聚类分析是统计学、模式识别和机器学习等领域的研究热点.通过有效的聚类分析,数据集的内在结构与特征可以被很好地发掘出来.然而,无监督学习的特性使得当前已有的聚类方法依旧面临着聚类效果不稳定、无法对多种结构的数据集进行正确聚...聚类分析是统计学、模式识别和机器学习等领域的研究热点.通过有效的聚类分析,数据集的内在结构与特征可以被很好地发掘出来.然而,无监督学习的特性使得当前已有的聚类方法依旧面临着聚类效果不稳定、无法对多种结构的数据集进行正确聚类等问题.针对这些问题,首先将K-means算法和层次聚类算法的聚类思想相结合,提出了一种混合聚类算法K-means-AHC;其次,采用拐点检测的思想,提出了一个基于平均综合度的新聚类有效性指标DAS(平均综合度之差,difference of average synthesis degree),以此来评估K-means-AHC算法聚类结果的质量;最后,将K-means-AHC算法和DAS指标相结合,设计了一种寻找数据集最佳类簇数和最优划分的有效方法.实验将K-means-AHC算法用于测试多种结构的数据集,结果表明:该算法在不过多增加时间开销的同时,提高了聚类分析的准确性.与此同时,新的DAS指标在聚类结果的评价上要优于当前已有的常用聚类有效性指标.展开更多
Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
Taxonomy is generated to effectively organize and access large volume of data. A taxonomy is a way of representing concepts that exist in data. It needs to continuously evolve to reflect changes in data. Existing auto...Taxonomy is generated to effectively organize and access large volume of data. A taxonomy is a way of representing concepts that exist in data. It needs to continuously evolve to reflect changes in data. Existing automatic taxonomy generation techniques do not handle the evolution of data; therefore, the generated taxonomies do not truly represent the data. The evolution of data can be handled by either regenerating taxonomy from scratch, or allowing taxonomy to incrementally evolve whenever changes occur in the data. The former approach is not economical in terms of time and resources. A taxonomy incremental evolution（TIE） algorithm, as proposed, is a novel attempt to handle the data that evolve in time. It serves as a layer over an existing clustering-based taxonomy generation technique and allows an existing taxonomy to incrementally evolve. The algorithm was evaluated in research articles selected from the computing domain. It was found that the taxonomy using the algorithm that evolved with data needed considerably shorter time, and had better quality per unit time as compared to the taxonomy regenerated from scratch.展开更多
Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorph...Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.展开更多
We introduce a class of categories, called clustered hyperbolic categories, which are constructed from a categorized version of preseeds called categorical preseeds using categorical mutations that are a ＂functorial...We introduce a class of categories, called clustered hyperbolic categories, which are constructed from a categorized version of preseeds called categorical preseeds using categorical mutations that are a ＂functorial＂ edition of preseed mutations. Every Weyl preseed p gives rise to a categorical preseed P which generates a clustered hyperbolic category; this is formed by copies of categories each one of which is equivalent to the category of representations of the Weyl cluster algebra H（p）. A ＂categorical realization＂ of Weyl cluster algebra is provided in the sense of defining a map Fp from any clustered hyperbolic category induced from p to the Weyl cluster algebra H（p）, where the image of Fp generates H（p）.展开更多
Adaptive cluster sampling （ACS） has been widely used for data collection of environment and natural resources. However, the randomness of its final sample size often impedes the use of this method. To control the fi...Adaptive cluster sampling （ACS） has been widely used for data collection of environment and natural resources. However, the randomness of its final sample size often impedes the use of this method. To control the final sample sizes, in this study, a k-step ACS based on Horvitz-Thompson （HT） estimator was developed and an unbiased estimator was derived. The k-step ACS-HT was assessed first using a simulated example and then using a real survey for numbers of plants for three species that were characterized by clustered and patchily spatial distributions. The effectiveness of this sampling design method was assessed in comparison with ACS Hansen-Hurwitz （ACS-HH） and ACS- HT estimators, and k-step ACS-HT estimator. The effectiveness of using different k- step sizes was also compared. The results showed that k-step ACS^HT estimator was most effective and ACS-HH was the least. Moreover, stable sample mean and variance estimates could be obtained after a certain number of steps, but depending on plant species, k-step ACS without replacement was slightly more effective than that with replacement. In k-step ACS, the variance estimate of one-step ACS is much larger than other k-step ACS （k 〉 1）, but it is smaller than ACS. This implies that k-step ACS is more effective than traditional ACS, besides, the final sample size can be controlled easily in population with big clusters.展开更多
