plot (a). \[experiment:gauss\]](./eps/graph_gauss3_rpcas.pdf "fig:") (f) sharp gaussian. effect of RSPCA. $\qquad \qquad \qquad \qquad \qquad$

First we use artificial gaussian data to observe theoretical behavior of the proposed algortihm, which is discussed above.

A 128-dimensional random variance-covariance matrix is created and used to generate mean-centered gaussian data. To create a variance-covariance matrix, a diagonal matrix with random positive eigenvalues that is distributed log-normally is generated. Then a diagonal matrix is rotated by random rotation. We consider two different eigenvalue distributions. One uses a log-normal distribution with log variance of one (sphere-like distribution), and the other uses a log-normal distribution with log variance of three (sharp distribution).

Fig. \[experiment:gauss\] shows the retrieval results. In the case of a sphere-like distribution (upper row), most of methods have little difference in accuracy because the shape of the distribution is insusceptible under rotational transformation. A notable point is that in the case of sharp distribution (lower row), completely isotropic PRH is obviously inferior to the other cases, although Isotropic Hashing, which also has completely isotropic variances, achieves reasonable performance. As discussed in Section \[sec:experimental\_protocols\], there are an infinite number of isotropic states. The Lift-and-Projection in Isotropic Hashing tends to find entropically favorable isotropic states. 