Wolfram ResearchProductsPurchasingServices & ResourcesAbout UsOur Sites
DOCUMENTATION CENTER SEARCH
Mathematica >
Mathematica TutorialFunctions »

Using Nearest

Nearest is used to find elements in a list that are closest to a given data point.
Nearest[{elem1,elem2,...},x]give the list of elemi to which x is nearest
Nearest[{elem1->v1,elem2->v2,...},x]
give the vi corresponding to the elemi to which x is nearest
Nearest[{elem1,elem2,...}->{v1,v2,...},x]
give the same result
Nearest[{elem1,elem2,...}->Automatic,x]
take the vi to be the integers 1, 2, 3, ...
Nearest[data,x,n]give the n nearest elements to x
Nearest[data,x,{n,r}]give up to the n nearest elements to x within a radius r
Nearest[data]generate a NearestFunction[...] which can be applied repeatedly to different x

Nearest function.

Nearest works with numeric lists, tensors, or a list of strings.
This finds the elements nearest to 4.5.
In[1]:=
Click for copyable input
Out[1]=
This finds 3 elements nearest to 4.5.
In[2]:=
Click for copyable input
Out[2]=
This finds all elements nearest to 4.5 within a radius of 2.
In[3]:=
Click for copyable input
Out[3]=
This finds the points nearest to {1, 2} in 2D.
In[4]:=
Click for copyable input
Out[4]=
This finds the nearest string to "cat".
In[5]:=
Click for copyable input
Out[5]=
The rule-based data syntax lets you use nearest elements to return their labels.
Here two-dimensional points are labeled.
In[6]:=
Click for copyable input
Out[6]=
In[7]:=
Click for copyable input
Out[7]=
This labels the elements using successive integers.
In[8]:=
Click for copyable input
Out[8]=
If Nearest is to be applied repeatedly to the same numerical data, you can get significant performance gains by first generating a NearestFunction.
This generates a set of 10,000 points in 2D and a NearestFunction.
In[9]:=
Click for copyable input
Out[9]=
This finds points in the set that are closest to the 10 target points.
In[10]:=
Click for copyable input
Out[10]=
It takes much longer if NearestFunction is not used.
In[11]:=
Click for copyable input
Out[11]=
In[12]:=
Click for copyable input
Out[12]=
option name
default value
DistanceFunctionAutomaticthe distance metric to use

Options for Nearest.

For numerical data, by default Nearest uses the EuclideanDistance. For strings, EditDistance is used.
© 2008 Wolfram Research, Inc. japanese.gif
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team