position-correlation scoring feature(PCSF)

PCSF

位置关联打分(PCSF)特征

position-correlation scoring feature

来源1

2020-11_Theory in Biosciences_Eukaryotic and prokaryotic promoter prediction using hybrid approach

https://link.springer.com/article/10.1007/s12064-010-0114-8

原文：

The PWM can be constructed by counting the frequencies of oligonucleotides in conserved sites of training sequences. The probability $p_{xi}$ of an oligonucleotide $x$ at the ith site can be formulated as (Li and Lin 2006; Wasserman and Sandelin 2004; Kielbasa et al. 2005):
$$p_x=(n_{xi}+b_{xi})/(N_i+B_i)p_{xi}$$
(2)

where $n_{xi}$ and $b_{xi}$ are real counts and pseudocounts of k-mer oligonucleotide x at the ith site, respectively. $N_i$ and $B_i$ are total number of real counts and pseudocounts at the ith site, respectively. If there are relatively few real counts, many k-mer variations may not be presented because of the small sample of sequences. The goal of adding pseudocounts is to obtain an improved estimate of the probability $p_{xi}$ of k-mer oligonucleotide x at the ith site. A relatively few pseudocounts should be added when there is a good sampling of sequences, and more pseudocounts should be added when the data is sparser. One simple formula that has worked well in some studies is to make $B_i$ equal to $\surd N_i$ and $b_{xi}$ equal to $p_0\surd N_i$ ($p_0$ is the average background frequency) in Eq. 2 (Wasserman and Sandelin 2004; Kielbasa et al. 2005), respectively. As $N_i$ increase, the influence of pseudocounts decrease because $\surd Ni$ increase more slowly. Due to the existence of pseudocounts, the estimated probabilities are strictly positive (Kielbasa et al. 2005). Based on the probabilities $p_{xi}$ , the PCSF of an arbitrary sequence can be defined as (Li and Lin 2006):
$$F=\sum _{i}ln(p_{xi}/p_0)$$
(3)

where $p_0$ is average background probability of k-mer. The score F shows the degree of sequence closed to matrix resource.

来源2

2019-09_Mol Ther-Nucleic Acids_iProEP：A Computational Predictor for Predicting Promoter

https://www.sciencedirect.com/science/article/pii/S2162253119301611

通过对每个物种的启动子序列进行比对，我们可以构建一个位置相关评分矩阵position-correlation scoring matrix。PCSM中的每一行都由因子$p_{xi}$组成，$p_{xi}$是启动子样本第i位的k-mer x的概率。$p_{xi}$可通过以下公式计算：
$$p_{xi}=\frac{n_{xi}+b_{xi}}{N_i+B_i}$$
其中$n_{xi}$是出现在第i位的x的实际计数，而$b_{xi}$是相应的伪计数。$N_i$表示第i个位置上所有k-mers的实数之和(即正样本数)，而$B_i$是相应的伪计数之和。如果样本量不够大，当k增加时，一些k-mers将不存在。因此，伪计数可以改善对第i位k-mer x的概率$p_{xi}$的估计。$B_i$和$b_{xi}$可以由下式给出:
KaTeX parse error: Expected 'EOF', got '&' at position 5: B_i&̲= \sqrt{N_i},\\…
其中$po$为k-mer的背景频率，等于$1/4^k$。随着样品数N_i的增加，由于$\sqrt{N_i}$增长缓慢，伪计数的影响会减弱。
通过对LIN和LI的大量复杂的保守分析和ACC评价，筛选出了五个物种三聚体的一些保护位点。基于这些位点和PCSM，五个物种的正负样本的PCSF特征可以表示为:
$$PCSF=[f_1{f}_2...f_i...f_n]$$
其中n是选定的保守位点的数量，每个元素定义为:
$$f_i=ln(p_{xi}/po)$$
在这个方程中，$po$是每个三聚体的本底概率($po=1/4^3$)，$p_{xi}$可以在PCSM的基础上得到。