This paper defines a pairing of two finite Hopf C*-algebras A and B, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C*algebra D(A,B). The canonical embedding maps of A and B into the double are both isometric.

The relationship between recursive sentence embedding and theory-of-mind (ToM) inference is investigated in three persons with Broca's aphasia, two persons with Wernicke's aphasia, and six persons with mild and moderate Alzheimer's disease (AD). We asked questions of four types about photographs of various real-life situations. Type 4 questions asked participants about intentions, thoughts, or ...

We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle which separates the surface into two pieces. This improves a result of Zha and Zhao for general orientable surfaces, in which the same conclusion holds for 6-representative graph embeddings. Noncontractible separating cycles have been studied because they provide a way to do induction on the...

We propose two strategies to improve the optimization in information geometry. First, a local Euclidean embedding is identified by whitening the tangent space, which leads to an additive parameter update sequence that approximates the geodesic flow to the optimal density model. Second, removal of the minor components of gradients enhances the estimation of the Fisher information matrix and redu...

In this paper, we propose a watermarking technique based on Haar Discrete Wavelet Transform-Discrete Cosine Transform (HDWT-DCT) by using matrixbased Two-dimensional Linear Discriminant Analysis (2DLDA) for color images. By embedding the reference watermark and using matrix-based 2DLDA scheme, we do not need all the embedded information of watermark and apply only part of matrix-based samples f...

Dimensionality reduction is very important in pattern recognition, machine learning, and image recognition. In this paper, we propose a novel linear dimensionality reduction technique using trace ratio criterion, namely Discriminant Neighbourhood Structure Embedding Using Trace Ratio Criterion (TR-DNSE). TR-DNSE preserves the local intrinsic geometric structure, characterizing properties of sim...

Feature extraction is a crucial step for pattern recognition. In this paper, a nonlinear feature extraction method is proposed. The objective function of the proposed method is formed by combining the ideas of locally linear embedding (LLE) and linear discriminant analysis (LDA). Optimizing the objective function in a kernel feature space, nonlinear features can be extracted. A major advantage ...

Clustering is the task of grouping a set of objects in such a way that objects in the same group (called cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). The dimension can be reduced by using some techniques of dimension reduction. Recently new non linear methods introduced for reducing the dimensionality of such data called Locally Li...

We propose adaptive nonlinear auto-associative modeling (ANAM) based on Locally Linear Embedding algorithm (LLE) for learning intrinsic principal features of each concept separately and recognition thereby. Unlike traditional supervised manifold learning algorithm, the proposed ANAM algorithm has several advantages: 1) it implicitly embodies discriminant information because the suboptimal param...

The Isomap method has demonstrated promising results in finding a low dimensional embedding from samples in the high dimensional input space. The crux of this method is to estimate geodesic distance with multidimensional scaling for dimensionality reduction. Since the Isomap method is developed based on the reconstruction principle, it may not be optimal from the classification viewpoint. We pr...