Combining Random Coverage with the Random Subspace Method
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Life Expectancy and Mortality by Race Using Random Subspace Method
International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-4S2 March, 2019 Life Expectancy and Mortality by Race Using Random Subspace Method Yong Gyu Jung, Dong Kyu Nam and Hee Wan Kim Abstract: In recent years, massive data is pouring out in the In ensemble learning one tries to combine the models information society. As collecting and processing of such vast produced by several learners into an ensemble that performs amount of data is becoming an important issue, it is widely used better than the original learners. One way of combining with various fields of data mining techniques for extracting learners is bootstrap aggregating or bagging, which shows information based on data. In this paper, we analyze the causes of the difference between the expected life expectancy and the each learner a randomly sampled subset of the training number of deaths by using the data of the expected life points so that the learners will produce different models that expectancy and the number of the deaths. To analyze the data can be sensibly averaged. In bagging, one samples training effectively, we will use the REP-tree for a small and simple size points with replacement from the full training set. problem using the Random subspace method, which is composed The random subspace method is similar to bagging except of random subspaces. The performance of the REP-tree that the features are randomly sampled, with replacement, algorithm was analyzed and evaluated for statistical data. Index Terms: Random subspace, REP-tree, racism, life for each learner. -
A Random Subspace Based Conic Functions Ensemble Classifier
Turkish Journal of Electrical Engineering & Computer Sciences Turk J Elec Eng & Comp Sci (2020) 28: 2165 – 2182 http://journals.tubitak.gov.tr/elektrik/ © TÜBİTAK Research Article doi:10.3906/elk-1911-89 A random subspace based conic functions ensemble classifier Emre ÇİMEN∗ Computational Intelligence and Optimization Laboratory (CIOL), Department of Industrial Engineering, Eskişehir Technical University, Eskişehir, Turkey Received: 14.11.2019 • Accepted/Published Online: 11.04.2020 • Final Version: 29.07.2020 Abstract: Classifiers overfit when the data dimensionality ratio to the number of samples is high in a dataset. This problem makes a classification model unreliable. When the overfitting problem occurs, one can achieve high accuracy in the training; however, test accuracy occurs significantly less than training accuracy. The random subspace method is a practical approach to overcome the overfitting problem. In random subspace methods, the classification algorithm selects a random subset of the features and trains a classifier function trained with the selected features. The classification algorithm repeats the process multiple times, and eventually obtains an ensemble of classifier functions. Conic functions based classifiers achieve high performance in the literature; however, these classifiers cannot overcome the overfitting problem when it is the case data dimensionality ratio to the number of samples is high. The proposed method fills the gap in the conic functions classifiers related literature. In this study, we combine the random subspace method andanovel conic function based classifier algorithm. We present the computational results by comparing the new approach witha wide range of models in the literature. The proposed method achieves better results than the previous implementations of conic function based classifiers and can compete with the other well-known methods. -
Random Forests
1 RANDOM FORESTS Leo Breiman Statistics Department University of California Berkeley, CA 94720 January 2001 Abstract Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a limit as the number of trees in the forest becomes large. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation between them. Using a random selection of features to split each node yields error rates that compare favorably to Adaboost (Freund and Schapire[1996]), but are more robust with respect to noise. Internal estimates monitor error, strength, and correlation and these are used to show the response to increasing the number of features used in the splitting. Internal estimates are also used to measure variable importance. These ideas are also applicable to regression. 2 1. Random Forests 1.1 Introduction Significant improvements in classification accuracy have resulted from growing an ensemble of trees and letting them vote for the most popular class. In order to grow these ensembles, often random vectors are generated that govern the growth of each tree in the ensemble. An early example is bagging (Breiman [1996]), where to grow each tree a random selection (without replacement) is made from the examples in the training set. Another example is random split selection (Dietterich [1998]) where at each node the split is selected at random from among the K best splits. -
Random Subspace Learning on Outlier Detection and Classification with Minimum Covariance Determinant Estimator
