One possible way to operationalize the requirement "When the point in the denser area, it has greater weight" is to weight each point by the number of neighbors within a specified distance:
nf = Nearest[pts];
radius = 50;
weightedData = WeightedData[pts, Length[nf[#, {All, radius}]] & /@ pts];
center = Mean[weightedData];
ListPlot[pts, Epilog -> {Red, PointSize[.02], Point[Mean[pts]], Green, Point @ center}]
With radius = 100 we get
One possible way:
nf = Nearest[pts];
radius = 50;
weightedData = WeightedData[pts, Length[nf[#, {All, radius}]] & /@ pts];
center = Mean[weightedData];
ListPlot[pts, Epilog -> {Red, PointSize[.02], Point[Mean[pts]], Green, Point @ center}]
With radius = 100 we get
One possible way to operationalize the requirement "When the point in the denser area, it has greater weight" is to weight each point by the number of neighbors within a specified distance:
nf = Nearest[pts];
radius = 50;
weightedData = WeightedData[pts, Length[nf[#, {All, radius}]] & /@ pts];
center = Mean[weightedData];
ListPlot[pts, Epilog -> {Red, PointSize[.02], Point[Mean[pts]], Green, Point @ center}]
With radius = 100 we get
One possible way:
nf = Nearest[pts];
radius = 50;
weightedData = WeightedData[pts, Length[nf[#, {All, radius}]] & /@ pts];
center = Mean[weightedData];
ListPlot[pts, Epilog -> {Red, PointSize[.02], Point[Mean[pts]], Green, Point @ center}]
With radius = 100 we get