Manifold Learning from Numeric Data

Generate a "Swiss roll" dataset:

In[1]:=

data=Table[Insert[AngleVector[1+{2,8}*RandomReal[]],RandomReal[],2],1000];

In[2]:=

ListPointPlot3D[data,BoxRatios{1,1,1},PlotStyleDirective[PointSizeLarge]]

Out[2]=

Use

to train a nonlinear dimension reducer on the dataset. The dimension is reduced from 3 to 2:

In[3]:=

reducer=DimensionReduction[data,2,Method"Isomap"]

Out[3]=

DimensionReducerFunction

Input type: NumericalVector

(3)

Output dimension: 2



Find and visualize the data coordinates in the reduced space:

In[4]:=

reducedpts=reducer[data];ListPlot[Style[#,Hue[First[#]/20]]&/@reducedpts,AspectRatio1/2,PlotStyleDirective[PointSizeSmall]]

Out[4]=

Now visualize the dataset in the original space, with each point colored according to its reduced variable

u

:

In[5]:=

ListPointPlot3DStyle[#,Hue[First[reducer[#]]/20]]&/@data,



Out[5]=

Related Symbols