Linear Decision Trees, Subspace Arrangements, and Mobius Functions

Topological methods are described for estimating the size and depth of decision trees where a linear test is performed at each node. The methods are applied, among others, to the questions of deciding by a linear decision tree whether given n n real numbers (1) some k k of them are equal, or (2) some k k of them are unequal. We show that the minimum depth of a linear decision tree for these problems is at least (1) max { n − 1 , n lo g 3 ( n / 3 k ) } {\text {max}}\{ n - 1,\quad n\;{\text {lo}}{{\text {g}}_3}(n/3k)\} , and (2) max { n − 1 , n lo g 3 ( k − 1 ) − k + 1 } {\text {max}}\{ n - 1,\quad n\;{\text {lo}}{{\text {g}}_3}(k - 1) - k + 1\} . Our main lower bound for the size of linear decision trees for polyhedra P P in R n {{\mathbf {R}}^n} is given by the sum of Betti numbers for the complement R n ∖ P {{\mathbf {R}}^n}\backslash P . The applications of this general topological bound involve the computation of the Möbius function of intersection lattices of certain subspace arrangements. In particular, this leads to computing various expressions for the Möbius function of posets of partitions with restricted block sizes. Some of these formulas have topological meaning. For instance, we derive a formula for the Euler characteristic of the subset of R n {{\mathbf {R}}^n} of points with no k k coordinates equal in terms of the roots of the truncated exponential ∑ i > k x i / i ! \sum \nolimits _{i > k} {{x^i}} /i! .

In this paper, we present a novel ensemble method random projection random discretization ensembles (RPRDE) to create ensembles of linear multivariate decision trees by using a univariate decision tree algorithm. The present method combines the better computational complexity of a univariate decision tree algorithm with the better representational power of linear multivariate decision trees. We develop random discretization (RD) method that creates random discretized features from continuous features. Random projection (RP) is used to create new features that are linear combinations of original features. A new dataset is created by augmenting discretized features (created by using RD) with features created by using RP. Each decision tree of a RPRD ensemble is trained on one dataset from the pool of these datasets by using a univariate decision tree algorithm. As these multivariate decision trees (because of features created by RP) have more representational power than univariate decision trees, we expect accurate decision trees in the ensemble. Diverse training datasets ensure diverse decision trees in the ensemble. We study the performance of RPRDE against other popular ensemble techniques using C4.5 tree as the base classifier. RPRDE matches or outperforms other popular ensemble methods. Experiments results also suggest that the proposed method is quite robust to the class noise.

Multiple machine learning (ML) algorithms were developed using artificial intelligence, including Linear Regression (LR), Decision Tree (DT), Random Forest (RF), and K-Nearest Neighbor (KNN), to predict the yield of biodiesel production in an acid-catalyzed alcoholysis process using green seed canola oil. Catalyst loading, methanol-to-oil (M/O) molar ratio, and reaction time were considered as input parameters, while the yield of biodiesel production was selected as the output parameter. The performance of the developed ML models was assessed using evaluation metrics such as the coefficient of determination (R2) and the root mean squared error (RMSE). The R2 values obtained for LR, RF, DT, and KNN models were 0.80, 0.95, 0.97, and 0.84, respectively. Furthermore, the corresponding RMSE values for these models were 2.48, 1.51, 0.89, and 4.51, respectively. According to the results, the DT model exhibited superior accuracy and reliability for predicting biodiesel production compared to the other models. The values of the input variables to potentially yield the highest biodiesel output were identified through a systematic trial-and-error approach using the DT model. The results showed that a biodiesel yield of 88 % can be achieved with 5 wt% catalyst loading, a 22 M/O molar ratio, and a reaction time of 5 hours.

