178 lines
6.5 KiB
Python
178 lines
6.5 KiB
Python
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# mlxtend Machine Learning Library Extensions
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#
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# A function for plotting a PCA correlation circle
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# File Author: Gabriel Azevedo Ferreira <az.fe.gabriel@gmail.com>
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import numpy as np
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import matplotlib.pyplot as plt
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import pandas as pd
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from mlxtend.externals.adjust_text import adjust_text
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from mlxtend.feature_extraction import PrincipalComponentAnalysis
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def corr2_coeff(A, B):
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"""
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Compute correlation coefficients and return as a np array
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"""
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A, B = np.array(A), np.array(B)
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# Rowwise mean of input arrays & subtract from input arrays themeselves
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A_mA = A - A.mean(1)[:, None]
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B_mB = B - B.mean(1)[:, None]
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# Sum of squares across rows
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ssA = (A_mA**2).sum(1)
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ssB = (B_mB**2).sum(1)
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# Finally get corr coeff
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return np.dot(A_mA, B_mB.T) / np.sqrt(np.dot(ssA[:, None], ssB[None]))
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def create_correlation_table(A, B, names_cols_A, names_cols_B):
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"""
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Compute correlation coefficients and return as a DataFrame.
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A and B: 2d array like.
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The columns represent the different variables and the rows are
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the samples of thos variables
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names_cols_A/B : name to be added to the final pandas table
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return: pandas DataFrame with the corelations.Columns and Indexes
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represent the different variables of A and B (respectvely)
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"""
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# corrs = np.corrcoef(np.transpose(A), np.transpose(B)
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# )[len(names_cols_A):, :len(names_cols_A)]
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corrs = corr2_coeff(A.T, B.T).T
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df_corrs = pd.DataFrame(corrs,
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columns=names_cols_A, index=names_cols_B)
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return df_corrs
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def plot_pca_correlation_graph(X, variables_names, dimensions=(1, 2),
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figure_axis_size=6, X_pca=None,
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explained_variance=None):
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"""
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Compute the PCA for X and plots the Correlation graph
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Parameters
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----------
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X : 2d array like.
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The columns represent the different variables and the rows are the
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samples of thos variables
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variables_names : array like
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Name of the columns (the variables) of X
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dimensions: tuple with two elements.
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dimensions to be plotted (x,y)
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figure_axis_size :
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size of the final frame. The figure created is a square with length
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and width equal to figure_axis_size.
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X_pca : np.ndarray, shape = [n_samples, n_components].
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Optional.
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`X_pca` is the matrix of the transformed components from X.
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If not provided, the function computes PCA automatically using
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mlxtend.feature_extraction.PrincipalComponentAnalysis
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Expected `n_componentes >= max(dimensions)`
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explained_variance : 1 dimension np.ndarray, length = n_components
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Optional.
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`explained_variance` are the eigenvalues from the diagonalized
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covariance matrix on the PCA transformatiopn.
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If not provided, the function computes PCA independently
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Expected `n_componentes == X.shape[1]`
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Returns
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----------
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matplotlib_figure, correlation_matrix
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Examples
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-----------
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For usage examples, please see
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http://rasbt.github.io/mlxtend/user_guide/plotting/plot_pca_correlation_graph/
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"""
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X = np.array(X)
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X = X - X.mean(axis=0)
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n_comp = max(dimensions)
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if (X_pca is None) and (explained_variance is None):
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pca = PrincipalComponentAnalysis(n_components=n_comp)
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pca.fit(X)
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X_pca = pca.transform(X)
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explained_variance = pca.e_vals_
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elif (X_pca is not None) and (explained_variance is None):
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raise ValueError("If `X_pca` is not None, the `explained variance`"
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" values should not be `None`.")
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elif (X_pca is None) and (explained_variance is not None):
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raise ValueError("If `explained variance` is not None, the `X_pca`"
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" values should not be `None`.")
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elif (X_pca is not None) and (explained_variance is not None):
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if X_pca.shape[1] != len(explained_variance):
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raise ValueError(f"Number of principal components must "
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f"match the number "
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f"of eigenvalues. Got "
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f"{X_pca.shape[1]} "
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f"!= "
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f"{len(explained_variance)}")
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if X_pca.shape[1] < n_comp:
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raise ValueError(f"Input array `X_pca` contains fewer principal"
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f" components than expected based on `dimensions`."
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f" Got {X_pca.shape[1]} components in X_pca, expected"
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f" at least `max(dimensions)={n_comp}`.")
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if len(explained_variance) < n_comp:
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raise ValueError(f"Input array `explained_variance` contains fewer"
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f" elements than expected. Got"
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f" {len(explained_variance)} elements, expected"
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f"`X.shape[1]={X.shape[1]}`.")
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corrs = create_correlation_table(X_pca, X, ['Dim ' + str(i + 1) for i in
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range(n_comp)],
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variables_names)
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tot = sum(X.var(0)) * X.shape[0] / (X.shape[0] - 1)
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explained_var_ratio = [(i / tot) * 100 for i in explained_variance]
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# Plotting circle
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fig_res = plt.figure(figsize=(figure_axis_size, figure_axis_size))
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plt.Circle((0, 0), radius=1, color='k', fill=False)
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circle1 = plt.Circle((0, 0), radius=1, color='k', fill=False)
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fig = plt.gcf()
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fig.gca().add_artist(circle1)
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# Plotting arrows
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texts = []
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for name, row in corrs.iterrows():
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x = row['Dim ' + str(dimensions[0])]
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y = row['Dim ' + str(dimensions[1])]
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plt.arrow(0.0, 0.0, x, y, color='k', length_includes_head=True,
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head_width=.05)
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plt.plot([0.0, x], [0.0, y], 'k-')
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texts.append(plt.text(x, y, name, fontsize=2 * figure_axis_size))
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# Plotting vertical lines
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plt.plot([-1.1, 1.1], [0, 0], 'k--')
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plt.plot([0, 0], [-1.1, 1.1], 'k--')
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# Adjusting text
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adjust_text(texts)
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# Setting limits and title
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plt.xlim((-1.1, 1.1))
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plt.ylim((-1.1, 1.1))
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plt.title("Correlation Circle", fontsize=figure_axis_size * 3)
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plt.xlabel("Dim " + str(dimensions[0]) + " (%s%%)" %
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str(explained_var_ratio[dimensions[0] - 1])[:4],
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fontsize=figure_axis_size * 2)
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plt.ylabel("Dim " + str(dimensions[1]) + " (%s%%)" %
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str(explained_var_ratio[dimensions[1] - 1])[:4],
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fontsize=figure_axis_size * 2)
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return fig_res, corrs
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