Functional Tree Research Articles

Shallow Landslide Prediction Using a Novel Hybrid Functional Machine Learning Algorithm

We used a novel hybrid functional machine learning algorithm to predict the spatial distribution of landslides in the Sarkhoon watershed, Iran. We developed a new ensemble model which is a combination of a functional algorithm, stochastic gradient descent (SGD) and an AdaBoost (AB) Meta classifier namely ABSGD model to predict the landslides. The model incorporates 20 landslide conditioning factors, which we ranked using the least-square support vector machine (LSSVM) technique. For the modeling, we considered 98 landslide locations, of which 70% (79) were used for training and 30% (19) for validation processes. Model validation was performed using sensitivity, specificity, accuracy, the root mean square error (RMSE) and the area under the receiver operatic characteristic (AUC) curve. We also used soft computing benchmark models, including SGD, logistic regression (LR), logistic model tree (LMT) and functional tree (FT) algorithms for model validation and comparison. The selected conditioning factors were significant in landslide occurrence but distance to road was found to be the most important factor. The ABSGD model (AUC= 0.860) outperformed the LR (0.797), SGD (0.776), LMT (0.740) and FT (0.734) models. Our results confirm that the combined use of a functional algorithm and a Meta classifier prevents over-fitting, reduces noise and enhances the power prediction of the individual SGD algorithm for the spatial prediction of landslides.

Discovering optimal features using static analysis and a genetic search based method for Android malware detection

Mobile device manufacturers are rapidly producing miscellaneous Android versions worldwide. Simultaneously, cyber criminals are executing malicious actions, such as tracking user activities, stealing personal data, and committing bank fraud. These criminals gain numerous benefits as too many people use Android for their daily routines, including important communi-cations. With this in mind, security practitioners have conducted static and dynamic analyses to identify malware. This study used static analysis because of its overall code coverage, low resource consumption, and rapid processing. However, static analysis requires a minimum number of features to efficiently classify malware. Therefore, we used genetic search (GS), which is a search based on a genetic algorithm (GA), to select the features among 106 strings. To evaluate the best features determined by GS, we used five machine learning classifiers, namely, Naive Bayes (NB), functional trees (FT), J48, random forest (RF), and multilayer perceptron (MLP). Among these classifiers, FT gave the highest accuracy (95%) and true positive rate (TPR) (96.7%) with the use of only six features.

GIS-based groundwater potential analysis using novel ensemble weights-of-evidence with logistic regression and functional tree models

The aim of the current study was to produce groundwater spring potential maps using novel ensemble weights-of-evidence (WoE) with logistic regression (LR) and functional tree (FT) models. First, a total of 66 springs were identified by field surveys, out of which 70% of the spring locations were used for training the models and 30% of the spring locations were employed for the validation process. Second, a total of 14 affecting factors including aspect, altitude, slope, plan curvature, profile curvature, stream power index (SPI), topographic wetness index (TWI), sediment transport index (STI), lithology, normalized difference vegetation index (NDVI), land use, soil, distance to roads, and distance to streams was used to analyze the spatial relationship between these affecting factors and spring occurrences. Multicollinearity analysis and feature selection of the correlation attribute evaluation (CAE) method were employed to optimize the affecting factors. Subsequently, the novel ensembles of the WoE, LR, and FT models were constructed using the training dataset. Finally, the receiver operating characteristic (ROC) curves, standard error, confidence interval (CI) at 95%, and significance level P were employed to validate and compare the performance of three models. Overall, all three models performed well for groundwater spring potential evaluation. The prediction capability of the FT model, with the highest AUC values, the smallest standard errors, the narrowest CIs, and the smallest P values for the training and validation datasets, is better compared to those of other models. The groundwater spring potential maps can be adopted for the management of water resources and land use by planners and engineers.

Wildfire spatial pattern analysis in the Zagros Mountains, Iran: A comparative study of decision tree based classifiers

Knowledge of wildfire behavior is of key importance for planning and allocating resources to fire suppression efforts. In this study, we analyzed the spatial pattern of wildfires with five decision tree based classifiers, including alternating decision tree (ADT), classification and regression tree (CART), functional tree (FT), logistic model tree (LMT), and Naïve Bayes tree (NBT). The classifiers were trained using historical fire locations in the Zagros Mountains (Iran) from the years 2007–2014 and a set of fifteen explanatory variables (i.e., slope degree, aspect, altitude, plan curvature, topographic position index (TPI), topographic roughness index (TRI), topographic wetness index (TWI), mean annual temperature and rainfall, wind effect, soil type, land use, and proximity to settlements, roads, and rivers) that were first optimized with a twostep process using multicollinearity analysis and the Gain Ratio variable selection method. The classifiers were then validated using the Kappa index and several statistical index-based evaluators (i.e., accuracy, sensitivity, specificity, precision, and F-measure). The global performance of the classifiers was measured using the ROC-AUC method. In this comparative study, the ADT classifier demonstrated the highest performance both in terms of goodness-of-fit with the training dataset (accuracy=99.8%, AUC=0.991) and the capability to predict future wildfires (accuracy=75.7%, AUC=0.903). This study contributes to the suite of research that evaluates data mining methods for the prediction of natural hazards.

