Optimal Tree Research Articles

Study on Model of Natural Gas Hydrate Formation Based on Extremely Randomized Trees

Abstract It is easy to form hydrates in the development of natural gas. It is of great significance to study the formation of prediction models to guide the safe production of oil and gas fields. Based on computer intelligence algorithms, a prediction model of natural gas hydrate formation based on Extremely randomized trees was established and compared with the BP Neral Network model. To objectively evaluate the predictive power of the model, an extensive database of more than 1000 hydrate formation conditions was established. The results show that the number of optimal decision trees for the Extremely randomized trees model is 6, and the decision tree depth is 32. The BP Neral Network model has a flat error distribution with a maximum error of 6.37%. The error distribution of the Extremely randomized trees model is abrupt, with a maximum error of 3.39%, with higher stability and accuracy. In terms of pure water, the BP Neral Network model performs well only in a small number of conditions due to over-fitting, but the Extremely randomized trees model can avoid over-fitting by using the large number theorem, showing a stronger advantage.

Decorated merge trees for persistent topology

This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both $$\pi _0$$ and $$H_n$$ information into a single data structure that distinguishes filtrations that merge trees and persistent homology cannot distinguish alone. Three variants on DMTs, which emphasize category theory, representation theory and persistence barcodes, respectively, offer different advantages in terms of theory and computation. Two notions of distance—an interleaving distance and bottleneck distance—for DMTs are defined and a hierarchy of stability results that both refine and generalize existing stability results is proved here. To overcome some of the computational complexity inherent in these distances, we provide a novel use of Gromov-Wasserstein couplings to compute optimal merge tree alignments for a combinatorial version of our interleaving distance which can be tractably estimated. We introduce computational frameworks for generating, visualizing and comparing decorated merge trees derived from synthetic and real data. Example applications include comparison of point clouds, interpretation of persistent homology of sliding window embeddings of time series, visualization of topological features in segmented brain tumor images and topology-driven graph alignment.

Optimal policy trees

Optimal policy trees

Prediction of molecular diffusivity of organic molecules based on group contribution with tree optimization and SVM models

Prediction of mass transfer diffusion coefficient as a functional of group contribution in the molecular structure was carried out using machine learning techniques. Two machine learning methods including Tree Optimization (TO) and SVM (Support Vector Machine) were implemented to simulate the values of diffusion coefficients for various compounds. A bunch of data were collected from references for the diffusivity of nonelectrolyte organic molecules at infinite dilution in aqueous solution. The results can be beneficial for design and applications for wastewater treatment processes where the organic molecules must be removed from aqueous streams. For the modeling, 148 diverse functional groups were taken into account as the model’s inputs, while the diffusivity of the compound was taken as the sole model’s output in the computational study in this work. For modeling of the diffusion coefficients, 3000 datasets are chosen at random for the training procedure of the machine learning models. The simulation results revealed that the optimized Tree model is better at estimating the output parameter. The SVM model, on the other hand, can only forecast the outcome marginally with low accuracy compared to the Tree model.

