DOCSLIB.ORG

Gaussian Universal Features, Canonical Correlations, and Common Information

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Gaussian Universal Features, Canonical Correlations, and Common Information Gaussian Universal Features, Canonical Correlations, and Common Information Shao-Lun Huang Gregory W. Wornell, Lizhong Zheng DSIT Research Center, TBSI, SZ, China 518055 Dept. EECS, MIT, Cambridge, MA 02139 USA Email: [email protected] Email: {gww, lizhong}@mit.edu Abstract—We address the problem of optimal feature selection we define a rotation-invariant ensemble (RIE) that assigns a for a Gaussian vector pair in the weak dependence regime, uniform prior for the unknown attributes, and formulate a when the inference task is not known in advance. In particular, universal feature selection problem that aims to select optimal we show that multiple formulations all yield the same solution, and correspond to the singular value decomposition (SVD) of features minimizing the averaged MSE over RIE. We show the canonical correlation matrix. Our results reveal key con- that the optimal features can be obtained from the SVD nections between canonical correlation analysis (CCA), principal of a canonical dependence matrix (CDM). In addition, we component analysis (PCA), the Gaussian information bottleneck, demonstrate that in a weak dependence regime, this SVD Wyner’s common information, and the Ky Fan (nuclear) norms. also provides the optimal features and solutions for several problems, such as CCA, information bottleneck, and Wyner’s common information, for jointly Gaussian variables. This I. INTRODUCTION reveals important connections between information theory and Typical applications of machine learning involve data whose machine learning problems. dimension is high relative to the amount of training data that is available. As a consequence, it is necessary to perform di- mensionality reduction before the regression or other inference II. GAUSSIAN LOCAL ANALYSIS FRAMEWORK task is carried out. This reduction corresponds to extracting a set of comparatively low-dimensional features from the data. In the sequel, we restrict our attention to zero-mean vari- When the inference task is fully specified, classical statistics ables, for simplicity of exposition. In the model of interest, K K establishes that the appropriate features take the form of a X 2 R X and Y 2 R Y . Moreover, h i (minimal) sufficient statistic. However, in most contemporary X T ΛX ΛXY Z = ∼ N(0; ΛZ ); ΛZ = E ZZ = ; settings, the task is not known in advance—or equivalently Y ΛYX ΛY T there are multiple tasks—and we require a set of universal so X ∼ N(0; ΛX ), Y ∼ N(0; ΛY ), ΛYX = E YX , and T features that are, in an appropriate sense, uniformly good. ΛXY = ΛYX . We assume without loss of generality that ΛX With this motivation, the Gaussian universal feature se- and ΛY are (strictly) positive definite. The joint distribution lection problem can be expressed as: given a pair of high- takes the form jΛ j−1=2 1 dimensional jointly distributed Gaussian data vectors X 2 P (x; y) = P (z) = Z exp − zT Λ−1 z K K X;Y Z K =2 Z (2) R X and, Y 2 R Y , how should we choose low-dimensional (2π) Z 2 features f(X) and g(Y ) before knowing the desired inference where KZ = KX +KY , and with j·j denoting the determinant task so to ensure that after the task is revealed, inference based of its argument. It will be convenient to normalize X and Y on the features performs as well as possible? according to ~ −1=2 ~ −1=2 Mathematically, we express this problem as one of making X = ΛX X and Y = ΛY Y inference about latent variables U; V 2 k, for 1 ≤ k ≤ K so that R , ~ T minfK ;K g, in the Gauss-Markov chain ~ X IB X Y Z = ~ ; ΛZ~ = ; (3) U $ X $ Y $ V; (1) Y BI where the (Gaussian) distributions for these variables, i.e., where B Λ−1=2 Λ Λ−1=2 = Λ−1=2 Γ Λ1=2 (4) PU , PXjU , PV , and PY jV are not known at the time of , Y YX X Y Y jX X feature extraction. Our results can be viewed as an extension is called the canonical dependence matrix (CDM). CDM plays of the framework for discrete variables described in [1]. We the key role in