Rochester Institute of Technology RIT Scholar Works Theses 5-2016 Random Subspace Learning on Outlier Detection and Classification with Minimum Covariance Determinant Estimator Bohan Liu [email protected] Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Liu, Bohan, "Random Subspace Learning on Outlier Detection and Classification with Minimum Covariance Determinant Estimator" (2016). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Random Subspace Learning on Outlier Detection and Classification with Minimum Covariance Determinant Estimator by Bohan Liu A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Applied Statistics School of Mathematical Sciences College of Science Supervised by Professor Dr. Ernest Fokoue´ Department of Mathematical Sciences School of Mathematical Sciences College of Science Rochester Institute of Technology Rochester, New York May 2016 ii Approved by: Dr. Ernest Fokoue,´ Professor Thesis Advisor, School of Mathematical Sciences Dr. Steven LaLonde, Associate Professor Committee Member, School of Mathematical Sciences Dr. Joseph Voelkel, Professor Committee Member, School of Mathematical Sciences Thesis Release Permission Form Rochester Institute of Technology School of Mathematical Sciences Title: Random Subspace Learning on Outlier Detection and Classification with Minimum Covariance Determinant Estimator I, Bohan Liu, hereby grant permission to the Wallace Memorial Library to reproduce my thesis in whole or part. Bohan Liu Date iv To Jiapei and my parents v Acknowledgments I am unspeakably grateful for my thesis advisor Dr. -
Improving Random Forests by Feature Dependence Analysis
University of Mississippi eGrove Electronic Theses and Dissertations Graduate School 1-1-2019 Improving random forests by feature dependence analysis Silu Zhang Follow this and additional works at: https://egrove.olemiss.edu/etd Part of the Computer Sciences Commons Recommended Citation Zhang, Silu, "Improving random forests by feature dependence analysis" (2019). Electronic Theses and Dissertations. 1800. https://egrove.olemiss.edu/etd/1800 This Dissertation is brought to you for free and open access by the Graduate School at eGrove. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of eGrove. For more information, please contact [email protected]. IMPROVING RANDOM FORESTS BY FEATURE DEPENDENCE ANALYSIS A Dissertation Presented in Partial Fulfillment of Requirements for the Degree of Doctor of Philosophy in the Computer and Information Science The University of Mississippi by Silu Zhang August 2019 Copyright Silu Zhang 2019 ALL RIGHTS RESERVED ABSTRACT Random forests (RFs) have been widely used for supervised learning tasks because of their high prediction accuracy, good model interpretability and fast training process. How- ever, they are not able to learn from local structures as convolutional neural networks (CNNs) do, when there exists high dependency among features. They also cannot utilize features that are jointly dependent on the label but marginally independent of it. In this disserta- tion, we present two approaches to address these two problems respectively by dependence analysis. First, a local feature sampling (LFS) approach is proposed to learn and use the locality information of features to group dependent/correlated features to train each tree. For image data, the local information of features (pixels) is defined by the 2-D grid of the image. -
Stratified Sampling for Feature Subspace Selection in Random Forests for High Dimensional Data
Pattern Recognition 46 (2013) 769–787 Contents lists available at SciVerse ScienceDirect Pattern Recognition journal homepage: www.elsevier.com/locate/pr Stratified sampling for feature subspace selection in random forests for high dimensional data Yunming Ye a,e,n, Qingyao Wu a,e, Joshua Zhexue Huang b,d, Michael K. Ng c, Xutao Li a,e a Department of Computer Science, Shenzhen Graduate School, Harbin Institute of Technology, China b Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China c Department of Mathematics, Hong Kong Baptist University, China d Shenzhen Key Laboratory of High Performance Data Mining, China e Shenzhen Key Laboratory of Internet Information Collaboration, Shenzhen, China article info abstract Article history: For high dimensional data a large portion of features are often not informative of the class of the objects. Received 3 November 2011 Random forest algorithms tend to use a simple random sampling of features in building their decision Received in revised form trees and consequently select many subspaces that contain few, if any, informative features. In this 1 September 2012 paper we propose a stratified sampling method to select the feature subspaces for random forests with Accepted 3 September 2012 high dimensional data. The key idea is to stratify features into two groups. One group will contain Available online 12 September 2012 strong informative features and the other weak informative features. Then, for feature subspace Keywords: selection, we randomly select features from each group proportionally. The advantage of stratified Stratified sampling sampling is that we can ensure that each subspace contains enough informative features for High-dimensional data classification in high dimensional data. -
Adaptive Random Subspace Learning (RSSL) Algorithm for Prediction
Adaptive Random SubSpace Learning (RSSL) Algorithm for Prediction Mohamed Elshrif [email protected] Rochester Institute of Technology (RIT), 102 Lomb Memorial Dr., Rochester, NY 14623 USA Ernest Fokoué [email protected] Rochester Institute of Technology (RIT), 102 Lomb Memorial Dr., Rochester, NY 14623 USA Abstract tion f for predicting the response Y given the vector X of explanatory variables. In keeping with the standard in sta- We present a novel adaptive random subspace tistical learning theory, we will measure the predictive per- learning algorithm (RSSL) for prediction pur- formance of any given function f using the theoretical risk pose. This new framework is flexible where it functional given by can be adapted with any learning technique. In this paper, we tested the algorithm for regression Z R( f ) = E[`(Y; f (X))] = `(x;y)dP(x;y); (1) and classification problems. In addition, we pro- X ×Y vide a variety of weighting schemes to increase with the ideal scenario corresponding to the universally the robustness of the developed algorithm. These best function defined by different wighting flavors were evaluated on sim- ∗ ulated as well as on real-world data sets con- fb = arginffR( f )g = arginffE[`(Y; f (X))]g: (2) f f sidering the cases where the ratio between fea- tures (attributes) and instances (samples) is large For classification tasks, the most commonly used loss func- and vice versa. The framework of the new algo- tion is the zero-one loss `(Y; f (X)) = 1fY6= f (X)g, for which rithm consists of many stages: first, calculate the the theoretical universal best defined in (2) is the Bayes weights of all features on the data set using the classifier given by f ∗(x) = argmax fPr[Y = yjx]g. -