Potential residential tree arrangement to optimise dwelling energy efficiency

Energy–efficient dwellings promote substantial urban energy conservation. Residential tree allocation, as an Urban Heat Island (UHI) mitigation strategy, stimulates climate responsivity, lowers Air Conditioner (AC) usage and heat distribution. This paper evaluates dwellings’ response to residential tree planting parameters to assess the building–surround relationship. These parameters include tree type (evergreen or deciduous), volume (1–3 trees), Tree–Building distance (3 m or 5 m) in each cardinal and inter–cardinal azimuth. These planting configurations highlight dominant Australian urban planning policy and green open space restrictions.This study quantifies tree planting configuration models, utilising both typical and extreme weather data and a bi–seasonal approach, to arrive at an Optimal Residential Tree arrangement (ORTa). The simulation process tailors local weather data to assess tree impact upon the diurnal and nocturnal microclimate.The ORTa dependence upon orientation ensures correct deep soil levels and viable private backyard volume. The result demonstrates a high probability that deciduous trees save energy bi–seasonally. Across all aspects and weather conditions, ORTa allows for an evergreen tree addition to boost energy conservation without detrimental annual or bi–seasonal effects on building thermal response. Annual weather data indicates two deciduous trees are optimal. These trees would be located east or west at 3 m Tree–Building distance (T-B distance), north at 5 m T-B distance or south at 3 m minimum with the maximum depending upon neighbour’s northerly aspect.In typical weather conditions, two deciduous tree arrangements lead to maximum 40% heating energy conservation from any potential ORTa in east, west or north. In addition, it provides 15% east or west cooling energy saving and 7% north. In extreme weather conditions, two tree arrangements provide 25% thermal heating conservation, in any aspect. During heatwaves easterly deciduous tree planting is optimal (18% energy conservation), followed by westerly (7%) and northerly (1%).This research recommends five ranked optimal tree arrangements depending on residential parcel deep soil availabilities. This optimisation result encourages decision–makers to appreciate residential green space and reanalyse future urban canopy cover target measurements.

Reinvasion of Native Invasive Trees After a Tree-Thinning Experiment in an African Savanna

Woody plant encroachment has serious negative consequences for ranchers because of the reduction in herbaceous fodder for domestic livestock. A long-term monitoring of a tree-thinning experiment was established near Magudu (northern KwaZulu-Natal, South Africa) in 1990. The objective of this experiment was to determine the optimal tree density that would maximize grass production while benefiting grasses from nitrogen fixation, hydraulic lift, and/or shade from the leguminous trees. The initial dominant species was the nitrogen-fixing tree, Dichrostachys cinerea. There were 12 plots (6 pairs) with trees removed to approximate 0, 179, 277, 428, and 625 trees ha−1, with 1 pair left as a control (unmanipulated). One plot of each replicate (except the controls) was treated with short-acting herbicide (picloram) once in 1990. We collected data on herbaceous cover and species composition, tree species composition, sizes, and mortality. We also used remote sensing to examine the patterns of herbaceous cover. Herbaceous biomass decreased as tree density increased. After 30 yr, the same dominant tree species (D. cinerea) had reinvaded all the removal plots despite the fact that several encroaching species (Vachellia karroo, V. tortilis, V. nilotica) occurred in these plots. These D. cinerea trees were mostly less dense and contained many more juvenile individuals in the cleared and partially cleared plots than those in the control plots after 30 yr. Should maximizing herbaceous cover be the goal, repeated brush management would be necessary to maintain adequate control of woody plants in these savannas.

On Huang and Wong’s algorithm for generalized binary split trees

Huang and Wong (Acta Inform 21(1):113–123, 1984) proposed a polynomial-time dynamic-programming algorithm for computing optimal generalized binary split trees. We show that their algorithm is incorrect. Thus, it remains open whether such trees can be computed in polynomial time. Spuler (Optimal search trees using two-way key comparisons, PhD thesis, 1994) proposed modifying Huang and Wong’s algorithm to obtain an algorithm for a different problem: computing optimal two-way comparison search trees. We show that the dynamic program underlying Spuler’s algorithm is not valid, in that it does not satisfy the necessary optimal-substructure property and its proposed recurrence relation is incorrect. It remains unknown whether the algorithm is guaranteed to compute a correct overall solution.

