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Say I have a set of points in 2D space. How would I find a line that maximizes the sum orthogonal projection of the points onto the line. The line does not have to go through the origin.
mfb said:@chiro: The problem is two-dimensional anyway.
@googleadbot: The video gives a formula for the quality of the separation. You can parameterize your line and express the quality as function of those two parameters. Then you have to minimize/maximize it: Find points where both derivatives (in the line parameters) are 0.
mfb said:@chiro: The problem is two-dimensional anyway.
@googleadbot: The video gives a formula for the quality of the separation. You can parameterize your line and express the quality as function of those two parameters. Then you have to minimize/maximize it: Find points where both derivatives (in the line parameters) are 0.
They just differ in their length, not in their direction (up to the sign, and in 2D).Doesn't the line have an infinite number of normal vectors corresponding to it?
A line maximizing orthogonal projection is a mathematical concept in which a line is drawn through a set of points in such a way that the distance between the points and the line is minimized, thus creating the most accurate representation of the data.
A line maximizing orthogonal projection is calculated using linear regression techniques, such as the method of least squares. This involves finding the line that minimizes the sum of the squared distances between the points and the line.
The purpose of using a line maximizing orthogonal projection is to find the best-fitting line through a set of data points, which can then be used to make predictions or identify patterns in the data. It is commonly used in statistical analysis and data visualization.
Line maximizing orthogonal projections are commonly used in various fields, such as finance, economics, engineering, and biology, to analyze and interpret data. They can also be used in image processing, computer graphics, and machine learning algorithms.
One limitation of using line maximizing orthogonal projections is that it assumes a linear relationship between the variables being analyzed. If the relationship is non-linear, the projection may not accurately represent the data. Additionally, outliers in the data can significantly affect the results of the projection.