""" ===================================================== k-prediction from MXS: step-by-step guide ===================================================== Real-world examples to generate the mixture learning strategy (MXS) target :math:`y*` for predicting the permeability coefficient :math:`k` parameter from two boreholes. """ # Author: L.Kouadio # Licence: BSD-3-clause # %% # Note that this is an example of two boreholes which results is quited less relevant compared to the tangible example implemented in # the `Hongliu coal mine `_ with 11 boreholes data [1]_. # %% # We start by importing the required modules import pandas as pd from watex.datasets import load_hlogs # %% # Preprocess data # =================== # Make a unique dataset from two boreholes data collected in Hongliu # coal mine :h502 and h2601 and reduce down dimensions if necessary # * load `load_hlogs` to get explicitly the features names and target names box = load_hlogs () # combine our test data # data = load_hlogs().frame + load_hlogs(key= 'h2601').frame data = load_hlogs (key ='*').frame X0, y0 = data [box.feature_names] , data [box.target_names ] # make copies for safety X, y = X0.copy() , y0.copy() # let's visualize the features names and target names print("feature_names:\n" , box.feature_names ) print("target names:\n", box.target_names ) # %% # Data contains some categorical values, we will drop the rock name, the hole_id # and well diameter which are subjective data and not useful for prediction # puposes and impute the remaining data using a bi-impute strategy from watex.utils import naive_imputer X.drop (columns = ['rock_name', 'hole_id', 'well_diameter'] , inplace =True ) # * Merge both depths into one to compose only a single depth column X['depth'] = ( X.depth_bottom + X.depth_top )/2 X.drop (columns =['depth_top', 'depth_bottom'], inplace =True ) data_imputed = naive_imputer( X , strategy='mean', mode='bi-impute') # %% # * Use PCA analysis to reduce the dimension to down the important features # to predict the naive aquifer group (NGA). # Note that for PCA analysis, we can remove the only categorial features # "strata_name" and scaled the remaining features as follows: from watex.utils import to_numeric_dtypes from watex.utils import naive_scaler # pop_cat_features auto-drop the only categorial features Xpca = to_numeric_dtypes (data_imputed , pop_cat_features= True, reset_index=True, drop_index =True, verbose =True) # Scale the data by default Xpca_scaled = naive_scaler( Xpca ) Xpca_scaled_columns = list( Xpca_scaled.columns ) # * Call the normal PCA and plot all components set to None from watex.analysis import nPCA # %% # * Plot explained variance ratio pca = nPCA (Xpca_scaled , return_X= False, view = True ) # return PCA object rather than the reduced X # %% # As a comment, here 5/6 features are enough since the explained variance ratio is already # got 98 % # * Set the number of components and use a convenient plot the both components from watex.utils import plot_pca_components pca = nPCA (Xpca_scaled ,n_components=2, return_X=False ) # return object for plot purpose components = pca.components_ features = pca.feature_names_in_ plot_pca_components (components, feature_names= features, cmap='jet_r') # %% # As comments, the matrix plot shows the contributions of all features in the first and second components. # Indeed, while most contributions are got in-depth resistivity gamma and gamma short distance # they are negatively correlated with layer thickness and natural gamma. However, # no-correlation is found with the sp log data # In the second components, the depth and natural gamma are more corollated and inversely # correlated with the resistivity gamma, sp, and short distance. # whereas the quasi-null correlation exists with layer thickness. # By summarizing the PC1 and PC2 analysis, all features are useful as prediction # and one of them can be skipped. This validates the explained variance ratio where # under 8 features, after 7 dimensions, the explained variance ratio is already # reached 98 %. Therefore features skipped should not influence the result of # prediction # %% # * Auto-preprocess the data using the default pipe # Note that the categorical data "strata_name" is one-hot-encoded and # generate a sparse matrix ready for the data for prediction, then we will use the function 'make_naive_pipe' # to fast encode and transform the data as output. from watex.utils import make_naive_pipe # auto scaled the data and store it into a compressed sparse matrix format csr_data = make_naive_pipe(data_imputed, transform= True) # auto-scaled the data using StandardScaler and transform the data in place csr_data # %% # Prediction of Naive Group of Aquifer (NGA) # ============================================ # We randomly set the number of clusters to 05 which might correspond to # the number of aquifer groups in the survey area according to the geological information. # KMeans is used to predict the class label instead and plot the clusters from watex.exlib.sklearn import KMeans from watex.utils import plot_clusters # %% # * Group the principal two components of PCA into the 5 clusters km = KMeans (n_clusters =5 , init= 'random' ) ykm = km.fit_predict(pca.X ) km3c = KMeans (n_clusters =3 , init= 'random' ) ykm3 = km3c.fit_predict(pca.X ) # plot