Error Minimizing Dimensional Reduction based on Manifold Analysis

The research presents the new method for manifold analysis. Error Minimizing method is a dimensional reduction method that find the new node coordinate by seeking minimal error. the error is equal to the square of new distance over the square of original distance. The new distance will be accordant with original distance when error is close to 0, therefore the new node coordinate in new 2-D space maintain the characteristic. As a research case, Taipei city has diverse geographical environment and the great dense of buildings, therefore the real path between two nodes can not be a straight line. The research is committed to develop a cartogram which the distance between two nodes will change according to the real distance constructed by traffic route for automobile. obtain the balance of that maintain the structure of the map and maintain the characteristic of distance.