# Loss Functions :Loss Function Notation , Loss Functions for Regression , Loss Functions for Classification, Loss Functions for Reconstruction

1. Loss Function Notation:
• The notation used for loss functions typically involves L(y, f(x)), where y is the true target value and f(x) is the predicted output of the model for a given input x.
• The goal of a loss function is to measure the difference between the true target value and the predicted output of the model, which is often called the “loss” or “error”.
1. Loss Functions for Regression:
• Mean Squared Error (MSE) is a popular loss function for regression problems that measures the average squared difference between the predicted output and the true target value.
• Mean Absolute Error (MAE) is another popular loss function for regression problems that measures the average absolute difference between the predicted output and the true target value.
• Huber Loss is a hybrid loss function that combines MSE and MAE, and is useful in situations where the data contains outliers.
1. Loss Functions for Classification:
• Binary Cross-Entropy is a popular loss function for binary classification problems that measures the difference between the true target value and the predicted probability of belonging to the positive class.
• Categorical Cross-Entropy is a popular loss function for multi-class classification problems that measures the difference between the true target value and the predicted probability distribution over all possible classes.
• Hinge Loss is a loss function commonly used for support vector machines (SVMs) and measures the difference between the predicted output and the true target value.
1. Loss Functions for Reconstruction:
• Mean Squared Error (MSE) is a popular loss function for reconstruction problems that measures the average squared difference between the input data and the reconstructed output.
• Binary Cross-Entropy is a popular loss function for binary image reconstruction problems that measures the difference between the input data and the reconstructed output.
• Structural Similarity Index (SSIM) is a loss function commonly used for image reconstruction problems that measures the structural similarity between the input data and the reconstructed output.