We present a source-to-source compiler that processes matrix formulae in the form of Kronecker product factorizations. The Kronecker product notation allows for simple expressions of algorithms such as Walsh-Hadamard, Haar, Slant, Hartley, and FFTs as well as transpositions and wavelet transforms. The compiler is based on a set of term rewriting rules that translate high level matrix descriptio...

We give a simple combinatorial proof of Ram’s rule for computing the characters of the Hecke Algebra. We also establish a relationship between the characters of the Hecke algebra and the Kronecker product of two irreducible representations of the Symmetric Group which allows us to give new combinatorial interpretations to the Kronecker product of two Schur functions evaluated at a Schur functio...

Bilinear pooling has achieved excellent performance in fine-grained recognition tasks. Nevertheless, high-dimensional bilinear features suffer from over-fitting and inefficiency. To alleviate these issues, compact (CBP) methods were developed to generate low-dimensional features. Although the existing CBP enable high efficiency subsequent classification, themselves are inefficient. Thus, ineffi...

The Kronecker product of two Schur functions sμ and sν , denoted by sμ ∗sν, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions μ and ν. The coefficient of sλ in this product is denoted by γ λ μν , and corresponds to the multiplicity of the irreducible character χ in χχ . We use Sergeev’s Formula for a S...

Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix P ∈ [0, 1]k×k. We develop a novel correspondence between the adjacencies in a general stochastic Kronecker graph and the action of a fixed Markov chain. Using this correspondence we are able to generalize the arguments of Horn and Radcl...

We explore the combinatorial properties of the extension monoid product of preinjective Kronecker modules. We state a theorem which characterizes the extension monoid product of preinjective (and dually preprojective) Kronecker modules in the most general case, over an arbitrary base field. As corollaries, we give another proof of an interesting theorem from [7] and restate the main theorem fro...

The displacement structure is extended to a Kronecker matrix W ⊗ Z. A new class of Kronecker-like matrices with the displacement rank r, r < n will be formulated and presented. The computational complexity of multiplication with vectors for Kronecker-like matrices has been accelerated. Applying the displacement, which was originally discovered by Kailath, Kung and Morf [15], a new superfast alg...