The analyzed study focuses on the application of predictive models, specifically Linear Regression and Decision Trees, for the management of delinquent debts in the public context of the United States. The main objective of the work is to compare the effectiveness of these models in predicting the compliance of debts older than 120 days, helping to direct these debts to the Treasury Offset Program (TOP), an essential initiative for government financial recovery. The problem that the study addresses is the need for effective management of delinquent public debts, seeking to ensure compliance with public financial policies that promote compliance and the proper redirection of financial resources to the government. This is particularly important to ensure fiscal transparency and accountability of federal agencies. The methodology used in the study was quantitative, based on the analysis of eligible debt data extracted from U.S. Treasury reports. The Linear Regression and Decision Trees models were applied, with performance metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and Coefficient of Determination (R²). The study dealt with financial and temporal variables to analyze the behavior of these debts and their compliance. The main results show that both models showed high accuracy in the predictions, with the Linear Regression showing a perfect fit (R² = 1) and the Decision Trees excelling in capturing nonlinear nuances of the data. The "Compliance Rate Amount" variable was identified as the most significant in the Decision Tree model, suggesting that the amount of the compliance rate is one of the most important factors to predict the compliance of delinquent debts. This study offers valuable contributions to the field of public management, by demonstrating that the use of predictive models can help optimize debt recovery, improve fiscal transparency, and contribute to more informed decision-making.

Regional landslide susceptibility prediction (LSP) research is of great significance to the prevention and control of landslides. This study focuses on the LSP modelling based on the decision tree model. Taking the northern part of An’yuan County of Jiangxi Province as an example, 14 environmental factors including elevation, gully density and lithology are obtained based on geographical information system (GIS) and remote sensing satellite. Frequency Ratio method and C5.0 decision tree (DT) model are coupled to build DT model for LSP modelling. Then the predicted results are graded into five attribute intervals. Finally, LSP performance of DT model is evaluated by comparing the area value under the receiver operating characteristic curve (ROC) and classification of landslide susceptibility. The results show that the AUC accuracy of the C5.0 DT model is 0.805, and the LSP results of the C5.0 DT model are consistent with the actual distribution pattern of landslides in this County.

A form of cancer known as lung cancer usually appears in the cells that line the lungs' air passages. It is the primary cause of cancer-related deaths in both genders. Lung adenocarcinoma (LUAD) and squamous cell carcinoma (LUSC) are two separate types of non-small cell lung cancer (NSCLC). Recognition of the differentially expressed genes (DEGs) is necessary to distinguish between healthy and diseased states molecularly. Biomedical books and microarray investigations are two common places to find details concerning gene expression variations. A gene is said to be highly expressed if there is a significant statistical distinction or change in reading counts or expression level indices between two different experimental conditions. A good gene expression strategy leads to a good gene silencing strategy, which subsequently slows or stops the cancer progression. In this paper, we present a robust analysis of the mRNA data from the LUAD data to find the most differentially expressed genes. Then we employ several machine learning techniques to categorize the samples into the five stages of lung cancer. We investigated four distinct models; including linear regression, logistic regression, RANSAC regression, and decision trees. The models achieved 100%, 91%, 98%, and 100% accuracies for 12 differential expression genes using linear regression, logistic regression, RANSAC regression, and decision trees respectively. The logistic regression and decision trees achieved 100% and 98% accuracies for 5665 differential expression genes. The proposed models achieved the highest accuracies in comparison with the state-of-the-art models.KeywordsGene expressionDEGsLUADLung cancerClassificationMachine learningDecision treeRANSACLogistic regressionLinear regression

In this paper, we investigate the task of predicting sales in the fashion companies -a very fascinating sector by utilizing advanced machine learning models incorporated with rich features.This can help businesses predict the sales by using data from past transactions and other factors.To this end, we propose a method to improve the performance of sale forecasting models by enriching the models with the information of customers' online feedbacks (i.e., consumers' ratings and comments).This method involves leveraging both historical sales data and direct customer feedback to create predictive models that offer a comprehensive understanding of market dynamics.To facilitate the experiments, we also introduce a newly-built dataset about fashion products on a large e-commerce platform in Vietnam.We conducted extensive experiments on this dataset using three robust regression models which are Linear Regression, Decision Tree, and Random Forest.To classify customers' reviews, we exploit the innovative pre-trained language model, namely Bidirectional Encoder Representation from Transformer (BERT).Experimental results on this dataset showed that integrating this kind of information indeed boosts the sale forecasting models' accuracy significantly by all conventional evaluation metrics such as MAE and RMSE scores.Specifically, the proposed sale forecasting models integrated with customers' feedbacks significantly decreased the error rates of RMSE scores by 12%, 23.3%, and 17,8% using Linear Regression, Decision Tree, and Random Forest respectively.