A novel hybrid artificial intelligence approach based on the rotation forest ensemble and naïve Bayes tree classifiers for a landslide susceptibility assessment in Langao County, China

ABSTRACTThe main objective of this study was to produce landslide susceptibility maps for Langao County, China, using a novel hybrid artificial intelligence method based on rotation forest ensembles (RFEs) and naïve Bayes tree (NBT) classifiers labeled the RF-NBT model. The spatial database consisted of eighteen conditioning factors that were selected using the information gain ratio (IGR) method. The model was evaluated using quantitative statistical criteria, including the sensitivity, specificity, accuracy, root mean squared error (RMSE), and area under the receiver operating characteristic curve (AUC). Furthermore, the new model was compared with the NBT, functional tree (FT), logistic model tree (LMT) and reduced-error pruning tree (REPTree) soft computing benchmark models. The findings indicated that the RF-NBT model showed an increased prediction accuracy relative to the NBT model using both the training and validation datasets, and the RF-NBT model exhibited a greater capability for landslide susceptibility mapping. The new RF-NBT model also showed the most preferable results compared with the FT, LMT and REPTree models. Finally, an analysis of the landslide density (LD) using the RF-NBT model demonstrated that the very high susceptibility (VHS) class had the highest LD (3.552) among the landslide susceptibility maps. These results can be used for the planning and management of areas vulnerable to landslides in order to prevent damages caused by such natural disasters.

Study of Structure-active Relationship for Inhibitors of HIV-1 Integrase LEDGF/p75 Interaction by Machine Learning Methods.

HIV-1 integrase (IN) is a promising target for anti-AIDS therapy, and LEDGF/p75 is proved to enhance the HIV-1 integrase strand transfer activity in vitro. Blocking the interaction between IN and LEDGF/p75 is an effective way to inhibit HIV replication infection. In this work, 274 LEDGF/p75-IN inhibitors were collected as the dataset. Support Vector Machine (SVM), Decision Tree (DT), Function Tree (FT) and Random Forest (RF) were applied to build several computational models for predicting whether a compound is an active or weakly active LEDGF/p75-IN inhibitor. Each compound is represented by MACCS fingerprints and CORINA Symphony descriptors. The prediction accuracies for the test sets of all the models are over 70 %. The best model Model 3B built by FT obtained a prediction accuracy and a Matthews Correlation Coefficient (MCC) of 81.08 % and 0.62 on test set, respectively. We found that the hydrogen bond and hydrophobic interactions are important for the bioactivity of an inhibitor.

Landslide susceptibility assesssment in the Uttarakhand area (India) using GIS: a comparison study of prediction capability of naïve bayes, multilayer perceptron neural networks, and functional trees methods

The objective of this study is to make a comparison of the prediction performance of three techniques, Functional Trees (FT), Multilayer Perceptron Neural Networks (MLP Neural Nets), and Naive Bayes (NB) for landslide susceptibility assessment at the Uttarakhand Area (India). Firstly, a landslide inventory map with 430 landslide locations in the study area was constructed from various sources. Landslide locations were then randomly split into two parts (i) 70 % landslide locations being used for training models (ii) 30 % landslide locations being employed for validation process. Secondly, a total of eleven landslide conditioning factors including slope angle, slope aspect, elevation, curvature, lithology, soil, land cover, distance to roads, distance to lineaments, distance to rivers, and rainfall were used in the analysis to elucidate the spatial relationship between these factors and landslide occurrences. Feature selection of Linear Support Vector Machine (LSVM) algorithm was employed to assess the prediction capability of these conditioning factors on landslide models. Subsequently, the NB, MLP Neural Nets, and FT models were constructed using training dataset. Finally, success rate and predictive rate curves were employed to validate and compare the predictive capability of three used models. Overall, all the three models performed very well for landslide susceptibility assessment. Out of these models, the MLP Neural Nets and the FT models had almost the same predictive capability whereas the MLP Neural Nets (AUC = 0.850) was slightly better than the FT model (AUC = 0.849). The NB model (AUC = 0.838) had the lowest predictive capability compared to other models. Landslide susceptibility maps were final developed using these three models. These maps would be helpful to planners and engineers for the development activities and land-use planning.

