Large-scale strongly supervised ensemble metric learning
View Patent ↗Systems and methods for metric learning include iteratively determining feature groups of images based on its derivative norm. Corresponding metrics of the feature groups are learned by gradient descent based on an expected loss. The corresponding metrics are combined to provide an intermediate metric matrix as a sparse representation of the images. A loss function of all metric parameters corresponding to features of the intermediate metric matrix are optimized, using a processor, to learn a final metric matrix. Eigenvalues of the final metric matrix are projected onto a simplex.
1. A method for metric learning, comprising:
iteratively determining feature groups of images based on its derivative norm;
learning corresponding metrics of the feature groups by gradient descent based on an expected loss;
combining the corresponding metrics to provide an intermediate metric matrix as a sparse representation of the images;
determining
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where K feature groups comprise
x=[x (1) ,x (2) , . . . ,x (K) ] T ε D ,x (K) ε D
and where x (K) is the k-th feature group with d features and the concatenated feature dimensionality D=Kd with Mahanalobis matrix A, training set χ, weak metrics A κ * corresponding to effective feature groups;
optimizing, using a processor, a loss function of all metric parameters corresponding to features of the intermediate metric matrix to learn a final metric matrix; and
projecting eigenvalues of the final metric matrix onto a simplex.
2. The method as recited in claim 1 , wherein iteratively determining feature groups of images includes projecting an opposite of partial derivative matrix onto positive semi-definite space.
3. The method as recited in claim 1 , wherein iteratively determining feature groups of images includes evaluating each feature group by a partial derivative of loss function.
4. The method as recited in claim 1 , wherein optimizing the loss function includes optimizing the loss function of all metric parameters corresponding to features of the intermediate metric matrix by gradient descent.
5. The method as recited in claim 4 , wherein optimizing the loss function includes determining a step size by line search.
6. A system for metric learning, comprising:
a sparse block diagonal metric ensembling module configured to iteratively determine feature groups of images based on its derivative norm, learn corresponding metrics of the feature groups by gradient descent based on an expected loss, and combine the corresponding metrics to provide an intermediate metric matrix as a sparse representation of the images using:
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1
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…
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where K feature groups include
x=[x (1) ,x (2) , . . . ,x (K) ] T ε D ,x (K) ε D
and where x (K) is the k-th feature group with d features and the concatenated feature dimensionality D=Kd with Mahanalobis matrix A, training set χ, weak metrics A κ * corresponding to effective feature groups; and
a joint metric learning module configured to optimize, using a processor, a loss function of all metric parameters corresponding to features of the intermediate metric matrix to learn a final metric matrix, and project eigenvalues of the final metric matrix onto a simplex.
7. The system as recited in claim 6 , wherein the sparse block diagonal metric ensembling module is further configured to project an opposite of partial derivative matrix onto positive semi-definite space.
8. The system as recited in claim 6 , wherein the sparse block diagonal metric ensembling module is further configured to evaluate each feature group by a partial derivative of loss function.
9. The system as recited in claim 6 , wherein the joint metric learning module is further configured to optimize the loss function of all metric parameters corresponding to features of the intermediate metric matrix by gradient descent.
10. The system as recited in claim 9 , wherein the joint metric learning module is further configured to determine a step size by line search.