Dynamic Feature Scaling for K-Nearest Neighbor Algorithm
Dynamic Feature Scaling for K-Nearest Neighbor Algorithm Chandrasekaran Anirudh Bhardwaj1, Megha Mishra 1, Kalyani Desikan2 1B-Tech, School of computing science and engineering, VIT University, Chennai, India 1B-Tech, School of computing science and engineering, VIT University, Chennai, India 2Faculty-School of Advanced Sciences, VIT University,Chennai, India E-mail:1 [email protected], [email protected], [email protected] Abstract Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors algorithm is based on averaging the target values of the spatial neighbors. The selection process for neighbors in the Hermitian space is done with the help of distance metrics such as Euclidean distance, Minkowski distance, Mahalanobis distance etc. A majority of the metrics such as Euclidean distance are scale variant, meaning that the results could vary for different range of values used for the features. Standard techniques used for the normalization of scaling factors are feature scaling method such as Z-score normalization technique, Min-Max scaling etc. Scaling methods uniformly assign equal weights to all the features, which might result in a non-ideal situation. This paper proposes a novel method to assign weights to individual feature with the help of out of bag errors obtained from constructing multiple decision tree models. Introduction Nearest Neighbors Algorithm is one of the oldest and most studied algorithms used in the history of learning algorithms. It uses an approximating function, which averages the target values for the unknown vector with the help of target values of the vectors which are a part of the training dataset which are closest to the unknown vector in the Hermitian Space. -
Final Project Report Application of Machine Learning Methods To
CS 229 Final Report Yitian Liang STANFORD UNIVERSITY CS 229 – Spring 2021 Machine Learning Final Project Report Application of Machine Learning Methods to Predict the Level of Buildings Damage in the Nepal Earthquake Yitian Liang (SUNetID: ytliang) June 2, 2021 CS 229 Final Report Yitian Liang 1 Abstract The assessment of damage level of post-earthquake structures through calculations is always complicated and time-consuming, and it is not suitable for situations when a large number of buildings need to be evaluated after an earthquake. One of the largest post-disaster datasets, which comes from the April 2015 Nepal earthquake, makes it possible to train models to predict damage levels based on building information. Here, we investigate the application of various machine learning methods to the problem of structural damage level prediction. 2 Introduction The ground movements in earthquakes will cause huge damage to building structures. There are different levels of earthquake magnitude, but there is no systematic classification of the buildings damage. The dynamic analysis of a single structure usually takes a long time, which is not suitable for situations where a large number of buildings need to be evaluated after an earthquake. After the April 2015 Nepal earthquake, which was the worst natural disaster to strike Nepal since 1934, the National Planning Commission, along with Kathmandu Living Labs and the Central Bureau of Statistics, has generated large post-disaster datasets, containing valuable information on earthquake impacts, household conditions, and socio- economic-demographic statistics. I hope that through the application of machine learning on this dataset, we can quickly classify the damage level of the structures in order to facilitate planning rescue and reconstruction and assessing the loss. -
Random Subspace Learning (Rassel) with Data Driven Weighting Schemes
Math. Appl. 7 (2018), 11{30 DOI: 10.13164/ma.2018.02 RANDOM SUBSPACE LEARNING (RASSEL) WITH DATA DRIVEN WEIGHTING SCHEMES MOHAMED ELSHRIF and ERNEST FOKOUE´ Abstract. We present a novel adaptation of the random subspace learning approach to regression analysis and classification of high dimension low sample size data, in which the use of the individual strength of each explanatory variable is harnessed to achieve a consistent selection of a predictively optimal collection of base learners. In the context of random subspace learning, random forest (RF) occupies a prominent place as can be seen by the vast number of extensions of the random forest idea and the multiplicity of machine learning applications of random forest. The adaptation of random subspace learning presented in this paper differs from random forest in the following ways: (a) instead of using trees as RF does, we use multiple linear regression (MLR) as our regression base learner and the generalized linear model (GLM) as our classification base learner and (b) rather than selecting the subset of variables uniformly as RF does, we present the new concept of sampling variables based on a multinomial distribution with weights (success 'probabilities') driven through p independent one-way analysis of variance (ANOVA) tests on the predic- tor variables. The proposed framework achieves two substantial benefits, namely, (1) the avoidance of the extra computational burden brought by the permutations needed by RF to de-correlate the predictor variables, and (2) the substantial reduc- tion in the average test error gained with the base learners used. 1. Introduction In machine learning, in order to improve the accuracy of a regression, or classifi- cation function, scholars tend to combine multiple estimators because it has been proven both theoretically and empirically [19, 20] that an appropriate combina- tion of good base learners leads to a reduction in prediction error.