An automated prognosis system for estrogen hormone status assessment in breast cancer tissue samples

Estrogen receptor (ER) status evaluation is a widely applied method in the prognosis of breast cancer. However, testing for the existence of the ER biomarker in a patient's tumor sample mainly depends on the subjective decisions of the doctors. The aim of this paper is to introduce the usage of a machine learning tool, functional trees (FTs), to attain an ER prognosis of the disease via an objective decision model. For this aim, 27 image files, each of which came from a biopsy sample of an invasive ductal carcinoma patient, were scanned and captured by a light microscope. From these images, 5150 nuclei were segmented with image processing methods. Several attributes, including statistical, wavelet, cooccurrence matrix, and Laws' texture features, were calculated inside the border area of each nucleus. A FT was trained over the feature dataset using a 10-fold cross-validation and then the obtained model was tested on a separate dataset. The assessment results of the model were compared with those of 2 experts. Consequently, the weighted kappa coefficient indicated a very good agreement (\kappa= 0.899 and \kappa= 0.927, P < 0.001) and the Spearman's rank order correlation showed a high level of correlation (\rho = 0.963 and \rho= 0.943, P < 0.001) between the results of the FT and those of the observers. The Wilcoxon test revealed that there was no significant difference between the results of the experts and the model (P = 0.051 and P = 0.316). Finally, it was concluded from the results that the FT could be used as a tool to support the decision of doctors by indicating consistent outputs and hence contribute to the objectiveness and reproducibility of the assessment results.

Construction of an automated screening system to predict breast cancer diagnosis and prognosis

Background and aim: Using machine learning methods can be helpful in the clinical decision processes such as pathological diagnosis with the aid of microscopic feature datasets. In the present study using the Breast Cancer Wisconsin dataset, an optimal algorithm (classifiers) which can predict both diagnosis (benign vs malignant) and prognosis (recur vs non-recur) was devised by comparing several classification algorithms. Methods: The performance of a two-step algorithm, which sequentially decides diagnosis and prognosis, was compared with that of a multi-class classifier, which divides classes simultaneously. Results: In the two-step classifier, it was discovered that the functional trees (FT) algorithm is the best for the first step of classification, and Naïve Bayes is the best for the second step of classification. On the other hand, the one-step classifier shows better accuracy and better prediction on benign and non-recurring cases than the two-step classifier, but it shows lower accuracy on predicting recurring cases, leading to lower sensitivity. Conclusions: We conclude that the two-step classifier with FT and Naïve Bayes is better than the one-step classifier. This work will be helpful in setting the automated screening system in real clinics and highlight clues to improve the accuracy by refining data and algorithm selection in data mining or machine learning processes.

Modeling Tumor Cellularity in Newly Diagnosed GBMs using MR Imaging and Spectroscopy

In this paper, we analyze the relationship between parameters of brain tumors obtained through in vivo magnetic resonance imaging (MRI), in vivo magneticnresonance spectroscopy (MRS), and ex vivo immunohistochemistry (IHC). The goal of our project is to provide a quantitative definition of tumor cellularity based on the in vivo parameters. Biopsy samples obtained from previously untreated patients with a diagnosis of GBM are used to find the link between imaging parameters at the specific biopsy locations and IHC parameters from the corresponding tissue samples. A functional tree (FT) model of tumor cellularity is learned from the in vivo parameters and the remaining histological parameters. The tumor cellularity model is then tested on examples which contain only in vivo parameters, by first estimating the remaining IHC parameters by applying the Expectation Maximization (EM) algorithm, and then using the complete parameter vector for classification.

Predictive models of autism spectrum disorder based on brain regional cortical thickness

