Dense trees: a new look at degenerate graphs

Dense trees are undirected graphs defined as natural extensions of trees. They are already known in the realm of graph coloring under the name of k-degenerate graphs. For a given integer k1, a k-dense cycle is a connected graph, where the degree of each vertex is greater than k. A k-dense forest F=(V,E) is a graph without k-dense cycles as subgraphs. If F is connected, then is a k-dense tree. 1-dense trees are standard trees. We have |E|k|V|−k(k+1)/2. If equality holds F is connected and is called a maximal k-dense tree. k-trees (a subfamily of triangulated graphs) are special cases of maximal k-dense trees.We review the basic theory of dense trees in the family of graphs and show their relation with k-trees. Vertex and edge connectivity is thoroughly investigated, and the role of maximal k-dense trees as “reinforced” spanning trees of arbitrary graphs is presented. Then it is shown how a k-dense forest or tree can be decomposed into a set of standard spanning trees connected through a common “root” of k vertices. All sections include efficient construction algorithms. Applications of k-dense trees in the fields of distributed systems and data structures are finally indicated.     

A random forest of combined features in the classification of cut tobacco based on gas chromatography fingerprinting

We applied the random forest method to discriminate among different kinds of cut tobacco. To overcome the influence of the descending resolution caused by column pollution and the subsequent deterioration of column efficacy at different testing times, we constructed combined peaks by summing the peaks over a specific elution time interval Δt. On constructing tree classifiers, both the original peaks and the combined peaks were considered. A data set of 75 samples from three grades of the same tobacco brand was used to evaluate our method. Two parameters of the random forest were optimized using out-of-bag error, and the relationship between Δt and classification rate was investigated. Experiments show that partial least squares discriminant analysis was not suitable because of the overfitting, and the random forest with the combined features performed more accurately than Naïve Bayes, support vector machines, bootstrap aggregating and the random forest using only its original features.     

Strong labelings of linear forests

A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.     

Average distance and maximum induced forest

With the help of the Graffiti system, Fajtlowicz conjectured around 1992 that the average distance between two vertices of a connected graph G is at most half the maximum order of an induced bipartite subgraph of G, denoted α₂(G). We prove a strengthening of this conjecture by showing that the average distance between two vertices of a connected graph G is at most half the maximum order of an induced forest, denoted F(G). Moreover, we characterize the graphs maximizing the average distance among all graphs G having a fixed number of vertices and a fixed value of F(G) or α₂(G). Finally, we conjecture that the average distance between two vertices of a connected graph is at most half the maximum order of an induced linear forest (where a linear forest is a union of paths). © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 31–54, 2009     

基于随机森林的激变变星候选体的数据挖掘

提出一种适用于在郭守敬望远镜海量光谱中自动、快速筛选激变变星的方法。利用已证认的激变变星光谱作为模板,通过随机森林分类训练,得到一个分类模型,该模型给出了各个波长对应流量的重要性排序,可根据该排序进行降维并用于激变变星判别,结果作为反馈进一步丰富模板库。实验中共发现了16个新的激变变星候选体,表明了该方法的可行性。     

Indoor human detection based on micro-Doppler features in the presence of interference from moving clutter sources

In this paper, to address the problem of detecting the presence of human in indoor environments in the presence of moving clutter sources, an indoor human detection method that utilizes random forest to process micro-Doppler signatures and a single pair of TX/RX unit is proposed. In contrast to most of the existing methods that use both distance information and micro-Doppler information assuming no interference from moving clutter sources (window curtains, blinds, table fans, etc.), our proposed method relies only on micro-Doppler information for human detection in indoor environments with curtain and fan interferences. Based on our time–frequency analyses on the measured radar data, seven features, i.e., the mean and standard deviation of the doppler centroid, the mean and standard deviation of the span of envelopes, the silhouette size, the positive peak values, and the peak spread, are extracted from spectrograms. These features are fed into a random forest classifier for categorizing the state of a room into one of the five scenarios considered in this work, namely (1) a person entering the room, (2) a person leaving the room, (3) interference from curtain/blind, (4) interference from fan, and (5) an empty room. The proposed system has been validated using real-world experiments and be able to deliver an accuracy of 97.5% in classifying the scenarios.     

森林公园声景对心理恢复效益的影响——以福州国家森林公园为例

声景是森林公园恢复性环境的重要组成部分。该研究以福州国家森林公园为例，其20个森林公园环境视听视频为研究材料(有声视频和无声视频各10个)，借助短版修订恢复量表和声景感知评价问卷探究森林公园声景对心理恢复效益的影响。结果表明：不同森林公园环境心理恢复效益不同，在综合恢复性评价、认知和行为维度上有显著差异；除谈话声和儿童嬉戏声较突出的样地(S5)外，视听组合刺激促进心理恢复的能力均比单一视觉刺激强；声景感知与综合恢复性评价及情感、认知和行为维度的最优尺度回归模型具有统计学意义，鸟鸣声、蝉鸣声、流水声等自然声是心理恢复效益的重要预测变量，对心理恢复有积极影响。基于研究结果提出森林公园恢复性声景设计策略，为森林公园恢复性声环境的优化设计提供参考思路。     

Raman spectroscopy based analysis of milk using random forest classification

The development of a classification system based on the Raman spectra of milk samples is proposed in present study. Such development could be useful for nutritionists in suggesting healthy food to infants for their proper growth. Previously, molecular structures in milk samples have been exploited by Raman spectroscopy. In the current study, Raman spectral data of milk samples of different species is utilized for multi-class classification using a dimensionality reduction technique in combination with random forest (RF) classifier. Quantitative and experimental analysis is based on locally collected milk samples of different species including cow, buffalo, goat and human. This classification is based on the variations (different concentrations of the components present in milk such as proteins, milk fats, lactose etc.) in the intensities of Raman peaks of milk samples. Principal component analysis (PCA) is used as a dimensionality reduction technique in combination with RF to highlight the variations which can differentiate the Raman spectra of milk samples from different species. The proposed technique has demonstrated sufficient potential to be used for differentiation between milk samples of different species as the average accuracy of about 93.7%, precision of about 94%, specificity of about 97% and sensitivity of about 93% has been achieved.