clusters into the general information of 5 groups of aquifers plot_clusters (5 , pca.X, ykm , km.cluster_centers_ ) #%% # * Plot the 03 clusters # Now test the sample lot with only 03 clusters as a theory group of aquifer # based on the distribution of the data. plot_clusters (3 , pca.X, ykm3 , km3c.cluster_centers_ ) #%% # * Plot the feature’s importance # We encode the strata_name and add it to the scale value and plot_the feature importance from watex.exlib.sklearn import RandomForestClassifier from watex.utils import plot_rf_feature_importances # add the strata_name to the remaining features strata_column = pd.Series ( X ['strata_name'].astype ('category').cat.codes , name ='strata_name' ) strata_column.index = range (len(strata_column)) # reindexing X_for_fi = pd.concat( [ strata_column , Xpca_scaled ], axis =1, ignore_index=True ) # # plot importance with the predicted label ykm X_for_fi=pd.DataFrame ( X_for_fi.values, columns= ['strata_name'] + Xpca_scaled_columns) plot_rf_feature_importances (RandomForestClassifier(), X_for_fi , y =ykm ) # %% # plot elbow to confirm or infirm the 05 clustering of aquifers from geological infos from watex.utils import plot_elbow plot_elbow(pca.X, n_clusters=11) # %% # As comments, we can see, the elbow is located at k=3 that i.e we can classify the aquifer # group based on the current datasets into three groups in hongliu coal mine. # Note that the dataset is only for boreholes, this can not confirm the # exact number of the aquifer. In the case study data applied in Honliu coal mine composed # of 11 boreholes, the number of 03 clusters is selected although the 05 clusters # do not indicate a bad clustering after a silhouette plot. The number of 03 is # finally ascertained using the Hierarchical Agglomerative clustering (HAC) dendrogram plot. # The step are enumerated below: # %% # Let’s confirm the 05 clusters using the silhouette plot from KMeans from watex.view import plotSilhouette # plot silhouette for the 05 clusters with pca reduced data plotSilhouette (pca.X, labels =ykm , prefit =True) # %% # Plot with the 03 custers; plot silhouette for the three clusters by # setting prefit to False since a new prediction should be made under the hood # after n-iterations to find the best clustering. Refer to # :func:`~watex.view.plotSilhouette` documentation. plotSilhouette (pca.X, n_clusters= 3 , prefit =False) #%% # Finally, we plot the dendrogram from HAC from watex.view import plotDendrogram plotDendrogram (pca.X , labels = ykm) # %% # As comments in the case of MXS target, merging the predicted y with cluster =5 # with create a lot of y=k33' where we expected to have a list a =balance target # with the true labels y (k1, k2 and k3 ) # therefore the cluster with 3 labels is used instead of 5 # thus the predicted NGA labels with true labels is combined with the # the true labels y for supervised learnings. Note that # the true labels are not altered by the predicted label y # not let plot the dendro-heat # %% # Before predicting the NGA labels, we can fit the aquifer group and find the # most representative of the true k labels to the predicted labels # test with the number of clusters set to 3 from watex.utils.hydroutils import find_aquifer_groups, classify_k # categorize the k-values using the default func yk_map =classify_k (y.k , default_func =True) groupobj = find_aquifer_groups (yk_map, ykm ) print(groupobj) # now make the prediction from watex.utils import predict_NGA_labels yNGA = predict_NGA_labels(pca.X, n_clusters= 3) # %% # Prediction of MXS target :math:`y*` # ===================================== # The prediction of MXS can simply be made by calling the function # :func:`~watex.utils.make_MXS_labels` or use the MXS class (:class:`~watex.methods.MXS` ) # of the module :mod:`~watex.methods.hydro` from watex.utils import make_MXS_labels yMXS = make_MXS_labels(y_true=yk_map , y_pred=yNGA ) # Let’s print the 12 firstMXS target print(yMXS[:12]) # %% # As a comment, the existing :math:`21` and math:`2*` in the :math:`y*(yMXS)` # indicates that there is a strong similarity found between label 2 in # the permeability coefficient dataset :math:`y` and the predicted `yNGA` labels. # This is validated by the group preponderance object above. Whilst, the math:`2*` # indicates that the label `2` in yNGA has no similarity found in :math:`y*(yMXS)`). # The label `3` in `yNGA` has no relationship with any labels in the :math:`y` # therefore no modification is occurred and kept safe. # If the parameter `return_obj` is set to True, it will return an MXS object # where many attributes like class mapping can be retrieved for understanding purposes. # for instance: mxso = make_MXS_labels(y_true=yk_map , y_pred=yNGA , return_obj=True ) # similar labels print(mxso.mxs_similarity_) # group classes for mapping print(mxso.mxs_group_classes_) #M XS class mapping. This is usefull to know the labels that have been # modified based on the similarity computation. print(mxso.mxs_classes_) # Once the :math:`y*(yMXS)` is predicted, the supervised learning model # training can be made with the predictor:math:`X`. # %% # A paper is under puclication in Engineering Geology for k-prediction which # explained a concrete study (Case study in Hongliu coal mine). See the # reference in the :ref:`citation ` page.