This study investigates the asymptotic performance of the Quadratic Discriminant Function (QDF) under correlated and uncorrelated normal training samples. This paper specifically examines the effect of correlation, uncorrelation considering different sample size ratios, number of variables and varying group centroid separators ([Formula: see text], [Formula: see text]) on classification accurac...

For any distinct two primes \(p_1\equiv p_2\equiv 3\) \((\text {mod }4)\), let \(h(-p_1)\), \(h(-p_2)\) and \(h(p_1p_2)\) be the class numbers of quadratic fields \(\mathbb {Q}(\sqrt{-p_1})\), {Q}(\sqrt{-p_2})\) {Q}(\sqrt{p_1p_2})\), respectively. Let \(\omega _{p_1p_2}:=(1+\sqrt{p_1p_2})/2\) \(\varPsi (\omega _{p_1p_2})\) Hirzebruch sum _{p_1p_2}\). We show that \(h(-p_1)h(-p_2)\equiv h(p_1p_2...

In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for classification error. Minimax lower bounds are established demonstrate necessity of structural assumptions such as sparsity conditions on discriminating direction differential graph possible construction consistent QDA rules. We then propose a algorithm ca...

Generation of massive data is increasing in big industries due to the evolution modern technologies. The include source from sensors, Internet Things, digital and social media. In particular, these systems consist extraction, preprocessing, integration, analysis, visualization mechanism. encountered sources are redundant, incomplete conflict. Moreover, real time applications, it a tedious proce...