Fast methods of learning distance metric for classification and retrieval

摘要

A nearest-neighbor-based distance metric learning process includes applying an exponential-based loss function to provide a smooth objective; and determining an objective and a gradient of both hinge-based and exponential-based loss function in a quadratic time of the number of instances using a computer.

主权项

1. A nearest-neighbor-based distance metric learning process implemented by a computer, comprising:
applying an exponential-based loss function to provide a smooth objective; and determining an objective and a gradient of both hinge-based and exponential-based loss function in a quadratic time of the number of instances using a computer;wherein the loss function and its gradient comprises:l=Ex,y∼x⁢1Nx-[(1+d2⁡(y,x))⁢Zx,y-∑z∈Zx,y⁢⁢d2⁡(z,x)]l.=Ex,y∼x⁢1Nx-⁢∑z∈Zx,y⁢{(y-x)⁢(y-x)-(z-x)⁢(z-x)}=∑x,v⁢⁢wx,v⁡(v-x)⁢(v-x)=X⁡(S-W-W)⁢X where d is distance, x and y are data points, z is sampled from a class which x does not belong to, Zx,y is the set of data not belonging to the class of x and satifying 1+d2(y,x)≧d2(z,x), wx,v isZx,vNNx+⁢Nx-if v in the same class of x, wx,v is-Yx,vNNx+⁢Nx-if v is not in the same class as x, X is an p×N matrix whose j-th column is the feature vector of xj, W is an N×N matrix whose i,j-th element is wxi,xj, S is an N×N diagonal matrix whose i-th diagonal element is Σj(wij+wji), NNx+ is the size of class of x, Nx− is the size of data not in the class of x, and E is the expection over values x,y˜x.