Gaussian local analysis as the divergence note in advance that to simplify the exposition, we treat transfer matrix (DTM) does in the discrete case [1]. ~ ~ PX;Y as known, though in practice we must estimate the We note that the MMSE estimate of Y based on X is ~^ ~ ~ ~ ~^ ~ relevant aspects of this distribution from training samples Y (X) = B X, and the associated error ν~ , Y − Y (X) T T f(x1; y1);:::; (xn; yn)g. has covariance E ν~ν~ = I − BB , so the resulting MSE 2 T 2 Our contribution of this paper is summarized as follows. To is σ~e = tr I − BB = KY − kBkF. with k · kF denoting deal with the inference for unknown attributes, in section III the Frobenius norm. The SVD of B takes the form [2], which interprets the power iteration method for SVD K Y X T X Y X T computation. B = Ψ Σ Ψ = σi i i ; (5) From this perspective, we see that approximations to PX;Y i=1 can be obtained by truncating the representation (8) to the first where K = minfKX ;KY g and where we order the singular k < K of the terms in the product, yielding values according to σ1 ≥ · · · ≥ σK . Note that since (3) is P (k) (k) (x; y) positive semidefinite, it follows that σi ≤ 1 for i = 1;:::;K. X ;Y k ! As in the discrete case [1], it is useful to define a local ∗ ∗ Y σi fi (x) gi (y) analysis regime for such variables. In particular, we make use = PX (x) PY (y) e 1 + o() ; of the following notion of neighborhood. i=1 This corresponds to jointly Gaussian X(k) and Y (k) with the Definition 1 (Gaussian -Neighborhood). For a given > 0, same marginals as X and Y , respectively, but the -neighborhood of a K0-dimensional Gaussian distribution k ! 1=2 X Y X T 1=2 P0 = N(0; Λ0) is the set of Gaussian distributions in a Λ (k) (k) = Λ σ Λ ; (9) 2 Y X Y i i i X covariance-divergence ball of radius about P0, i.e., i=1 K0 | {z } G (P0) (k) ,B n −1=2 −1=2 2 2 o so , P = N(0; Λ): Λ0 Λ − Λ0 Λ0 F ≤ K0 k (k) (k) 1 X 2 2 I(X ; Y ) = σi + o( ): Note that PX;Y lies in an -neighborhood of PX PY if and 2 i=1 only if PX;~ Y~ lies in an -neighborhood of PX~ PY~ . Hence, KX +KY 2 2 III. UNIVERSAL LINEAR FEATURE SELECTION PX;Y 2 G (PX PY ) when kΛZ~ − IkF ≤ (KX + K ). We conclude that the neighborhood constraint limits how We use our framework to address the problem of Gaussian Y ~ ~ ~ ~ much the mean-square error (MSE) in the estimate of Y~ based universal feature selection. In our analysis, U; X; Y; V denote on observing X~ can be reduced relative to the MSE in the normalized versions of the variables in (1), so are N(0; I) estimate of Y~ based on no data. In the rest of this paper, we random vectors of appropriate dimension. In the sequel, we focus on the regime that is small. The K-L divergence and consider several different formulations, all of which yield the mutual information in this regime admits the following useful same linear features, and coincide with those defined by the asymptotic expressions. modal expansion (8). In our development, the following lemma will be useful (see, e.g., [3, Corollary 4.3.39, p. 248]). Lemma 1. In the weak dependence regime, 1 2 2 Lemma 2. Given an arbitrary k1 × k2 matrix A and any D(PY jX (·|x)kPY ) = Bx~ + o( ); 2 k 2 1;:::; minfk1; k2g , we have and k 1 K 2 X 2 X 2 2 max AM F = σi(A) ; (10) I(X; Y ) = σi + o( ): (6) k2×k T 2 fM2R : M M=Ig i=1 i=1 with σ (A) ≥ · · · ≥ σ (A) denoting the (ordered) 1 minfk1;k2g Proof. This is straightforward from the fact that, for an singular values of A. Moreover, the maximum in (10) is 2 T 2 2 2 arbitrary matrix A, ln jI − AA j = − kAkF + o( ). achieved by M = 1(A) ··· k(A) , with i(A) de- noting the right singular vector of A corresponding to σi(A), To interpret (6), consider the modal decomposition of PX;Y . In particular, observe that as ! 0, for i = 1;:::; minfk1; k2g. T −1 I −B A. Optimum Features, Rotation-Invariant Ensembles ΛZ~ = + o(): (7) −BI In this formulation, we seek to determine optimum features Hence, K ! for estimating an unknown k-dimensional U from Y , in the ∗ ∗ Y σi fi (x) gi (y) case where U and X are weakly dependent; specifically, PX;Y (x; y) = PX (x) PY (y) e 1 + o() ; KX +k i=1 PX;U 2 G (PX PU ). Accordingly, from the innovations XjU (8a) form X~ = Φ U~ + ν ~ ~ , where U~ and ν ~ ~ are ∗ ∗ U!X U!X where fi and gi are (linear) functions given by independent, it follows that weak dependence means, using ∗ X T −1=2 ∗ Y T −1=2 XjU fi (x) = ( i ) ΛX x and gi (y) = ( i ) ΛY y: Definition 1, that Φ satisfies | {z } | {z } XjU 2 1 ∗T ∗T Φ ≤ (KX + k); (11) ,fi ,gi F 2 (8b) but is otherwise unknown. Moreover, using (8b) with (4) and (5) we obtain the covariance ~ ~ XjU ~ We observe Y = B X + νX~ !Y~ = BΦ U + νU~!Y~ .
