Manifold learning is a powerful tool for solving nonlinear dimension reduction problems. By assuming that the high-dimensional data usually lie on a low-dimensional manifold, many algorithms have been proposed. However, most algorithms simply adopt the traditional graph Laplacian to encode the data locality, so the discriminative ability is limited and the embedding results are not always suita...

We present a steganalysis scheme for LSB matching steganography based on feature vectors extracted from integer wavelet transform (IWT). In integer wavelet decomposition of an image, the coefficients will be integer, so we can calculate co-occurrence matrix of them without rounding the coefficients. Before calculation of co-occurrence matrices, we clip some of the most significant bitplanes of ...

The embedding of time series provides a valuable, and sometimes indispensable, tool in order to analyze the dynamical properties of a chaotic system. To this purpose, the choice of the embedding dimension and lag is decisive. The scientific literature describes several methods for selecting the most appropriate parameter pairs. Unfortunately, no conclusive criterion to decide which method – and...

Let G be an n-dimensional geometric lattice. Suppose that 1 < e, f < n 1, e + f > n, but e and f are not both n 1. Then, in general, there are E, FE G with dimE=e, dimF=f, EvF=l, and dimEhF=e+f-n-l; any exception can be embedded in an n-dimensional modular geometric lattice M in such a way that joins and dimensions agree in G and M, as do intersections of modular pairs, while each point and lin...

Let us consider a 3-numerical semigroup S = 〈a, b,N 〉. Given m ∈ S, the triple (x, y, z) ∈ N3 is a factorization of m in S if xa+ yb+ zN = m. This work is focused on finding the full set of factorizations of any m ∈ S and as an application we compute the catenary degree of S. To this end, we relate a 2D tessellation to S and we use it as a main tool.

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain geometric features of the set. The question is how large the embedding dimens...

Curto, et. al., in 2013 outlined the neural ring, and neural ideal for describing receptive field structures of groups of neurons. In this paper we review their results, and explores some bounds that the algebraic and simplicial complex structures induce on the minimal embedding dimension of the receptive fields.

Let f ̸= 1, 3 be a positive integer. We prove that there exists a numerical semigroup S with embedding dimension three such that f is the Frobenius number of S. We also show that the same fact holds for affine semigroups in higher dimensional monoids.

In this paper, Locally Linear Embedding (LLE) has been implemented for unsupervised non-linear dimension reduction that computes low dimensional, neighborhood preserving embeddings of high dimensional data. Inputs are mapped into a single global coordinate system of lower dimensionality, and its optimizations though capable of generating highly nonlinear embeddings but local minima are not invo...

Even though the study and relevance of maximal embedding dimension numerical semigroups arises in a natural way among the other numerical semigroups, they have become specially renowned due to the existing applications to commutative algebra via their associated semigroup ring (see for instance [1, 5, 15, 16, 99, 100]). They are a source of examples of commutative rings with some maximal proper...