116 lines
4.5 KiB
Python
116 lines
4.5 KiB
Python
import scipy.stats
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import numpy as np
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from scipy.linalg import qr, inv, pinv
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import scipy.stats
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from progress.bar import Bar
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from matplotlib import pyplot as plt
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class SPA:
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def _projections_qr(self, X, k, M):
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X_projected = X.copy()
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norms = np.sum((X ** 2), axis=0)
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norm_max = np.amax(norms)
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X_projected.iloc[:, k] = X_projected.iloc[:, k] * 2 * norm_max / norms[k]
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_, __, order = qr(X_projected.to_numpy(), 0, pivoting=True)
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return order[:M].T
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def _validation(self, Xcal, ycal, var_sel, Xval=None, yval=None):
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N = Xcal.shape[0]
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NV = Xval.shape[0] if Xval is not None else 0
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yhat, e = None, None
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if NV > 0:
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Xcal_ones = np.hstack([np.ones((N, 1)), Xcal.iloc[:, var_sel].to_numpy()])
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b = np.linalg.lstsq(Xcal_ones, ycal, rcond=None)[0]
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Xval_ones = np.hstack([np.ones((NV, 1)), Xval.iloc[:, var_sel].to_numpy()])
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yhat = Xval_ones.dot(b)
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e = yval - yhat
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else:
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yhat = np.zeros((N, 1))
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for i in range(N):
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cal = np.hstack([np.arange(i), np.arange(i + 1, N)])
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X = Xcal.iloc[cal, var_sel]
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y = ycal.iloc[cal]
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X_ones = np.hstack([np.ones((N - 1, 1)), X.to_numpy()])
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b = np.linalg.lstsq(X_ones, y, rcond=None)[0]
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xtest = Xcal.iloc[i, var_sel].to_numpy()
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yhat[i] = np.hstack([1, xtest]).dot(b)
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e = ycal.to_numpy() - yhat
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return yhat, e
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def spa(self, Xcal, ycal, m_min=1, m_max=None, Xval=None, yval=None, autoscaling=1, save_path=None):
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N, K = Xcal.shape
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m_max = min(N - 1, K) if m_max is None else m_max
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normalization_factor = Xcal.std(ddof=1, axis=0) if autoscaling else np.ones(K)
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Xcaln = (Xcal - Xcal.mean()) / normalization_factor
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SEL = np.zeros((m_max, K))
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with Bar('Projections :', max=K) as bar:
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for k in range(K):
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SEL[:, k] = self._projections_qr(Xcaln, k, m_max)
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bar.next()
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PRESS = np.full((m_max + 1, K), np.inf)
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with Bar('Evaluating subsets:', max=K * (m_max - m_min + 1)) as bar:
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for k in range(K):
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for m in range(m_min, m_max + 1):
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var_sel = SEL[:m, k].astype(int)
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_, e = self._validation(Xcal, ycal, var_sel, Xval, yval)
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PRESS[m, k] = e.T @ e
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bar.next()
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m_sel = np.argmin(PRESS, axis=0)
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k_sel = np.argmin(np.min(PRESS, axis=0))
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var_sel_phase2 = SEL[:m_sel[k_sel], k_sel].astype(int)
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Xcal2 = np.hstack([np.ones((N, 1)), Xcal.iloc[:, var_sel_phase2].to_numpy()])
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b = np.linalg.lstsq(Xcal2, ycal, rcond=None)[0]
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std_deviation = Xcal2.std(ddof=1, axis=0)
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relev = np.abs(b * std_deviation)[1:]
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index_decreasing_relev = np.argsort(-relev)
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PRESS_scree = np.empty(len(var_sel_phase2))
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for i in range(len(var_sel_phase2)):
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var_sel = var_sel_phase2[index_decreasing_relev[:i + 1]]
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_, e = self._validation(Xcal, ycal, var_sel, Xval, yval)
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PRESS_scree[i] = np.conj(e).T @ e
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RMSEP_scree = np.sqrt(PRESS_scree / len(e))
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alpha = 0.25
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dof = len(e)
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fcrit = scipy.stats.f.ppf(1 - alpha, dof, dof)
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PRESS_crit = np.min(PRESS_scree) * fcrit
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i_crit = np.min(np.nonzero(PRESS_scree < PRESS_crit))
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i_crit = max(m_min, i_crit)
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var_sel = var_sel_phase2[index_decreasing_relev[:i_crit]]
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# 绘图
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plt.figure()
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# 设置字体为 Times New Roman
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plt.rcParams['font.sans-serif'] = ['Times New Roman']
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plt.rcParams['axes.unicode_minus'] = False # 确保负号显示正常
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# 设置标题、标签和网格
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plt.xlabel('Number of variables included in the model', fontsize=14)
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plt.ylabel('RMSE', fontsize=14)
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plt.title(f'Final number of selected variables: {len(var_sel)} (RMSE={RMSEP_scree[i_crit]:.4f})', fontsize=16)
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# 绘制 RMSEP 曲线
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plt.plot(RMSEP_scree, label='RMSEP Scree Plot')
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plt.scatter(i_crit, RMSEP_scree[i_crit], color='r', marker='s', label='Selected Point')
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# 添加网格和图例
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plt.grid(True)
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plt.legend()
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# 显示或保存图像
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if save_path:
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plt.savefig(save_path, bbox_inches='tight', dpi=300)
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print(f"图像已保存至: {save_path}")
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else:
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plt.show()
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return var_sel, var_sel_phase2
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def __repr__(self):
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return "SPA()" |