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Recently, deep learning-based algorithms are widely adopted due to theadvantage of being able to establish anomaly detection models without or withminimal domain knowledge of the task. Instead, to train the artificial neuralnetwork more stable, it should be better to define the appropriate neuralnetwork structure or the loss function. For the training anomaly detectionmodel, the mean squared error (MSE) function is adopted widely. On the otherhand, the novel loss function, logarithmic mean squared error (LMSE), isproposed in this paper to train the neural network more stable. This studycovers a variety of comparisons from mathematical comparisons, visualization inthe differential domain for backpropagation, loss convergence in the trainingprocess, and anomaly detection performance. In an overall view, LMSE issuperior to the existing MSE function in terms of strongness of lossconvergence, anomaly detection performance. The LMSE function is expected to beapplicable for training not only the anomaly detection model but also thegeneral generative neural network.

Concise Logarithmic Loss Function for Robust Training of Anomaly Detection Model