Wolfram Research

Function Repository Resource:

LineFit

Source Notebook

Fit a line to data points in n-dimensional space

Contributed by: Sander Huisman

ResourceFunction["LineFit"][pts]

returns a Line that fits best through the points pts.

ResourceFunction["LineFit"][pts,"Association"]

returns an Association containing properties of the best fit line.

Details

The returned function in the Association will correspond to a domain of 0 to 1.
The best fit is determined by minimizing the sum of squares of distances from the points to the best-fit line.

Examples

Basic Examples (2) 

Fit a line in 2D:

In[1]:=
pts = CompressedData["
1:eJwVl3cgFY7XxmUL2VtcXOu6xnWneY+dIpJUkqREafgpviF7FC0atGyiSSpZ
dY9VGqQks5KyKiI74vX+df4+5zznOZ9HzfeImx83FxdX6iourv+vB7a+sohJ
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"];
fit = ResourceFunction["LineFit"][pts]
Out[1]=

Compare the points and the fit:

In[2]:=
ListPlot[pts, Epilog -> {Red, fit}]
Out[2]=

Scope (2) 

Do a fit with points in 3D:

In[3]:=
pts = CompressedData["
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/g==
"];
fit = ResourceFunction["LineFit"][pts];
Graphics3D[{Point[pts], Red, Thick, fit}]
Out[3]=

Get a Dataset with all the fitting details:

In[4]:=
pts = CompressedData["
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"];
Dataset[ResourceFunction["LineFit"][pts, "Association"]]
Out[4]=

Properties and Relations (2) 

Compare the result of LineFit with the result of computing the orthogonal fit through the definition:

In[5]:=
pts = CompressedData["
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"];
fit1 = ResourceFunction["LineFit"][pts];
fit2 = InfiniteLine @@ Partition[
    NArgMin[Total[
      RegionDistance[
          InfiniteLine[{px, py, pz}, {vx, vy, vz}], #]^2 & /@ pts], {px, py, pz, vx, vy, vz}], 3];
In[6]:=
Simplify[RegionMember[fit1, {x, y, z}], {x, y, z} \[Element] Reals]
Out[6]=
In[7]:=
Simplify[RegionMember[fit2, {x, y, z}], {x, y, z} \[Element] Reals]
Out[7]=

The one-argument case of LineFit is equivalent to the resource function OrthogonalLineFit:

In[8]:=
pts = CompressedData["
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"];
fit1 = ResourceFunction["LineFit"][pts];
fit2 = ResourceFunction["OrthogonalLineFit"][pts];
In[9]:=
Simplify[RegionMember[fit1, {x, y}], {x, y} \[Element] Reals]
Out[9]=
In[10]:=
Simplify[RegionMember[fit2, {x, y}], {x, y} \[Element] Reals]
Out[10]=

Possible Issues (3) 

All points have to be numeric:

In[11]:=
ResourceFunction["LineFit"][{{1, 1}, {2, 3}, {2, b}}]
Out[11]=

All points have to be in the same dimension:

In[12]:=
ResourceFunction["LineFit"][{{1, 1}, {2, 3}, {1, 2, 3}}]
Out[12]=

Real numbers have to be used:

In[13]:=
ResourceFunction["LineFit"][{{1, 1}, {2, 3}, {1, 2 + I}}]
Out[13]=

Neat Examples (1) 

Do a fit in 10D:

In[14]:=
SeedRandom[1234];
n = 10;
m = 200;
a = Normalize[RandomVariate[NormalDistribution[], n]];
t = RandomVariate[NormalDistribution[0, 10], m];
pts = # a & /@ t;
pts += RandomVariate[NormalDistribution[0, 1], {m, n}];
ResourceFunction["LineFit"][pts, "Association"]
Out[14]=

Resource History

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