Autism spectrum disorder (ASD) is a neurodevelopmental disorder with a wide phenotypic range, often affecting personality and communication. Previous voxel-based morphometry (VBM) studies of ASD have identified both gray- and white-matter volume changes. However, the cerebral cortex is a 2-D sheet with a highly folded and curved geometry, which VBM cannot directly measure. Surface-based morphometry (SBM) has the advantage of being able to measure cortical surface features, such as thickness. The goals of this study were twofold: to construct diagnostic models for ASD, based on regional thickness measurements extracted from SBM, and to compare these models to diagnostic models based on volumetric morphometry. Our study included 22 subjects with ASD (mean age 9.2±2.1 years) and 16 volunteer controls (mean age 10.0±1.9 years). Using SBM, we obtained regional cortical thicknesses for 66 brain structures for each subject. In addition, we obtained volumes for the same 66 structures for these subjects. To generate diagnostic models, we employed four machine-learning techniques: support vector machines (SVMs), multilayer perceptrons (MLPs), functional trees (FTs), and logistic model trees (LMTs). We found that thickness-based diagnostic models were superior to those based on regional volumes. For thickness-based classification, LMT achieved the best classification performance, with accuracy=87%, area under the receiver operating characteristic (ROC) curve (AUC)=0.93, sensitivity=95%, and specificity=75%. For volume-based classification, LMT achieved the highest accuracy, with accuracy=74%, AUC=0.77, sensitivity=77%, and specificity=69%. The thickness-based diagnostic model generated by LMT included 7 structures. Relative to controls, children with ASD had decreased cortical thickness in the left and right pars triangularis, left medial orbitofrontal gyrus, left parahippocampal gyrus, and left frontal pole, and increased cortical thickness in the left caudal anterior cingulate and left precuneus. Overall, thickness-based classification outperformed volume-based classification across a variety of classification methods.

A Hierarchical Object-oriented Functional Modeling Framework for Co-Design of Mechatronic Products

The existing co-design methods of mechatronic products focus on co-design of mechanical and electronic components or co-design of computer hardware and software components. There exist no effective co-design methods for mechanical, electronic, and software components. This article proposes an integrated object-oriented and functional decomposition framework, developed for co-design and co-analysis of product functions, structures, and their mapping relations in a top-down manner. The framework has three operational models: Function Model, Object Model, and Information Flow Model. The function model is implemented as a function tree (FT), which is a hierarchical structure for the functional decomposition and behavioral analysis of the product under functional domain commonly used in classical engineering design. The object model is a high order object model (HOOM) designed for system and component decomposition for analysis and design of the structure of a system and its components under physical domain. The information flow model is a function and object mapping model, which describes and analyzes implementation parameters and mapping relations between FT functions and HOOM objects. These three models are decomposed and constructed level-by-level and side-by-side to form the concurrent and coordinated design paradigm for the product design team. The components of the resulting design are then carefully reviewed and summarized in a design summary and task assignment table by the product design team, and assigned to their respective disciplinary engineers for detail design or implementation according to their attributes. The proposed methodology enables mechanical, electronic, and software engineers to develop mechatronic products concurrently in a seamlessly integrated fashion.

A CRITICAL ANALYSIS OF CTLA'S DEPRECIATION FACTORS—DO INHERENT INCONSISTENCIES OF METHOD COMPLICATE THE SIMPLICITY OF PROCESS?

CTLA methods follow a cost approach to value. Their adherence to DRC* methodology is perhaps fortuitous, but nonetheless confers some authenticity to the methods, in so far as they are grounded upon universal valuation principles. Strength lies in the closeness of fit. However, because CTLA methods were not designed specifically for this purpose, there are anomalies in the system that warrant reconsideration. A common criticism of CTLA methods is that they are overly complicated. DRC theory is complex, but essentially simple by comparison: the lines of process are clean and uncluttered. It is the anomalies within the CTLA methods that complicate matters; stricter realignment with DRC theory could achieve greater simplicity without sacrificing complexity. Specifically, the efficiency of a tree's function (its site suitability) should be considered under the Species factor, not Location, and the Site Rating, within the Location factor, should be altered to Site Occupancy Rating.

On some relations between 2-trees and tree metrics

A tree function (TF) t on a finite set X is a real function on the set of the pairs of elements of X satisfying the four-point condition: for all distinct x, y, z, w ∈ X, t( xy)+ t( zw)⩽ max{ t( xz) + t( yw), t( xw) + t( yz)}. Equivalently, t is representable by the lengths of the paths between the leaves of a valued tree T ℓ. TFs are a straightforward generalization of the tree dissimilarities and tree metrics of the literature. A graph Θ is a 2- tree if it belongs to the following class Q : an edge-graph belongs to Q : if Θ′ ∈ Q and yz is an edge of Θ′, then the graph obtained by the addition to Θ l of a new vertex x adjacent to y and z belongs to Q . These graphs, and the more general k-trees, have been studied in the literature as generalizations of trees. It is first explicited here how to make a TF t Θ, d correspond to any positively valued 2-tree Θ d on X. Then, given a tree dissimilarity t, the set Q( t) of the 2-trees Θ such that t = t Θ, t is studied. Any element of Q( t) gives a way of summarizing t by its restriction to a minimal subset of entries. Several characterizations and properties of the elements of Q( t) are given. We describe five classes of such elements, including two new ones. Associated with a dissimilarity of the general type, these classes of 2-trees lead to methods for the recognition and fitting of tree dissimilarities.