Risk Factors of Mortality in Hospitalized Patients With COVID-19 Applying a Machine Learning Algorithm

IntroductionRisk stratification of patients with COVID-19 can be fundamental to support clinical decision-making and optimize resources. The objective of our study is to identify among the routinely tested clinical and analytical parameters those that would allow us to determine patients with the highest risk of dying from COVID-19. Material and methodsWe carried out a retrospective cohort multicentric study by consecutively, including hospitalized patients with COVID-19 admitted in any of the 11 hospitals in the healthcare network of HM Hospitals-Spain. We collected the clinical, demographic, analytical, and radiological data from the patient's medical records.To assess each of the biomarkers’ predictive impact and measure the statistical significance of the variables involved in the analysis, we applied a random forest with a permutation method. We used the similarity measure induced by a previously classification model and adjusted the k-groups clustering algorithm based on the energy distance to stratify patients into a high and low-risk group. Finally, we adjusted two optimal classification trees to have a schematic representation of the cut-off points. ResultsWe included 1246 patients (average age of 65.36 years, 62% males). During the study one hundred sixty-eight patients (13%) died. High values of age, D-Dimer, White Blood Cell, Na, CRP, and creatinine represent the factors that identify high-risk patients who would die. ConclusionsAge seems to be the primary predictor of mortality in patients with SARS-CoV-2 infection, while the impact of acute phase reactants and blood cellularity is also highly relevant.

Gene\u2013gene interaction of AhRwith and within the Wntcascade affects susceptibility to lung cancer

BackgroundAberrant Wnt signalling, regulating cell development and stemness, influences the development of many cancer types. The Aryl hydrocarbon receptor (AhR) mediates tumorigenesis of environmental pollutants. Complex interaction patterns of genes assigned to AhR/Wnt-signalling were recently associated with lung cancer susceptibility.AimTo assess the association and predictive ability of AhR/Wnt-genes with lung cancer in cases and controls of European descent.MethodsOdds ratios (OR) were estimated for genomic variants assigned to the Wnt agonist and the antagonistic genes DKK2, DKK3, DKK4, FRZB, SFRP4 and Axin2. Logistic regression models with variable selection were trained, validated and tested to predict lung cancer, at which other previously identified SNPs that have been robustly associated with lung cancer risk could also enter the model. Furthermore, decision trees were created to investigate variant × variant interaction. All analyses were performed for overall lung cancer and for subgroups.ResultsNo genome-wide significant association of AhR/Wnt-genes with overall lung cancer was observed, but within the subgroups of ever smokers (e.g., maker rs2722278 SFRP4; OR = 1.20; 95% CI 1.13–1.27; p = 5.6 × 10–10) and never smokers (e.g., maker rs1133683 Axin2; OR = 1.27; 95% CI 1.19–1.35; p = 1.0 × 10–12). Although predictability is poor, AhR/Wnt-variants are unexpectedly overrepresented in optimized prediction scores for overall lung cancer and for small cell lung cancer. Remarkably, the score for never-smokers contained solely two AhR/Wnt-variants. The optimal decision tree for never smokers consists of 7 AhR/Wnt-variants and only two lung cancer variants.ConclusionsThe role of variants belonging to Wnt/AhR-pathways in lung cancer susceptibility may be underrated in main-effects association analysis. Complex interaction patterns in individuals of European descent have moderate predictive capacity for lung cancer or subgroups thereof, especially in never smokers.

A Simple Methodology that Efficiently Generates All Optimal Spanning Trees for the Cable-Trench Problem

The Cable-Trench Problem (CTP) is defined as a combination of the Shortest Path and Minimum Spanning Tree Problems. Specifically, let G = (V , E) be a connected weighted graph with specified vertex v1 ∈ V (referred to as the root), length l(e) ≥ 0 for each e ∈ E, and positive parameters τ and γ. The Cable-Trench Problem is the problem of finding, for given values of τ and γ, a spanning tree T of G such that τlτ(T) + γlγ(T) is minimized, where lτ(T) is the total length of the spanning tree T and lγ(T) is the total path length in T from v1 to all other vertices of V. Consider the ratio R = τ/γ. For R large enough the solution will be a minimum spanning tree and for R small enough the solution will be a shortest path. This is the first article to present a methodology that iteratively uses integer programming software (CPLEX in this article) to efficiently generate all optimal spanning trees (GEAOST) for a CTP (for all values of R). An example will illustrate how sensitive the spanning trees solution can be to small changes in edge lengths. Also, GEAOST will be used to generate all optimal spanning trees for graphs based on a real-world radio astronomy application. How the sequence of all optimal spanning trees can be used for sensitivity analysis will be demonstrated.

