The L1 norm, also known as the Manhattan norm or taxicab norm, is a mathematical concept used to measure the magnitude of a vector in a multi-dimensional space. It is calculated by summing the absolute values of the vector's components.
In the context of minimal solution, the L1 norm is used to find the solution that minimizes the distance between the observed data and the estimated model. This is achieved by minimizing the sum of the absolute differences between the observed data and the predicted data.
The main difference between L1 norm and L2 norm is the way they measure the magnitude of a vector. While the L1 norm uses the sum of absolute values, the L2 norm uses the square root of the sum of squared values. Additionally, the L1 norm is more robust to outliers compared to the L2 norm.
The minimal L1 norm solution has various applications in different fields such as signal processing, image and video processing, and machine learning. It is used for tasks such as denoising, feature selection, and regression, to name a few.
One of the main advantages of using minimal L1 norm solution is its ability to handle outliers in the data. It is also computationally efficient and has a unique solution, unlike other methods such as L2 norm which may have multiple solutions. Additionally, it can handle high-dimensional data and is robust to noise.