Physics-based Features

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Physical properties of the wafer map if each failure points are assumed as point-like mass. Following features will be extracted:

1. Distance of the center of mass from the center
2. Moment of inertia when regarding the center as the rotational axis

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Implementation

def extract_physics(x):

  coor = np.argwhere(x==2)-(np.array(x.shape)//2)
  norm_distance = np.linalg.norm(x.shape, ord=2)

  physics = {}

  center_of_mass = np.linalg.norm(np.mean(coor, axis=0), ord=2)
  physics['center_of_mass'] = center_of_mass/norm_distance

  moment_of_inertia = np.sum(coor**2, axis=None)
  physics['moment_of_inertia'] = moment_of_inertia/(np.sum(x==2)*(norm_distance**2))

  return pd.Series(physics)

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Visualization

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Evaluation

Control: Density-based + Radon-based + Geometry-based Estimator 1 (LR) :           Accuracy : 62.51%           AUC : 0.9142 Estimator 2 (RF) :           Accuracy : 80.08%           AUC : 0.9752 Estimator 3 (GBM) :           Accuracy : 79.53%           AUC : 0.9708 Estimator 4 (ANN) :           Accuracy : 67.76%           AUC : 0.9360

Experiment: Density-based + Radon-based + Geometry-based + *Physics-based Estimator 1 (LR) :           Accuracy : 63.53%           AUC : 0.9221 Estimator 2 (RF) :           Accuracy : 80.55%           AUC : 0.9757 Estimator 3 (GBM) :           Accuracy : 78.82%           AUC : 0.9726 Estimator 4 (ANN) :           Accuracy : 66.35%           AUC : 0.9331

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Analysis

Showed minor improvement on LR and RF but minor deterioration on other classifiers.