Machine Learning Reimagined: The Promise of Interpretability to Combat Bias.

Machine Learning Reimagined: The Promise of Interpretability to Combat Bias.

A Path Planning Method for Underground Intelligent Vehicles Based on an Improved RRT* Algorithm

Path planning is one of the key technologies for unmanned driving of underground intelligent vehicles. Due to the complexity of the drift environment and the vehicle structure, some improvements should be made to adapt to underground mining conditions. This paper proposes a path planning method based on an improved RRT* (Rapidly-Exploring Random Tree Star) algorithm for solving the problem of path planning for underground intelligent vehicles based on articulated structure and drift environment conditions. The kinematics of underground intelligent vehicles are realized by vectorized map and dynamic constraints. The RRT* algorithm is selected for improvement, including dynamic step size, steering angle constraints, and optimal tree reconnection. The simulation case study proves the effectiveness of the algorithm, with a lower path length, lower node count, and 100% steering angle efficiency.

Benchmarking cesarean delivery rates using machine learning-derived optimal classification trees.

To establish a case-adjusted hospital-specific performance evaluation tool using machine learning methodology for cesarean delivery. Secondary data were collected from patients between January 1, 2015 and February 28, 2018 using a hospital's "Electronic Data Warehouse" database from Illinois, USA. The machine learning methodology of optimal classification trees (OCTs) was used to predict cesarean delivery rate by physician group, thereby establishing the case-adjusted benchmarking standards in comparison to the overall hospital cesarean delivery rate. Outcomes of specific patient populations of each participating practice were predicted, as if each were treated in the overall hospital environment. The resulting OCTs estimate physician group expected cesarean delivery outcomes, both aggregate and in specific clinical situations. Twelve thousand eight hunderd and forty one singleton, vertex, term deliveries, cared for by practices with ≥50 births. The overall rate of cesarean delivery was 18.6% (n=2384), with a range of 13.3%-33.7% amongst 22 physician practices. An optimal decision tree was used to create a prediction model for the hospital overall, which defined 23 patient cohorts divided by 46 nodes. The model's performance for prediction of cesarean delivery is as follows: area under the curve 0.73, sensitivity 98.4%, specificity 16.1%, positive predictive value 83.7%, negative predictive value 70.6%. Comparisons with the overall hospital's specific-case adjusted benchmark groups revealed that several groups outperformed the overall hospital benchmark, and some practice groups underperformed in comparison to the overall hospital benchmark. OCT benchmarking can assess physician practice-specific case-adjusted performance, both overall and clinical situation-specific, and can serve as a valuable tool for hospital self-assessment and quality improvement.

Estimation of Individual Tree Biomass in Natural Secondary Forests Based on ALS Data and WorldView-3 Imagery

Individual-tree aboveground biomass (AGB) estimation can highlight the spatial distribution of AGB and is vital for precision forestry. Accurately estimating individual tree AGB is a requisite for accurate forest carbon stock assessment of natural secondary forests (NSFs). In this study, we investigated the performance of three machine learning and three ensemble learning algorithms in tree species classification based on airborne laser scanning (ALS) and WorldView-3 imagery, inversed the diameter at breast height (DBH) using an optimal tree height curve model, and mapped individual tree AGB for a site in northeast China using additive biomass equations, tree species, and inversed DBH. The results showed that the combination of ALS and WorldView-3 performed better than either single data source in tree species classification, and ensemble learning algorithms outperformed machine learning algorithms (except CNN). Seven tree species had satisfactory accuracy of individual tree AGB estimation, with R2 values ranging from 0.68 to 0.85 and RMSE ranging from 7.47 kg to 36.83 kg. The average individual tree AGB was 125.32 kg and the forest AGB was 113.58 Mg/ha in the Maoershan study site in Heilongjiang Province, China. This study provides a way to classify tree species and estimate individual tree AGB of NSFs based on ALS data and WorldView-3 imagery.