Agribusiness is the foundation of Indian Economy. Its prosperity depends overwhelmingly on the climatic parameters. Occasions like erratic atmosphere are outside human capacity to control. Water assumes a noteworthy element in the development of a product (crop). If there is lacking water supply, chances of product disaster are more. Agriculturists fall into commitments since they have to go up against an uncommon yield’s effectiveness in view of deficient water supply and other atmospheric conditions which increase the peril of their benefit and the high expense of living. Along these lines, it winds up critical to anticipate the measure of rainfall utilized for irrigation. This will guarantee the budgetary use of water. This research paper presents a study and experimentation of predictive analytics to predict the amount of rainfall for irrigation. Predictive analytics include the extraction procedure of valuable data from the informational collection given by the client and foresee critical highlights or patterns. Prediction process is performed using supervised machine learning techniques. Multiple linear regression, k-nearest neighbour, decision tree, and random forest techniques are considered for building the predictive model, where these models are evaluated using root mean squared error. Root mean squared error obtained for multiple linear regression, k-nearest neighbour, decision tree, and random forest are 0.165, 0.103, 0.094, 0.083, respectively. Evidently, random forest shows less root mean squared error compared to other models and is considered for the prediction process. Also, an IoT-based weather station has been built to retrieve the real-time data from a sample area.

To develop and test decision tree (DT) models to classify physical activity (PA) intensity from accelerometer output and Gross Motor Function Classification System (GMFCS) classification level in ambulatory youth with cerebral palsy (CP) and compare the classification accuracy of the new DT models to that achieved by previously published cut points for youth with CP. Youth with CP (GMFCS levels I-III) (N = 51) completed seven activity trials with increasing PA intensity while wearing a portable metabolic system and ActiGraph GT3X accelerometers. DT models were used to identify vertical axis (VA) and vector magnitude (VM) count thresholds corresponding to sedentary (SED) (<1.5 METs), light-intensity PA (LPA) (≥1.5 and <3 METs) and moderate-to-vigorous PA (MVPA) (≥3 METs). Models were trained and cross-validated using the "rpart" and "caret" packages within R. For the VA (VA_DT) and VM DT (VM_DT), a single threshold differentiated LPA from SED, whereas the threshold for differentiating MVPA from LPA decreased as the level of impairment increased. The average cross-validation accuracies for the VC_DT were 81.1%, 76.7%, and 82.9% for GMFCS levels I, II, and III. The corresponding cross-validation accuracies for the VM_DT were 80.5%, 75.6%, and 84.2%. Within each GMFCS level, the DT models achieved better PA intensity recognition than previously published cut points. The accuracy differential was greatest among GMFCS level III participants, in whom the previously published cut points misclassified 40% of the MVPA activity trials. The GMFCS-specific cut points provide more accurate assessments of MVPA levels in youth with CP across the full spectrum of ambulatory ability.

