空间填充曲线映射算法研究

空间填充曲线是一种降低空间维度的方法。空间填充曲线能够将高维空间中的数据映射到一维空间,使用经典线性索引结构存储数据。空间填充曲线有Hilbert曲线、Z曲线和Gray曲线。本文详细叙述这些曲线的映射算法,分析算法的时间复杂度和空间复杂度。     

文本分类实现技术

文本分类是文本数据挖掘的重要技术.从文本分类实现过程的各个环节,包括建立文档模型、特征提取、维数约简、选择分类策略几个方面分别给出了目前实用的解决方案,同时对各种算法进行了分类和性能上的定性与定量的比较,最后讨论了国内文本分类研究中的一些问题和未来的发展.     

KPCA与LTSA融合的转子故障数据集降维算法

针对核主成分分析(kernel principal component analysis,KPCA)和局部切空间排列算法(local tangent space,LTSA)在降维过程中无法兼顾保持数据全局结构特性和局部结构特性的问题,利用核函数的可线性叠加性质,提出一种将KPCA算法与LTSA算法融合的非线性降维算法....     

对比变分自编码器的近红外光谱测量及其在液态样品检测中的应用

近红外光谱是热门的食品检测方法之一,对于这种高维光谱数据的分析常常需采用数据降维算法提取其中的特征,然而绝大多数算法都只能针对单个数据集进行分析。虽然已有基于对比学习的对比主成分分析成功应用于不同水果表面农残的近红外光谱检测中,但是该方法只能以线性的方式组合原有特征,特征提取效果存在局限性,并且需要调节对比参数来控制背景集影响,需要消耗更大的时间成本。cVAE(contrastive variational autoencoder)是一种基于对比学习和变分自编码器的改进算法,被用于图像去噪和RNA序列分析中,它仍然具备分析多个数据集的特点,同时因为组合了神经网络的概率生成模型而具备了提取非线性隐含特征的能力。将cVAE算法应用于近红外光谱分析,建立了准确的近红外光谱数据降维模型。在实际验证中,使用cVAE算法对购买的不同品牌和批次纯牛奶中掺假三聚氰胺进行检测。结果表明,使用VAE算法只能区分出不同品牌和批次的纯牛奶,而其中是否掺假三聚氰胺这一重要信息无法表现出来;而使用cVAE算法进行数据分析时,由于添加了背景数据集分离了无关变量,能够清晰的将有无掺假三聚氰胺的样本分类。这说明了,cV...     

2D and 3D Porphyrinic Covalent Organic Frameworks: The Influence of Dimensionality on Functionality

The construction of 2D and 3D covalent organic frameworks (COFs) from functional moieties for desired properties has gained much attention. However, the influence of COFs dimensionality on their functionalities, which can further assist in COF design, has never been explored. Now, by selecting designed precursors and topology diagrams, 2D and 3D porphyrinic COFs (2D‐PdPor‐COF and 3D‐PdPor‐COF) are synthesized. By model building and Rietveld refinement of powder X‐ray diffraction, 2D‐PdPor‐COF crystallizes as 2D sheets while 3D‐PdPor‐COF adopts a five‐fold interpenetrated pts topology. Interestingly, compared with 2D‐PdPor‐COF, 3D‐PdPor‐COF showed interesting properties, including 1) higher CO₂ adsorption capacity; 2) better photocatalytic performance; and 3) size‐selective photocatalysis. Based on this study, we believe that with the incorporation of functional moieties, the dimensionality of COFs can definitely influence their functionalities.     

Approximation Schemes for Functional Optimization Problems

Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared, which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow “fast” with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the “curse of dimensionality,” which often makes unfeasible traditional linear approximation techniques for functional optimization problems, when admissible solutions depend on a large number d of variables. Marcello Sanguineti was partially supported by a PRIN grant from the Italian Ministry for University and Research (project “Models and Algorithms for Robust Network Optimization”).     

Search for and elimination of dependences between vibrational coordinates in modeling spectra of large molecules

We have investigated an algorithm allowing us to reliably identify an arbitrary number of complex linear dependences between vibrational coordinates in a molecular model of very high dimensionality. These dependences are eliminated in the step for diagonalization of the kinetic part of the vibrational Hamiltonian. We have carried out computer experiments allowing us to propose optimal rules for designing appropriate computer programs for working with a vibrational Hamiltonian of very high dimensionality. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 561–565, September–October, 2006.     

Binary nonadditive hard-sphere mixtures at high dimension

At high spatial dimension, a suitably scaled classical system of interacting particles truncates at second virial terms. A binary mixture of nonadditive hard spheres with sufficiently repulsive interaction between unlike particles decomposes at sufficiently high density into two coexisting phases. The region around the critical density behaves classically.     

Electronic Excitation Energy Transfer between Different Types of Dye Molecules in a Porous Glass Matrix

The processes of electronic excitation energy transfer (EEET) between different types of dye molecules inserted into the matrix of a porous glass have been investigated. An extreme character of the dependence of the EEET efficiency on the size of pores has been revealed. The dependence of the fractal dimensionality of the distribution of dye molecules on the sizes of the pores has been determined. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 4, pp. 446–449, July–August, 2005.     

Possible realisation and generalisation of two specific 2×2 forms

For each of a couple of two-dimensional forms for quark mass matrix, it is discussed how that form may be realised in a certain gauge scheme (one of them in the standard model and the other in a scheme based on simple rank two times U(1)) by imposing suitable discrete symmetries and how under a certain small angle approximation that form may be regarded as the simplest member of a family of higher dimensionality forms.