Load more

Recommended publications
  • A New Wrapper Feature Selection Approach Using Neural Network
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Community Repository of Fukui Neurocomputing 73 (2010) 3273–3283 Contents lists available at ScienceDirect Neurocomputing journal homepage: www.elsevier.com/locate/neucom A new wrapper feature selection approach using neural network Md. Monirul Kabir a, Md. Monirul Islam b, Kazuyuki Murase c,n a Department of System Design Engineering, University of Fukui, Fukui 910-8507, Japan b Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000, Bangladesh c Department of Human and Artificial Intelligence Systems, Graduate School of Engineering, and Research and Education Program for Life Science, University of Fukui, Fukui 910-8507, Japan article info abstract Article history: This paper presents a new feature selection (FS) algorithm based on the wrapper approach using neural Received 5 December 2008 networks (NNs). The vital aspect of this algorithm is the automatic determination of NN architectures Received in revised form during the FS process. Our algorithm uses a constructive approach involving correlation information in 9 November 2009 selecting features and determining NN architectures. We call this algorithm as constructive approach Accepted 2 April 2010 for FS (CAFS). The aim of using correlation information in CAFS is to encourage the search strategy for Communicated by M.T. Manry Available online 21 May 2010 selecting less correlated (distinct) features if they enhance accuracy of NNs. Such an encouragement will reduce redundancy of information resulting in compact NN architectures. We evaluate the Keywords: performance of CAFS on eight benchmark classification problems. The experimental results show the Feature selection essence of CAFS in selecting features with compact NN architectures.
    [Show full text]
  • ``Preconditioning'' for Feature Selection and Regression in High-Dimensional Problems
    The Annals of Statistics 2008, Vol. 36, No. 4, 1595–1618 DOI: 10.1214/009053607000000578 © Institute of Mathematical Statistics, 2008 “PRECONDITIONING” FOR FEATURE SELECTION AND REGRESSION IN HIGH-DIMENSIONAL PROBLEMS1 BY DEBASHIS PAUL,ERIC BAIR,TREVOR HASTIE1 AND ROBERT TIBSHIRANI2 University of California, Davis, Stanford University, Stanford University and Stanford University We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selec- tion that first estimates the regression function, yielding a “preconditioned” response variable. The primary method used for this initial regression is su- pervised principal components. Then we apply a standard procedure such as forward stepwise selection or the LASSO to the preconditioned response variable. In a number of simulated and real data examples, this two-step pro- cedure outperforms forward stepwise selection or the usual LASSO (applied directly to the raw outcome). We also show that under a certain Gaussian la- tent variable model, application of the LASSO to the preconditioned response variable is consistent as the number of predictors and observations increases. Moreover, when the observational noise is rather large, the suggested proce- dure can give a more accurate estimate than LASSO. We illustrate our method on some real problems, including survival analysis with microarray data. 1. Introduction. In this paper, we consider the problem of fitting linear (and other related) models to data for which the number of features p greatly exceeds the number of samples n. This problem occurs frequently in genomics, for exam- ple, in microarray studies in which p genes are measured on n biological samples.