Teicoplanin 24-h loading dose regimen using a decision tree model to target serum trough concentration of 15–30 μg/mL: A retrospective study

Decision tree induction has been studied extensively in machine learning as a solution for classification problems. The way the linear decision trees partition the search space is found to be comprehensible and hence appealing to data modelers. Comprehensibility is an important aspect of models used in medical data mining as it determines model credibility and even acceptability. In the practical sense though, inordinately long decision trees compounded by replication problems detracts from comprehensibility. This demerit can be partially attributed to their rigid structure that is unable to handle complex non-linear or/and continuous data. To address this issue we introduce a novel hybrid multivariate decision tree composed of polynomial, fuzzy and decision tree structures. The polynomial nature of these multivariate trees enable them to perform well in non-linear territory while the fuzzy members are used to squash continuous variables. By trading-off comprehensibility and performance using a multi-objective genetic programming optimization algorithm, we can induce polynomial-fuzzy decision trees (PFDT) that are smaller, more compact and of better performance than their linear decision tree (LDT) counterparts. In this paper we discuss the structural differences between PFDT and LDT (C4.5) and compare the size and performance of their models using medical data.

Badminton is a demanding sport that requires effective workload management to enhance performance and prevent injuries. This study developed a machine learning-based Decision Tree (DT) model to create personalized workload management strategies for 73 young elite badminton players, averaging 6 years of experience. Players underwent anthropometric and fitness assessments, with external loads measured via triaxial accelerometers and internal loads through rate of perceived exertion (RPE) during training and competition. K-means clustering categorized players into high, moderate, and low external workload levels. High-load players were generally older, taller, heavier, and exhibited superior flexibility, grip strength, and countermovement jump performance. Moderate-load players excelled in balance and leg endurance, while low-load players showed greater upper body strength, quicker reaction times, and higher perceived exertion. A sensitivity analysis was conducted to evaluate the impact of tree depth on model performance, followed by a comparative assessment of the Decision Tree (DT) model and multinomial Logistic Regression (MLR). The results demonstrated that the DT model outperformed the MLR, achieving 92% accuracy in predicting external loads compared to the MLR's 57%. This highlights the DT model's superior capability to provide tailored workload recommendations, thereby enhancing athletic performance and reducing the risk of injury.

To develop a logistic regression model, artificial neural network (ANN) model and decision tree (DT) model for the progression of mild cognitive impairment (MCI) to Alzheimer's disease (AD) to compare the performance of the three models. A total of 425 patients with MCI were screened from the original cohort. The actual follow up included 361 patients, with AD as the outcome variable. Three kinds of prediction models were developed: a logistic regression model, ANN model and DT model. The performance of all three models was measured with accuracy, sensitivity, positive predictive value and area under the receiver operating characteristic curve. A total of 121 patients with MCI developed AD, and the average conversion rate was 9.49% per year. The ANN model had higher accuracy (89.52 ± 0.36%), area under the receiver operating characteristic curve (92.08 ± 0.12), sensitivity (82.11 ± 0.42%) and positive predictive value (75.26 ± 0.86%) than the other two models. The first five important predictors of the ANN model were, in order, ADL score, age, urine AD-associated neuronal thread protein, alcohol consumption and smoking. For the DT model, they were age, activities of daily living score, family history of dementia, urine AD-associated neuronal thread protein and alcohol consumption. For the logistic regression model, they were age, sex, activities of daily living score, alcohol consumption and smoking. The logistic regression, ANN and DT models performed well at predicting the transition from MCI to AD with ideal stability. However, the ANN model had the best predictive value. Increased age, activities of daily living score, urine AD-associated neuronal thread protein, alcohol consumption, smoking and sex were important factors. Geriatr Gerontol Int 2021; 21: 43-47.

This work presents a new technique for the identification of multiple power quality disturbances in industrial power systems. This new technique is developed based on change detection filter (CDF) and machine intelligence techniques like the local linear radial basis function neural network (LLRBFNN) and decision tree (DT). The proposed change detection filter has been designed in one cycle back fashion for the multiple non–stationary transient power signal disturbances for localisation, and feature extraction. The extracted features are fed as inputs to either a LLRBFNN or a decision tree–based classifier (DTC) for characterisation of the power quality events. The performance of LLRBFNN and DTC are evaluated and compared with local linear wavelet neural network (LLWNN), wavelet neural network (WNN), radial basis function neural network (RBFNN), etc., to highlight the superior performance of the proposed classifiers.

A data science approach for advanced solid polymer electrolyte design