Analysis of error rate for various attributes to obtain the optimal decision tree

The competitiveness and computational intelligence are required to increase the gross profit of the product in a market. The classification algorithm rpart is applied on retail market dataset. The regression rpart decision tree algorithm is implemented with principal component analysis to impute data in the missing part of the dataset. The objective is to obtain an optimal tree by analysing cross validation error, standard deviation error, and number of splits and relative error of various attributes. The results of various attributes by ANOVA method are compared to choose the best optimal tree. The tree with minimum error rate is considered for the optimal tree.

On optimal molecular trees with respect to Sombor indices

<abstract><p>The Sombor index and reduced Sombor index, introduced by mathematical chemist Ivan Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16], are the recently proposed degree-based graph invariants that attained a lot of attention from researchers in a very short time. In this paper, the best possible upper bounds on the both aforementioned indices for molecular trees are obtained in terms of order and number of branching vertices or vertices of degree 2. The optimal molecular trees achieving the obtained bounds are also completely characterized.</p></abstract>

Optimal Causal Decision Trees Ensemble for Improved Prediction and Causal Inference

Ensemble methods can be used to identify causal relationships in data for a better understanding and taking the right decision in processes that involve high risk. This paper explores the idea of a causal decision tree forest and proposes a regularized ensemble method by integrating optimal causal trees for improved prediction accuracy while not compromising on accurately estimating heterogeneous treatment effects. The proposed method is based on selecting a subset of the most accurate causal trees from a sufficiently large pool based on their out-of-sample error estimates. The selected trees are integrated to form an ensemble that is used for estimating heterogeneous treatment effect and predicting unseen data. The proposed method is applied on Pakistan’s income function consisting of 27964 observations on wages of workers age 10 and above as an example dataset. The paper gives a detailed simulation study where datasets are generated under 5 different designs. The proposed method is assessed against ordinary least square (OLS), least absolute shrinkage and selection operator (LASSO), Ridge, Causal Tree and the standard decision trees forest (i.e. the causal forest) via mean square error ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MSE</i> ), root mean square error ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</i> ), mean absolute deviation ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAD</i> ) and Pearson correlation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${r}$ </tex-math></inline-formula> ) as performance metrics. The analyses given in the paper reveal that the proposed method can be used effectively for estimating heterogeneous treatment effects and achieves better prediction performance and as compared to the rest of the methods given in the paper.

Reliable Keyword Query Interpretation on Summary Graphs

The semantic gap between keyword queries and search intents behind them motivates intensive studies on keyword query interpretation, which aims to interpret a keyword query to structured queries (a.k.a. patterns) representing most possibly relevant search intents. However, there still lacks of study on an important issue: how to guarantee the patterns are "reliable", which means the structured queries can be evaluated as really existing results. In this paper, we regard the reliability as a new metric for ranking patterns, and present a keyword query interpretation approach to find both reliable and relevant pattern trees on an arbitrary summary graph of underlying data. Specifically, we firstly propose a reliability estimation model to measure how possibly a pattern tree can be evaluated as a nonempty result set by statistics under reasonable assumptions. Secondly, we develop constrained top-k search algorithms that guarantee to return the optimal pattern trees for a specific keyword query. Moreover, to improve the efficiency of online search, we also design elaborate indexes, search heuristics and pruning strategies. Lastly, we perform comprehensive experiments on two real-world datasets, DBpedia and Yago, with both QALD-9 queries and random queries. The observations indicate our approach improves the accuracy and overall quality of top-k results significantly.

Extraction of Speed-Control Strategy in En-Route Air Traffic using Multi- Objective Optimization and Decision Tree

Extraction of Speed-Control Strategy in En-Route Air Traffic using Multi- Objective Optimization and Decision Tree

Analysis of error rate for various attributes to obtain the optimal decision tree

Analysis of error rate for various attributes to obtain the optimal decision tree