    [Show full text]
  • Feature Selection Via Dependence Maximization
    JournalofMachineLearningResearch13(2012)1393-1434 Submitted 5/07; Revised 6/11; Published 5/12 Feature Selection via Dependence Maximization Le Song [email protected] Computational Science and Engineering Georgia Institute of Technology 266 Ferst Drive Atlanta, GA 30332, USA Alex Smola [email protected] Yahoo! Research 4301 Great America Pky Santa Clara, CA 95053, USA Arthur Gretton∗ [email protected] Gatsby Computational Neuroscience Unit 17 Queen Square London WC1N 3AR, UK Justin Bedo† [email protected] Statistical Machine Learning Program National ICT Australia Canberra, ACT 0200, Australia Karsten Borgwardt [email protected] Machine Learning and Computational Biology Research Group Max Planck Institutes Spemannstr. 38 72076 Tubingen,¨ Germany Editor: Aapo Hyvarinen¨ Abstract We introduce a framework for feature selection based on dependence maximization between the selected features and the labels of an estimation problem, using the Hilbert-Schmidt Independence Criterion. The key idea is that good features should be highly dependent on the labels. Our ap- proach leads to a greedy procedure for feature selection. We show that a number of existing feature selectors are special cases of this framework. Experiments on both artificial and real-world data show that our feature selector works well in practice. Keywords: kernel methods, feature selection, independence measure, Hilbert-Schmidt indepen- dence criterion, Hilbert space embedding of distribution 1. Introduction In data analysis we are typically given a set of observations X = x1,...,xm X which can be { } used for a number of tasks, such as novelty detection, low-dimensional representation,⊆ or a range of . Also at Intelligent Systems Group, Max Planck Institutes, Spemannstr.
    [Show full text]
  • Feature Selection in Convolutional Neural Network with MNIST Handwritten Digits
    Feature Selection in Convolutional Neural Network with MNIST Handwritten Digits Zhuochen Wu College of Engineering and Computer Science, Australian National University [email protected] Abstract. Feature selection is an important technique to improve neural network performances due to the redundant attributes and the massive amount in original data sets. In this paper, a CNN with two convolutional layers followed by a dropout, then two fully connected layers, is equipped with a feature selection algorithm. Accuracy rate of the networks with different attribute input weight as zero are calculated and ranked so that the machine can decide which attribute is the least important for each run of the algorithm. The algorithm repeats itself to remove multiple attributes. When the network will not achieve a satisfying accuracy rate as defined in the algorithm, the process terminates and no more attributes to be removed. A CNN is chosen the image recognition task and one dropout is applied to reduce the overfitting of training data. This implementation of deep learning method proves its ability to rise accuracy and neural network performance with up to 80% less attributes fed in. This paper also compares the technique with other the result of LeNet-5 to see the differences and common facts. Keywords: CNN, Feature selection, Classification, Real world problem, Deep learning 1. Introduction Feature selection has been a focus in many study domains like econometrics, statistics and pattern recognition. It is a process to select a subset of attributes in given data and improve the algorithm performance in efficient and accuracy, etc. It is commonly understood that the more features being fed into a neural network, the more information machine could learn from in order to achieve a better outcome.
