highly variable gene | 高变异基因的选择 | feature selection | 特征选择

在做单细胞的时候，有很多基因属于noise，就是变化没有规律，或者无显著变化的基因。在后续分析之前，我们需要把它们去掉。

以下是一种找出highly variable gene的方法：

The feature selection procedure is based on the largest difference between the observed coefficient of variation (CV) and the predicted CV (estimated by a non-linear noise model learned from the data) See Figure S1C. In particular, Support Vector Regression (SVR, Smola and Vapnik, 1997) was used for this purpose (scikit-learn python implementation, default parameters with gamma = 0.06; Pedregosa et al., 2011).

#Pre-filtering
df_f = df_merge.copy()
df_f = df_f.ix[sum(df_f>=1, 1)>=5,:] # is at least 1 in X cells
df_f = df_f.ix[sum(df_f>=2, 1)>=2,:] # is at least 2 in X cells
df_f = df_f.ix[sum(df_f>=3, 1)>=1,:] # is at least 2 in X cells

#Fitting
mu = df_f.mean(1).values
sigma = df_f.std(1, ddof=1).values
cv = sigma/mu
score, mu_linspace, cv_fit , params = fit_CV(mu,cv, 'SVR', svr_gamma=0.005)

#Plotting
def plot_cvmean():
    figure()
    scatter(log2(mu),log2(cv), marker='o', edgecolor ='none',alpha=0.1, s=5)
    mu_sorted = mu[argsort(score)[::-1]]
    cv_sorted = cv[argsort(score)[::-1]]
    scatter(log2(mu_sorted[:thrs]),log2(cv_sorted[:thrs]), marker='o', edgecolor ='none',alpha=0.15, s=8, c='r')
    plot(mu_linspace, cv_fit,'-k', linewidth=1, label='$Fit$')
    plot(linspace(-9,7), -0.5*linspace(-9,7), '-r', label='$Poisson$')
    ylabel('log2 CV')
    xlabel('log2 mean')
    grid(alpha=0.3)
    xlim(-8.6,6.5)
    ylim(-2,6.5)
    legend(loc=1, fontsize='small')
    gca().set_aspect(1.2)

plot_cvmean()

#Adjusting plot

对每一个基因在不同细胞中的表达量的mean和CV散点图，通过SVR拟合出noise的曲线。

通过the largest difference between the observed coefficient of variation (CV) and the predicted CV (estimated by a non-linear noise model learned from the data)就能找出highly variable gene了。