Time-series Anomaly Detection by PCA (3)

PCA에서의 Explainable AI다. [1] 논문에서는 complete decomposition contribution (CDC), partial decompostition contribution (PDC), diagonal contribution (DC), reconstruction-based contribution (RBC), angle-based contribution (ABC)를 비교하고, 위 방법들에다가 relative contribution을 적용하는 방법을 제안하였다. Simulation study로 특정 센서에 임의로 fault를 일으켜 그 센서에서 contribution 값이 실제로 증가하는지를 실험/증명하였는데, CDC를 제외하고는 대체로 비슷한 성능을 보였다. CDC와 PDC만 빠르게 구현해보았다.

# CDC_Tsq_index
C = np.dot(U[:, :num_comp], inv(np.sqrt(S_inv)))
C = np.dot(C, U[:, :num_comp].T)
CDC_Tsq_index = np.square(np.dot(C, X_test[fault_num].T))

for i in range(0, CDC_Tsq_index.shape[0]):
    plt.plot(CDC_Tsq_index[i])
plt.show()

# CDC_SPE_index
C = np.dot(U[:, num_comp:], U[:, num_comp:].T)
CDC_SPE_index = np.square(np.dot(C, X_test[fault_num].T))

for i in range(0, CDC_SPE_index.shape[0]):
    plt.plot(CDC_SPE_index[i])
plt.show()

# PDC_Tsq_index
C = np.dot(np.dot(U[:, :num_comp], S_inv), U[:, :num_comp].T)

for i in range(0, C.shape[0]):
    # contribution for each variable
    CI = np.dot(X_test[fault_num], C)[i, :]
    # partial decompostion contribution
    plt.plot(np.dot(X_test[fault_num], CI))
    
plt.show()

# PDC_SPE_index
C = np.dot(U[:, num_comp:], U[:, num_comp:].T)

for i in range(0, C.shape[0]):
    # contribution for each variable
    CI = np.dot(X_test[fault_num], C)[i, :]
    # partial decompostion contribution
    plt.plot(np.dot(X_test[fault_num], CI))
    
plt.show()

 

References

[1] C. F. Alcala et al., Analysis and generalization of fault diagnosis methods for process monitoring, J. of Process Control, 2011