    [Show full text]
  • Classification with Costly Features Using Deep Reinforcement Learning
    Classification with Costly Features using Deep Reinforcement Learning Jarom´ır Janisch and Toma´sˇ Pevny´ and Viliam Lisy´ Artificial Intelligence Center, Department of Computer Science Faculty of Electrical Engineering, Czech Technical University in Prague jaromir.janisch, tomas.pevny, viliam.lisy @fel.cvut.cz f g Abstract y1 We study a classification problem where each feature can be y2 acquired for a cost and the goal is to optimize a trade-off be- af3 af5 af1 ac tween the expected classification error and the feature cost. We y3 revisit a former approach that has framed the problem as a se- ··· quential decision-making problem and solved it by Q-learning . with a linear approximation, where individual actions are ei- . ther requests for feature values or terminate the episode by providing a classification decision. On a set of eight problems, we demonstrate that by replacing the linear approximation Figure 1: Illustrative sequential process of classification. The with neural networks the approach becomes comparable to the agent sequentially asks for different features (actions af ) and state-of-the-art algorithms developed specifically for this prob- finally performs a classification (ac). The particular decisions lem. The approach is flexible, as it can be improved with any are influenced by the observed values. new reinforcement learning enhancement, it allows inclusion of pre-trained high-performance classifier, and unlike prior art, its performance is robust across all evaluated datasets. a different subset of features can be selected for different samples. The goal is to minimize the expected classification Introduction error, while also minimizing the expected incurred cost.
    [Show full text]
  • Feature Selection for Regression Problems
    Feature Selection for Regression Problems M. Karagiannopoulos, D. Anyfantis, S. B. Kotsiantis, P. E. Pintelas unreliable data, then knowledge discovery Abstract-- Feature subset selection is the during the training phase is more difficult. In process of identifying and removing from a real-world data, the representation of data training data set as much irrelevant and often uses too many features, but only a few redundant features as possible. This reduces the of them may be related to the target concept. dimensionality of the data and may enable There may be redundancy, where certain regression algorithms to operate faster and features are correlated so that is not necessary more effectively. In some cases, correlation coefficient can be improved; in others, the result to include all of them in modelling; and is a more compact, easily interpreted interdependence, where two or more features representation of the target concept. This paper between them convey important information compares five well-known wrapper feature that is obscure if any of them is included on selection methods. Experimental results are its own. reported using four well known representative regression algorithms. Generally, features are characterized [2] as: 1. Relevant: These are features which have Index terms: supervised machine learning, an influence on the output and their role feature selection, regression models can not be assumed by the rest 2. Irrelevant: Irrelevant features are defined as those features not having any influence I. INTRODUCTION on the output, and whose values are generated at random for each example. In this paper we consider the following 3. Redundant: A redundancy exists regression setting.
    [Show full text]
  • Feature Selection for Unsupervised Learning
    Journal of Machine Learning Research 5 (2004) 845–889 Submitted 11/2000; Published 8/04 Feature Selection for Unsupervised Learning Jennifer G. Dy [email protected] Department of Electrical and Computer Engineering Northeastern University Boston, MA 02115, USA Carla E. Brodley [email protected] School of Electrical and Computer Engineering Purdue University West Lafayette, IN 47907, USA Editor: Stefan Wrobel Abstract In this paper, we identify two issues involved in developing an automated feature subset selec- tion algorithm for unlabeled data: the need for finding the number of clusters in conjunction with feature selection, and the need for normalizing the bias of feature selection criteria with respect to dimension. We explore the feature selection problem and these issues through FSSEM (Fea- ture Subset Selection using Expectation-Maximization (EM) clustering) and through two different performance criteria for evaluating candidate feature subsets: scatter separability and maximum likelihood. We present proofs on the dimensionality biases of these feature criteria, and present a cross-projection normalization scheme that can be applied to any criterion to ameliorate these bi- ases. Our experiments show the need for feature selection, the need for addressing these two issues, and the effectiveness of our proposed solutions. Keywords: clustering, feature selection, unsupervised learning, expectation-maximization 1. Introduction In this paper, we explore the issues involved in developing automated feature subset selection algo- rithms for unsupervised learning. By unsupervised learning we mean unsupervised classification, or clustering. Cluster analysis is the process of finding “natural” groupings by grouping “similar” (based on some similarity measure) objects together. For many learning domains, a human defines the features that are potentially useful.