文摘聚类分析是统计学、模式识别和机器学习等领域的研究热点.通过有效的聚类分析,数据集的内在结构与特征可以被很好地发掘出来.然而,无监督学习的特性使得当前已有的聚类方法依旧面临着聚类效果不稳定、无法对多种结构的数据集进行正确聚类等问题.针对这些问题,首先将K-means算法和层次聚类算法的聚类思想相结合,提出了一种混合聚类算法K-means-AHC;其次,采用拐点检测的思想,提出了一个基于平均综合度的新聚类有效性指标DAS(平均综合度之差,difference of average synthesis degree),以此来评估K-means-AHC算法聚类结果的质量;最后,将K-means-AHC算法和DAS指标相结合,设计了一种寻找数据集最佳类簇数和最优划分的有效方法.实验将K-means-AHC算法用于测试多种结构的数据集,结果表明:该算法在不过多增加时间开销的同时,提高了聚类分析的准确性.与此同时,新的DAS指标在聚类结果的评价上要优于当前已有的常用聚类有效性指标.
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
文摘Taxonomy is generated to effectively organize and access large volume of data. A taxonomy is a way of representing concepts that exist in data. It needs to continuously evolve to reflect changes in data. Existing automatic taxonomy generation techniques do not handle the evolution of data; therefore, the generated taxonomies do not truly represent the data. The evolution of data can be handled by either regenerating taxonomy from scratch, or allowing taxonomy to incrementally evolve whenever changes occur in the data. The former approach is not economical in terms of time and resources. A taxonomy incremental evolution（TIE） algorithm, as proposed, is a novel attempt to handle the data that evolve in time. It serves as a layer over an existing clustering-based taxonomy generation technique and allows an existing taxonomy to incrementally evolve. The algorithm was evaluated in research articles selected from the computing domain. It was found that the taxonomy using the algorithm that evolved with data needed considerably shorter time, and had better quality per unit time as compared to the taxonomy regenerated from scratch.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671350 and 11571173)
文摘Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.
文摘We introduce a class of categories, called clustered hyperbolic categories, which are constructed from a categorized version of preseeds called categorical preseeds using categorical mutations that are a ＂functorial＂ edition of preseed mutations. Every Weyl preseed p gives rise to a categorical preseed P which generates a clustered hyperbolic category; this is formed by copies of categories each one of which is equivalent to the category of representations of the Weyl cluster algebra H（p）. A ＂categorical realization＂ of Weyl cluster algebra is provided in the sense of defining a map Fp from any clustered hyperbolic category induced from p to the Weyl cluster algebra H（p）, where the image of Fp generates H（p）.
文摘Adaptive cluster sampling （ACS） has been widely used for data collection of environment and natural resources. However, the randomness of its final sample size often impedes the use of this method. To control the final sample sizes, in this study, a k-step ACS based on Horvitz-Thompson （HT） estimator was developed and an unbiased estimator was derived. The k-step ACS-HT was assessed first using a simulated example and then using a real survey for numbers of plants for three species that were characterized by clustered and patchily spatial distributions. The effectiveness of this sampling design method was assessed in comparison with ACS Hansen-Hurwitz （ACS-HH） and ACS- HT estimators, and k-step ACS-HT estimator. The effectiveness of using different k- step sizes was also compared. The results showed that k-step ACS^HT estimator was most effective and ACS-HH was the least. Moreover, stable sample mean and variance estimates could be obtained after a certain number of steps, but depending on plant species, k-step ACS without replacement was slightly more effective than that with replacement. In k-step ACS, the variance estimate of one-step ACS is much larger than other k-step ACS （k 〉 1）, but it is smaller than ACS. This implies that k-step ACS is more effective than traditional ACS, besides, the final sample size can be controlled easily in population with big clusters.
