A new algorithm, Laplacian MinMax Discriminant Projection (LMMDP), is proposed in this paper for supervised dimensionality reduction. LMMDP aims at learning a discriminant linear transformation. Specifically, we define the within-class scatter and the between-class scatter using similarities which are based on pairwise distances in sample space. After the transformation, the considered pairwise...

Identity transformations, used as skip-connections in residual networks, directly connect convolutional layers close to the input and those close to the output in deep neural networks, improving information flow and thus easing the training. In this paper, we introduce two alternative linear transforms, orthogonal transformation and idempotent transformation. According to the definition and pro...

Recently, a novel flow for computing the eigenvectors associated with the smallest eigenvalues of a symmetric but not necessarily positive definite matrix was introduced. This meant that the eigenvectors associated with the smallest eigenvalues could be found simply by reversing the sign of the matrix. The current paper derives a cost function and the corresponding negative gradient flow which ...

This paper describes one of the solutions for the ninth Transformation Tool Contest (TTC ’16), which resolves the Class Responsibility Assignment Case using a transformation tool based on Microsoft Excel and Visual Basic. In this project, these relatively unusual technologies are used to effectively enhance the processing of large models and matrices throughout different test cases proposed for...

“Learning by doing” (for example see [MAT-88]) is an informal way to describe a constructivist philosophy to the design of educational tools. This paper presents the current state of a project to develop an interactive graphical tool “LEG” to support computer graphics students learning the use of matrix arithmetic to calculate two-dimensional geometric transformations. The tool supports a simpl...

This paper proposes a constrained structural maximum a posteriori linear regression (CSMAPLR) algorithm for further improvement of speaker adaptation performance in HMM-based speech synthesis. In the algorithm, the concept of structural maximum a posteriori (SMAP) adaptation is applied to estimation of transformation matrices of the constrained MLLR (CMLLR), where recursive MAP-based estimation...

We present a covariant form for the dynamics of a canonical GA of arbitrary cardinality, showing how each genetic operator can be uniquely represented by a mathematical object - a tensor - that transforms simply under a general linear coordinate transformation. For mutation and recombination these tensors can be written as tensor products of the analogous tensors for one-bit strings thus giving...

Imposing sparsity constraints (such as l1-regularization) on the model parameters is a practical and efficient way of handling very high-dimensional data, which also yields interpretable models due to embedded feature-selection. Compressed sensing (CS) theory provides guarantees on the quality of sparse signal (in our case, model) reconstruction that relies on the so-called restricted isometry ...

Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...