[Data regression] Levenberg-Marquardt BUT force to intersect 2 KNWON points

In summary, the speaker is using the Levenberg-Marquardt method to estimate the best polynomial function for a large data set with two known data points. They have considered weighting the known points but have not found a correct solution yet. They are open to other ideas and have been working on this for over a week.
  • #1
berlinkind
1
0
Hi,

I have a large data set (2D Coordinates with errors) and i am using the Levenberg-Marquardt method to estimate the best polynomial function.
That part is working fine.

Now in my data set are exactly two KNOWN data points that are 100% correct. Therefore I want my function to go through these two points and fit the curve considering the other datapoints.

My polynom currently looks like
[tex]
y=a_3*x^3+a_2*x^2+a_1*x+a_0
[/tex]

One idea I had, was to weight the two known points with very high values. But the result still is not correct.

Any Ideas – or maybe an idea of a totally other solution is welcome. I'm working more than a week on LM :-(

Thanks
 
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  • #2
Well, if your function must go through (x1, y1) and (x2, y2) exactly, then you can use those values to calculate a2 and a3, given a1 and a0 (find the formula for them by hand). So instead of optimizing a function in 4 parameters you just optimize a function in 2 parameters, a1 and a0.
 

What is data regression?

Data regression is a statistical method used to analyze and model the relationship between two or more variables. It helps to identify patterns and trends in the data and make predictions based on the observed data.

What is Levenberg-Marquardt?

Levenberg-Marquardt is an algorithm used in data regression to minimize the sum of squared errors between the predicted values and the actual values. It is commonly used in nonlinear regression problems.

How does Levenberg-Marquardt work?

Levenberg-Marquardt works by iteratively adjusting the parameters of a mathematical model to minimize the sum of squared errors. This is achieved by combining the gradient descent method and the Gauss-Newton method.

Why is it necessary to force the regression line to intersect two known points?

Forcing the regression line to intersect two known points helps to improve the accuracy of the model by ensuring that it passes through the specific points of interest. This can be helpful in situations where the data is not evenly distributed or when there is a known relationship between the two variables being analyzed.

What are some applications of Levenberg-Marquardt in data regression?

Levenberg-Marquardt is commonly used in a variety of fields, including economics, engineering, and science, for data analysis and prediction. It can be used to model nonlinear relationships, such as in population growth or stock market trends, and to make forecasts based on historical data.

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