function?mappedX=?LE（X?no_dims?k?sigma）
%LAPLACIAN_EIGEN?Performs?non-linear?dimensionality?reduction?using?Laplacian?Eigenmaps
%
%???[mappedX?mapping]?=?laplacian_eigen（X?no_dims?k?sigma?eig_impl）
%
%?Performs?non-linear?dimensionality?reduction?using?Laplacian?Eigenmaps.
%?The?data?is?in?matrix?X?in?which?the?rows?are?the?observations?and?the
%?columns?the?dimensions.?
%?The?reduced?data?is?returned?in?the?matrix?mappedX.

????if?~exist（‘no_dims‘?‘var‘）
????????no_dims?=?2;
????end
????if?~exist（‘k‘?‘var‘）
????????k?=?12;
????end
	if?~exist（‘sigma‘?‘var‘）
		sigma?=?1;
????end
??
????%?Construct?neighborhood?graph
????disp（‘Constructing?neighborhood?graph...‘）;
????if?size（X?1）?????????G?=?squareform（pdist（X?‘euclidean‘））;
????????%?Compute?neighbourhood?graph
????????[tmp?ind]?=?sort（G）;?
????????for?i=1:size（G?1）
????????????G（i?ind（（2?+?k）:end?i））?=?0;?
????????end
????????G?=?sparse（double（G））;
????????G?=?max（G?G‘）;?????????????%?Make?sure?distance?matrix?i