I was asked to review this summary. A few comments follow below.
The article is a summary of the TPAMI paper by He et. al., and accurately reproduces much of the material from that paper. I feel it is a bit short on motivation, though - presumably the goal of this forum is to give students and researchers from outside the area the ituition for how algorithms are derived and why they work. The technical details (for example the relationships between the various scatter matrices) are much less important than providing a broad and accessible introduction to the work. Readers can (and should) refer to the original paper to understand the details.
The writing is ok, but could use another proofreading - there appears to be a bug in copying and pasting text from a different source, resulting in spaces missing, ect.
Finally, the text under "Laplacianfaces Extension" should be reworked or deleted. For example, the sentence
"By discovering the face manifold structure,Laplacianfaces can identify the person with different expression,poses,and lighting condition."
is a very strong technical claim, requiring similarly strong technical justification. To what extent is the algorithm guaranteed to handle these variations? What training data is necessary? It is definitely not enough to assert that the algorithm is motivated from differential geometric considerations, and then assert that faces with varying pose (or illumination) lie near a manifold. What properties of these image sets enable a solution with guaranteed good performance?
I have no problem accepting the article once the above changes are made - as mentioned above, it is an accurate summary of a fairly influential work.