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import pandas as pd |
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import numpy as np |
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from sklearn.decomposition import PCA as pca |
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from sklearn.preprocessing import StandardScaler as stscale |
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from sklearn.preprocessing import Imputer |
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import scipy.stats as stats |
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from scipy import stats, linalg |
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import numpy as np |
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import matplotlib.pyplot as plt |
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from matplotlib.pyplot import cm |
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View Code Duplication |
def partial_corr(C): |
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""" |
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Returns the sample linear partial correlation coefficients between pairs of variables in C, controlling |
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for the remaining variables in C. |
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Partial Correlation in Python (clone of Matlab's partialcorr) |
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This uses the linear regression approach to compute the partial |
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correlation (might be slow for a huge number of variables). The |
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algorithm is detailed here: |
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http://en.wikipedia.org/wiki/Partial_correlation#Using_linear_regression |
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Taking X and Y two variables of interest and Z the matrix with all the variable minus {X, Y}, |
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the algorithm can be summarized as |
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1) perform a normal linear least-squares regression with X as the target and Z as the predictor |
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2) calculate the residuals in Step #1 |
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3) perform a normal linear least-squares regression with Y as the target and Z as the predictor |
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4) calculate the residuals in Step #3 |
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5) calculate the correlation coefficient between the residuals from Steps #2 and #4; |
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The result is the partial correlation between X and Y while controlling for the effect of Z |
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Date: Nov 2014 |
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Author: Fabian Pedregosa-Izquierdo, [email protected] |
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Testing: Valentina Borghesani, [email protected] |
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Parameters |
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---------- |
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C : array-like, shape (n, p) |
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Array with the different variables. Each column of C is taken as a variable |
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Returns |
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------- |
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P : array-like, shape (p, p) |
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P[i, j] contains the partial correlation of C[:, i] and C[:, j] controlling |
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for the remaining variables in C. |
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""" |
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C = np.asarray(C) |
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p = C.shape[1] |
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P_corr = np.zeros((p, p), dtype=np.float) |
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for i in range(p): |
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P_corr[i, i] = 1 |
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for j in range(i+1, p): |
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idx = np.ones(p, dtype=np.bool) |
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idx[i] = False |
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idx[j] = False |
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beta_i = linalg.lstsq(C[:, idx], C[:, j])[0] |
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beta_j = linalg.lstsq(C[:, idx], C[:, i])[0] |
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res_j = C[:, j] - C[:, idx].dot( beta_i) |
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res_i = C[:, i] - C[:, idx].dot(beta_j) |
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corr = stats.pearsonr(res_i, res_j)[0] |
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P_corr[i, j] = corr |
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P_corr[j, i] = corr |
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return P_corr |
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View Code Duplication |
def kmo(dataset): |
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""" |
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Calculates the Kaiser-Meyer-Olkin measure on an input dataset. |
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Based on calculations shown here: |
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http://www.statisticshowto.com/kaiser-meyer-olkin/ |
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-- 0.00-0.49 unacceptable |
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-- 0.50-0.59 miserable |
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-- 0.60-0.69 mediocre |
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-- 0.70-0.79 middling |
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-- 0.80-0.89 meritorious |
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-- 0.90-1.00 marvelous |
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Parameters |
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---------- |
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dataset : array-like, shape (n, p) |
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Array containing n samples and p features. Must have no NaNs. |
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Ideally scaled before performing test. |
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Returns |
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------- |
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mo : KMO test value |
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""" |
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#Correlation matrix and the partial covariance matrix. |
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corrmatrix = np.corrcoef(dataset.transpose()) |
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pcorr = partial_corr(dataset) |
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#Calculation of the KMO statistic |
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matrix = corrmatrix*corrmatrix |
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rows = matrix.shape[0] |
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cols = matrix.shape[1] |
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rij = 0 |
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uij = 0 |
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for row in range(0, rows): |
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for col in range(0, cols): |
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if not row == col: |
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rij = rij + matrix[row, col] |
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uij = uij + pcorr[row, col] |
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mo = rij/(rij+uij) |
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print(mo) |
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return mo |
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View Code Duplication |
def pca_analysis(dataset, dropcols=[], imputenans=True, scale=True, n_components=5): |
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""" |
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Performs a primary component analysis on an input dataset |
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Parameters |
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---------- |
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dataset : pandas dataframe of shape (n, p) |
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Input dataset with n samples and p features |
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dropcols : list |
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Columns to exclude from pca analysis. At a minimum, user must exclude |
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non-numeric columns. |
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imputenans : boolean |
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If True, impute NaN values as column means. |
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scale : boolean |
