Abstract Principal Component Analysis (PCA) is one of the most widely used data analysis methods in machine learning and AI. This manuscript focuses on mathematical foundation classical PCA its application to a small-sample-size scenario large dataset high-dimensional space scenario. In particular, we discuss simple method that can be approximate latter case. also help kernel or (KPCA) for larg...

This paper proposes a new efficiency benchmarking methodology that is capable of incorporating probability while still preserving the advantages of a distribution-free and nonparametric modeling technique. This new technique developed in this paper will be known as the DEA-Chebyshev model. The foundation of DEA-Chebyshev model is based on the model pioneered by Charnes, Cooper, and Rhodes in 19...

In Chen, Cook, Kao, and Zhu (2013), it is demonstrated, as a network DEA pitfall, that while the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEAmodels in deriving divisional efficiency scores and frontier projections. As a reaction to this work, we demonstrate that the duality in the stand...

Data Envelopment Analysis (DEA) is the most commonly used approach for evaluating healthcare efficiency (Hollingsworth, 2008), but a long-standing concern is that DEA assumes that data are measured without error. This is quite unlikely, and DEA and other efficiency analysis techniques may yield biased efficiency estimates if it is not realized (Gajewski, Lee, Bott, Piamjariyakul and Taunton, 20...

In humans, cytochrome P450 3A (CYP3A4) is a major enzyme involved in the metabolism of amiodarone (AM) to its major metabolite, desethylamiodarone (DEA). In rat, a commonly used animal model, metabolism of AM has not been well studied. To determine whether DEA is formed by CYP3A isoenzymes in the rat, microsomal protein was harvested from liver and intestine of male Sprague-Dawley rats. The met...

Original scientific paper Electronic vehicle identification (EVI) technology is often introduced to implement congestion-based toll. This paper presented an ex ante evaluation method for EVI adaptability and discussed the feasibility of this technology in congestion charge on the basis of assessment. First, system dynamics was introduced to qualitatively analyze the effect of EVI on urban traff...

This paper adopts two mathematical approaches, data envelopment analysis (DEA) and grey relation analysis (GRA) to measure DEA efficiency using the sample of 69 listed US internet companies. A total of 40 indicators were initially selected for the efficiency evaluation, with 21 related to DEA-input indicators and 19 to DEAoutput indicators. Eight representative indicators selected using GRA are...

In this paper, grey system theory and DEA are combined to establish a grey DEA model. In traditional DEA model, Input and output values of decision-making groups are all real numbers and real variables. They are replaced by grey numbers and grey variables in grey DEA model respectively. Using positioning solution method of grey linear programming, we prove the necessary condition for grey effec...

The spectroscopic and electrochemical properties of a series of four RuII polypyridyl complexes are reported. Compounds of the form [Ru(dmb)x(dea)3-x] (x ) 0-3), where dmb is 4,4′-dimethyl-2,2′-bipyridine and dea is 4,4′-bis(diethylamino)-2,2′-bipyridine, have been prepared and studied using static and time-resolved electronic and vibrational spectroscopies as a prelude to femtosecond spectrosc...