Billera, Holmes, and Vogtmann introduced an intriguing new phylogenetic tree metric for weighted trees with useful properties related to statistical analysis. However, the best known algorithm for calculating this distance is exponential in the number of leaves of the trees compared. We point out that lower and upper bounds for this distance, which can be calculated in linear time, can differ b...

Co-localization is the problem of localizing categorical objects using only positive sets of example images, without any form of further supervision. This is a challenging task as there is no pixel-level annotations. Motivated by human visual learning, we find the common features of an object category from convolutional kernels of a pretrained convolutional neural network (CNN). We call these c...

It has been known that the curvature of data spaces plays a role in data analysis. For example, the Frechet mean (intrinsic mean) always exists uniquely for a probability measure on a non-positively curved metric space. In this paper, we use the curvature of data spaces in a novel manner. A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. The p...

In this paper, we present two feature extraction methods for two-dimensional face recognition. Our approaches are based on facial feature points detection then compute the Euclidean Distance between all pairs of this points for a first method (ED-FFP) and Geodesic Distance in the second approach (GD-FFP). These measures are employed as inputs to a commonly used classification techniques such as...

this study was performed with objective land cover change prediction (forest, agriculture, residential and orchard) using logistic regression and markov chain in the gis environment in east of mazandaran province. land cover change detected using satellite imageries belonging to the years 1987 and 2001. transition potential modeling was conducted using a logistic regression. seven variables (de...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic e...