function?[eigvector?eigvalue?elapse]?=?LPP（W?options?data）
%?LPP:?Locality?Preserving?Projections
%
%???????[eigvector?eigvalue]?=?LPP（W?options?data）
%?
%?????????????Input:
%???????????????data???????-?Data?matrix.?Each?row?vector?of?fea?is?a?data?point.
%???????????????W???????-?Affinity?matrix.?You?can?either?call?“constructW“
%?????????????????????????to?construct?the?W?or?construct?it?by?yourself.
%???????????????options?-?Struct?value?in?Matlab.?The?fields?in?options
%?????????????????????????that?can?be?set:
%???????????????????????????
%?????????????????????????Please?see?LGE.m?for?other?options.
%
%?????????????Output:
%???????????????eigvector?-?Each?column?is?an?embedding?function?for?a?new
%???????????????????????????data?point?（row?vector）?x??y?=?x*eigvector
%???????????????????????????will?be?the?embedding?result?of?x.
%???????????????eigvalue??-?The?sorted?eigvalue?of?LPP?eigen-problem.?
%???????????????elapse????-?Time?spent?on?different?steps?
%?
%
%????Examples:
%
%???????fea?=?rand（5070）;
%???????options?=?[];
%???????options.Metric?=?‘Euclidean‘;
%???????options.NeighborMode?=?‘KNN‘;
%???????options.k?=?5;
%???????options.WeightMode?=?‘HeatKernel‘;
%???????options.t?=?5;
%???????W?=?constructW（feaoptions）;
%???????options.PCARatio?=?0.99
%???????[eigvector?eigvalue]?=?LPP（W?options?fea）;
%???????Y?=?fea*eigvector;
%???????
%???????
%???????fea?=?rand（5070）;
%???????gnd?=?[ones（101）;ones（151）*2;ones（101）*3;ones（151）*4];
%???????options?=?[];
%???????options.Metric?=?‘Euclidean‘;
%???????options.NeighborMode?=?‘Supervised‘;
%???????options.gnd?=?gnd;
%???????options.bLDA?=?1;
%???????W?=?constructW（feaoptions）;??????
%???????options.PCARatio?=?1;
%???????[eigvector?eigvalue]?=?LPP（W?options?fea）;
%???????Y?=?fea*eigvector;
%?
%?
%?Note:?After?applying?some?simple?algebra?the?smallest?eigenvalue?problem:
%				data^T*L*data?=?\lemda?data^T*D*data
%??????is?equivalent?to?the?largest?eigenvalue?problem:
%				data^T*W*data?=?\beta?data^T*D*data
%		where?L=D-W;??\lemda=?1?-?\beta.
%?Thus?the?smallest?eigenvalue?problem?can?be?transformed?to?a?largest?
%?eigenvalue?problem.?Such?tricks?are?adopted?in?this?code?for?the?
%?consideration?of?calculation?precision?of?Matlab.
%?
%
%?See?also?constructW?LGE
%
%Reference:
%	Xiaofei?He?and?Partha?Niyogi?“Locality?Preserving?Projections“
%	Advances?in?Neural?Information?Processing?Systems?16?（NIPS?2003）
%	Vancouver?Canada?2003.
%