }^m\frac{S_{i(k)}}{m-k+1};p_i=\frac{S_i^{neg}}{S_i^{pos}},\text{ rank descending}$$

   Wang et al. 2021 §2 SPROBID variant

Edge cases and pitfalls

• For m < 4, quartile selection degenerates (pymcdm fallback: Si_pos = Si[:,0], Si_neg = Si[:,-1]).

How to cite