Supplemental Information: Metric Learning for Enzyme Active-Site Search

Vectors are denoted by boldfaced lower-case letters, and matrices by boldfaced upper-case letters. Elements of vectors and matrices are not bold-faced. The transposition of a matrix A is denoted by A and the inverse of A is denoted by A−1. The n × n identity matrix is denoted by In. We use Eij to denote a matrix in which (i, j) element is one and all the others are zero. The n-dimensional vector, all of whose elements are one, is denoted by 1n. The n-dimensional vector all of whose elements are zero, is denoted by 0n. R is used to denote the set of real numbers, R is used to denote the set of n-dimensional real vectors, and Rm×n is used to denote the set of m× n real matrices. The set of real nonnegative numbers is denoted by R+. The set of n-dimensional nonnegative vectors is denoted by R+. We use O n to denote the set of n×n rotation matrices. The definition of rotation matrices is given later. The symbol Δ is used to denote the probability simplex in R and is defined by