A Lightweight Learning Method for Stochastic Configuration Networks Using Non-Inverse Solution

Stochastic configuration networks (SCNs) face time-consuming issues when dealing with complex modeling tasks that usually require a mass of hidden nodes to build an enormous network. An important reason behind this issue is that SCNs always employ the Moore–Penrose generalized inverse method with high complexity to update the output weights in each increment. To tackle this problem, this paper proposes a lightweight SCNs, called L-SCNs. First, to avoid using the Moore–Penrose generalized inverse method, a positive definite equation is proposed to replace the over-determined equation, and the consistency of their solution is proved. Then, to reduce the complexity of calculating the output weight, a low complexity method based on Cholesky decomposition is proposed. The experimental results based on both the benchmark function approximation and real-world problems including regression and classification applications show that L-SCNs are sufficiently lightweight.

Brand Awareness via Online Media: An Evidence Using Instagram Medium with Statistical Analysis

Online marketing refers to the practices of promoting a company’s brand to its potential customers. It helps the companies to find new venues and trade worldwide. Numerous online media such as Facebook, YouTube, Twitter, and Instagram are available for marketing to promote and sell a company’s product. However, in this study, we use Instagram as a marketing medium to see its impact on sales. To carry out the computational process, the approach of linear regression modeling is adopted. Certain statistical tests are implemented to check the significance of Instagram as a marketing tool. Furthermore, a new statistical model, namely a new generalized inverse Weibull distribution, is introduced. This model is obtained using the inverse Weibull model with the new generalized family approach. Certain mathematical properties of the new generalized inverse Weibull model such as moments, order statistics, and incomplete moments are derived. A complete mathematical treatment of the heavy-tailed characteristics of the new generalized inverse Weibull distribution is also provided. Different estimation methods are discussed to obtain the estimators of the new model. Finally, the applicability of the new generalized inverse Weibull model is established via analyzing Instagram advertising data. The comparison of the new distribution is made with two other models. Based on seven analytical tools, it is observed that the new distribution is a better model to deal with data in the business, finance, and management sectors.

Generalized Version of ISI Invariant for some Molecular Structures

Degree related topological invariants are the bygone and most victorioustype of graph invariants so far. In this article, we are interested in finding the generalized inverse indeg invariant of the nanostar dendrimers D[r],fullerene dendrimerNS4[r], and polymer dendrimerNS5[r]. Keywords: nanotubes; inverse indeg invariant; nanostar dendrimers; fullerene dendrimer; polymer dendrimer

On the Minimum Polynomial and Applications

In this note we study the computation of the minimum polynomial of a matrix $A$ and how we can use it for the computation of the matrix $A^n$. We also describe the form of the elements of the matrix $A^{-n}$ and we will see that it is closely related with the computation of the Drazin generalized inverse of $A$. Next we study the computation of the exponential matrix and finally we give a simple proof of the Leverrier - Faddeev algorithm for the computation of the characteristic polynomial.

An Extended Reweighted ℓ1 Minimization Algorithm for Image Restoration

This paper proposes an effective extended reweighted ℓ1 minimization algorithm (ERMA) to solve the basis pursuit problem minu∈Rnu1:Au=f in compressed sensing, where A∈Rm×n, m≪n. The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse iteration. At the same time, it also combines the iterative reweighted strategy that is used to solve minu∈Rnupp:Au=f problem, with the weight ωiu,p=ε+ui2p/2−1. Numerical experiments show that this l1 minimization persistently performs better than other methods. Especially when p=0, the restored signal by the algorithm has the highest signal to noise ratio. Additionally, this approach has no effect on workload or calculation time when matrix A is ill-conditioned.