Answers.Body: <p><span class="math-container">$F$</span> in this context is the output of the Convolutional Neural Network that's being trained, which is of the same size as <span class="math-container">$X$</span>.   </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-07-18T15:22:10.760Z
Answers.Text: That makes total sense, because $\hat{y}$ is missing in the equation. Thank you.
Answers.UserDisplayName: oezguensi
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-07-18T15:13:04.387Z
Answers.LastActivityDate: 2019-07-18T18:03:08.133Z
Answers.LastEditDate: 2019-07-18T18:03:08.133Z
Answers.UserDisplayName: mshlis
Body: <p>I would like to implement the approach represented in <a href="https://arxiv.org/pdf/1811.06861.pdf" rel="nofollow noreferrer">this</a> paper. Here they used following reconstruction loss:</p>
  
  <p><span class="math-container">$$
  L(X)= \frac{\lambda \cdot || M \odot (X - F(\overline{M} \odot X)) ||_{1} + (1 - \lambda) \cdot || \overline{M} \odot (X - F(\overline{M} \odot X)) ||_{1}}{N}
  $$</span></p>
  
  <p>Unfortunately, the author does not explain the function <span class="math-container">$F$</span>.
  Does someone know a similar function or could understand the function's purpose from the context?</p>
  
Tags: <convolutional-neural-networks><papers><anomaly-detection>
Title: Understanding the reconstruction loss in the paper "Anomaly Detection using Deep Learning based Image Completion"
UserDisplayName: oezguensi
ThreadText: # Understanding the reconstruction loss in the paper "Anomaly Detection using Deep Learning based Image Completion"
  
  (Asked by: username_0 on 2019-07-18)
  
  I would like to implement the approach represented in [this](https://arxiv.org/pdf/1811.06861.pdf) paper. Here they used following reconstruction loss:
  
  $$
  L(X)= \frac{\lambda \cdot || M \odot (X - F(\overline{M} \odot X)) ||\_{1} + (1 - \lambda) \cdot || \overline{M} \odot (X - F(\overline{M} \odot X)) ||\_{1}}{N}
  $$
  
  Unfortunately, the author does not explain the function $F$.
  Does someone know a similar function or could understand the function's purpose from the context?
  
  **Tags:** convolutional-neural-networks, papers, anomaly-detection
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2019-07-18. Score: 1 | Accepted answer
  
  $F$ in this context is the output of the Convolutional Neural Network that's being trained, which is of the same size as $X$.
  
  > **Comments:**
  > **username_0**: That makes total sense, because $\hat{y}$ is missing in the equation. Thank you.  
  
  ---
  
  