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If True, columns will be scaled to a mean of zero and a standard deviation of 1. |
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n_components : integer |
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Desired number of components in principle component analysis. |
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Returns |
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------- |
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dataset_scaled : numpy array of shape (n, p) |
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Scaled dataset with n samples and p features |
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dataset_pca : Pandas dataframe of shape (n, n_components) |
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Output array of n_component features of each original sample |
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dataset_final : Pandas dataframe of shape (n, p+n_components) |
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Output array with principle components append to original array. |
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prcs : Pandas dataframe of shape (5, n_components) |
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Output array displaying the top 5 features contributing to each |
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principle component. |
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prim_vals : Dictionary of lists |
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Output dictionary of of the pca scores for the top 5 features |
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contributing to each principle component. |
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components : Pandas dataframe of shape (p, n_components) |
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Raw pca scores. |
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Examples |
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-------- |
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""" |
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dataset_num = dataset.drop(dropcols, axis=1) |
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dataset_raw = dataset.as_matrix() |
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if imputenans: |
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imp = Imputer(missing_values='NaN', strategy='mean', axis=0) |
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imp.fit(dataset_raw) |
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dataset_clean = imp.transform(dataset_raw) |
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else: |
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dataset_clean = dataset_raw |
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if scale: |
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scaler = stscale() |
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scaler.fit(dataset_clean) |
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dataset_scaled = scaler.transform(dataset_clean) |
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else: |
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dataset_scaled = dataset_clean |
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pca1 = pca(n_components=n_components) |
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pca1.fit(dataset_scaled) |
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#Cumulative explained variance ratio |
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x = 0 |
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explained_v = pca1.explained_variance_ratio_ |
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print('Cumulative explained variance:') |
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for i in range(0, n_components): |
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x = x + explained_v[i] |
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print('{} component: {}'.format(i, x)) |
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prim_comps = {} |
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prim_vals = {} |
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comps = pca1.components_ |
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components = pd.DataFrame(comps.transpose()) |
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for num in range(0, n_components): |
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highest = np.abs(components[num]).as_matrix().argsort()[-5:][::-1] |
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pels = [] |
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prim_vals[num] = components[num].as_matrix()[highest] |
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for col in highest: |
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pels.append(dataset.columns[col]) |
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prim_comps[num] = pels |
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#Main contributors to each primary component |
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prcs = pd.DataFrame.from_dict(prim_comps) |
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dataset_pca = pd.DataFrame(pca1.transform(dataset_scaled)) |
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dataset_final = pd.concat([dataset, dataset_pca], axis=1) |
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return dataset_scaled, dataset_pca, dataset_final, prcs, prim_vals, components |
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View Code Duplication |
def plot_pca(datasets, figsize=(8, 8), lwidth=8.0, |
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labels = ['Sample1', 'Sample2'], savefig=True, filename='test.png'): |
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""" |
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Plots the average output features from a PCA analysis in polar coordinates. |
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Parameters |
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---------- |
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datasets : dictionary (keys = n) of numpy arrays of shape p |
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Dictionary with n samples and p features to plot. |
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figize : list |
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Dimensions of output figure e.g. (8, 8) |
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lwidth : float |
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Width of plotted lines in figure |
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labels : list of string |
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Labels to display in legend. |
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savefig : boolean |
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If True, saves figure |
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filename : string |
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Desired output filename |
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Returns |
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------- |
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""" |
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fig = plt.figure(figsize=figsize) |
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for key in datasets: |
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N = datasets[key].shape[0] |
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width = (2*np.pi) / N |
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color=iter(cm.viridis(np.linspace(0,1,N))) |
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theta = np.linspace(0.0, 2 * np.pi, N+1, endpoint=True) |
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radii = {} |
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bars = {} |
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ax = plt.subplot(111, polar=True) |
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counter = 0 |
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for key in datasets: |
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c=next(color) |
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radii[key] = np.append(datasets[key], datasets[key][0]) |
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bars[key] = ax.plot(theta, radii[key], linewidth=lwidth, color=c, label=labels[counter]) |
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counter = counter + 1 |
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plt.legend(bbox_to_anchor=(0.90, 1), loc=2, borderaxespad=0., frameon=False, fontsize=20) |
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# # Use custom colors and opacity |
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# for r, bar in zip(radii, bars): |
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# bar.set_facecolor(plt.cm.jet(np.abs(r / 2.5))) |
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# bar.set_alpha(0.8) |
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ax.set_xticks(np.pi/180. * np.linspace(0, 360, N, endpoint=False)) |
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ax.set_xticklabels(list(range(0, N))) |
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if savefig: |
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plt.savefig(filename, bbox_inches='tight') |
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plt.show() |
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ccurtis7 /
diff_classifier
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