Reducing Triangle Inequality Violations with Deep Learning and Its Application to Image Retrieval

Izat Khamiyev, Magzhan Gabidolla, Alisher Iskakov, M. Fatih Demirci

Abstract: Given a distance matrix with triangular inequality violations, the metric nearness problem requires to find the closest matrix that satisfies the triangle inequality. It has been experimentally shown that deep neural networks can be used to efficiently produce close matrices with a fewer number of triangular inequality violations. This paper further extends the deep learning approach to the metric nearness problem by applying it to the content-based image retrieval. Since vantage space representation of an image database requires distances to satisfy triangle inequalities, applying deep learning to the matrices in the vantage space with triangular inequality violations produces distance matrices with a fewer number of violations. Experiments performed on the Corel-1k dataset demonstrate that fully convolutional autoencoders considerably reduce triangular inequality violations on distance matrices. Overall, the image retrieval accuracy based on the distance matrices generated by the deep learning model is better than that based on the original matrices in 91.16% of the time.