change standardization for plot report using std and iqr

justclust/quarto.py

@@ -549,10 +549,10 @@ qmd.plot_clst_boxplot_loop(
 To provide an overview of the cluster characteristics, we consider cluster mean and median values. In @fig-mean-heatmap, cluster mean values are reported for each variable and colored according to the difference with the average mean among clusters (`Avg mean`). In @fig-cluster-comp-mean, the cluster mean value is standardized with respect to the average mean among clusters for each variable). That is,
 
 $$
-\\frac{graph_open}\\bar{graph_open}x{graph_close}_i  - \\bar{graph_open}x{graph_close}_{graph_open}Avg{graph_close}{graph_close}{graph_open}\\bar{graph_open}x{graph_close}_{graph_open}Avg{graph_close}{graph_close}
+\\frac{graph_open}\\bar{graph_open}x{graph_close}_i  - \\bar{graph_open}x{graph_close}_{graph_open}Avg{graph_close}{graph_close}{graph_open}\\bar{graph_open}x{graph_close}_{graph_open}Std{graph_close}{graph_close}
 $$
 
-where $\\bar{graph_open}x{graph_close}_i$ is the mean value of a given variable for cluster $i$ and $\\bar{graph_open}x{graph_close}_{graph_open}Avg{graph_close}$ is the average mean among clusters (i.e, $\\frac{graph_open}\\sum_i{graph_open}\\bar{graph_open}x{graph_close}_i{graph_close}{graph_close}{graph_open}\\#i{graph_close}$).
+where $\\bar{graph_open}x{graph_close}_i$ is the mean value of a given variable for cluster $i$, $\\bar{graph_open}x{graph_close}_{graph_open}Avg{graph_close}$ is the average mean among clusters (i.e, $\\frac{graph_open}\\sum_i{graph_open}\\bar{graph_open}x{graph_close}_i{graph_close}{graph_close}{graph_open}\\#i{graph_close}$), and $\\bar{graph_open}x{graph_close}_{graph_open}Std{graph_close}$ is the standard deviation of the cluster means (i.e, $Std(\\bar{graph_open}x{graph_close}_i)$).
 
 ```{graph_open}python{graph_close}
 #| fig-align: center
@@ -594,10 +594,10 @@ qmd.plot_cluster_comp_loop(
 In @fig-median-heatmap, cluster median values are reported for each variable and colored according to the difference with the average median among clusters (`Avg median`). In @fig-cluster-comp-median, the cluster median value is standardized with respect to the average median among clusters for each variable). That is,
 
 $$
-\\frac{graph_open}\\tilde{graph_open}x{graph_close}_i  - \\tilde{graph_open}x{graph_close}_{graph_open}Avg{graph_close}{graph_close}{graph_open}\\tilde{graph_open}x{graph_close}_{graph_open}Avg{graph_close}{graph_close}
+\\frac{graph_open}\\tilde{graph_open}x{graph_close}_i  - \\tilde{graph_open}x{graph_close}_{graph_open}Avg{graph_close}{graph_close}{graph_open}\\tilde{graph_open}x{graph_close}_{graph_open}IQR{graph_close}{graph_close}
 $$
 
-where $\\tilde{graph_open}x{graph_close}_i$ is the median value of a given variable for cluster $i$ and $\\tilde{graph_open}x{graph_close}_{graph_open}Avg{graph_close}$ is the average median among clusters (i.e, $\\frac{graph_open}\\sum_i{graph_open}\\tilde{graph_open}x{graph_close}_i{graph_close}{graph_close}{graph_open}\\#i{graph_close}$).
+where $\\tilde{graph_open}x{graph_close}_i$ is the median value of a given variable for cluster $i$, $\\tilde{graph_open}x{graph_close}_{graph_open}Avg{graph_close}$ is the average median among clusters (i.e, $\\frac{graph_open}\\sum_i{graph_open}\\tilde{graph_open}x{graph_close}_i{graph_close}{graph_close}{graph_open}\\#i{graph_close}$), , and $\\tilde{graph_open}x{graph_close}_{graph_open}Avg{graph_close}$ is the interquantile range of the cluster medians (i.e, $IQR(\\tilde{graph_open}x{graph_close}_i)$)..
 
 
 ```{graph_open}python{graph_close}
@@ -776,19 +776,25 @@ def get_dict_stat(
     selected_grouped = data.groupby(['cluster_lab'])
     cluster_means = selected_grouped.mean()
     cluster_medians = selected_grouped.median()
+
     overall_mean = cluster_means.mean()
+    ovarall_sd = cluster_means.std()
+
     overall_median = cluster_medians.mean()
+    ovarall_iqr = cluster_medians.apply(  # interqunaitle range
+        lambda x: np.round(np.percentile(x, 75) - np.percentile(x, 25),8),
+        axis=0)
 
     res = {
         'cluster_means':cluster_means.T,
         'cluster_means_cent':cluster_means.T\
             .sub(overall_mean, axis = 0)\
-                .divide(np.abs(overall_mean), axis = 0),
+                .divide(ovarall_sd, axis = 0),
 
         'cluster_medians':cluster_medians.T,
         'cluster_medians_cent':cluster_medians.T\
             .sub(overall_median, axis = 0)\
-                .divide(np.abs(overall_median), axis = 0)
+                .divide(ovarall_iqr, axis = 0)
     }
 
     return res
@@ -1374,6 +1380,7 @@ def plot_cluster_comp_single(
             xmax=xmax,
         )
     axes[0].set(title='Mean')
+    axes[0].set(xlabel=r'$\frac{\bar{x}_i  - \bar{x}_{Avg}}{\bar{x}_{std}}$')
 
     plot_cluster_comp(
                 serie_plot=data_plot_median,
@@ -1385,6 +1392,7 @@ def plot_cluster_comp_single(
                 xmax=xmax,
                 )
     axes[1].set(title='Median')
+    axes[1].set(xlabel=r'$\frac{\tilde{x}_i  - \tilde{x}_{Avg}}{\tilde{x}_{IQR}}$')
     plt.show()
 
 #----    plot_map_single_cluster    ----