    [Show full text]
  • Feature Selection Convolutional Neural Networks for Visual Tracking Zhiyan Cui, Na Lu*
    1 Feature Selection Convolutional Neural Networks for Visual Tracking Zhiyan Cui, Na Lu* Abstract—Most of the existing tracking methods based on such amount of data for tracking to train a deep network. CNN(convolutional neural networks) are too slow for real-time MDNet [12] is a novel solution for tracking problem with application despite the excellent tracking precision compared detection method. It is trained by learning the shared with the traditional ones. Moreover, neural networks are memory intensive which will take up lots of hardware resources. In this representations of targets from multiple video sequences, paper, a feature selection visual tracking algorithm combining where each video is regarded as a separate domain. There CNN based MDNet(Multi-Domain Network) and RoIAlign was are several branches in the last layer of the network for developed. We find that there is a lot of redundancy in feature binary classification and each of them is corresponding to maps from convolutional layers. So valid feature maps are a video sequence. The preceding layers are in charge of selected by mutual information and others are abandoned which can reduce the complexity and computation of the network and capturing common representations of targets. While tracking, do not affect the precision. The major problem of MDNet also lies the last layer is removed and a new single branch is added in the time efficiency. Considering the computational complexity to the network to compute the scores in the test sequences. of MDNet is mainly caused by the large amount of convolution Parameters in the fully-connected layers are fine-tuned online operations and fine-tuning of the network during tracking, a during tracking.
    [Show full text]
  • Feature Selection
    Feature Selection Suhang Wang, Jiliang Tang and Huan Liu Arizona State University Abstract Data dimensionality is growing exponentially, which poses chal- lenges to the vast majority of existing mining and learning algorithms, such as the curse of dimensionality, large storage requirement, and high computational cost. Feature selection has been proven to be an effec- tive and efficient way to prepare high dimensional data for data mining and machine learning. The recent emergence of novel techniques and new types of data and features not only advances existing feature se- lection research but also makes feature selection evolve more rapidly, becoming applicable to a broader range of applications. In this article, we aim to provide a basic introduction to feature selection including basic concepts, classifications of existing systems, recent development, and applications. Synonyms: Feature subset selection, Feature weighting, Attributes selec- tion Definition (or Synopsis): Feature selection, as a dimensionality reduction technique, aims to choosing a small subset of the relevant features from the original ones by removing irrelevant, redundant or noisy features. Feature selection usually leads to better learning performance, i.e., higher learning accuracy, lower computational cost, and better model interpretability. Generally speaking, irrelevant features are features that cannot discrim- inate samples from different classes(supervised) or clusters(unsupervised). Removing irrelevant features will not affect learning performance. In fact, removal of irrelevant features may help learn a better model, as irrelevant features may confuse the learning system and cause memory and computa- tion inefficiency. For example, in figure 1(a), f1 is a relevant feature because f1 can discriminate class1 and class2.
    [Show full text]
  • Concrete Autoencoders
    Differentiable Feature Selection with Concrete Autoencoders Abubakar Abid★ Muhammed Fatih Balin★ James Zou Poster: Thu Jun 13th 06:30 - 09:00 PM @ Pacific Ballroom #188 Unsupervised Feature Selection (UFS) is Widely Used in Machine Learning ● Identify the subset of most informative features in dataset ● Simplifies the process of training models ● Especially useful if the data is difficult or expensive to collect Differentiable Feature Selection and Reconstruction with Concrete Autoencoders 2 Unsupervised Feature Selection (UFS) is Used Widely in Applied ML ● Example: the L1000 Landmark Genes [Lamb et al., 2006] All Genes L1000 Genes All Genes Samples Samples Samples Recons truction Feature Selection Differentiable Feature Selection and Reconstruction with Concrete Autoencoders 3 UFS Methods Typically Rely on Regularization Unsupervised Discriminative Feature Selection (UDFS) [Yang et al., 2011] Multi-Cluster Feature Selection (MCFS) All based on [Cai et al., 2010] L1 or L21 regularization Autoencoder Feature Selection (AEFS) [Han et al., 2017] Differentiable Feature Selection and Reconstruction with Concrete Autoencoders 4 What about directly backpropagating through discrete “feature selection” nodes? Differentiable Feature Selection and Reconstruction with Concrete Autoencoders 5 What about directly backpropagating through discrete “feature selection” nodes? Replace the weights of the encoder with parameters of a Concrete Random Variable (Maddison, 2016) Differentiable Feature Selection and Reconstruction with Concrete Autoencoders 6
    [Show full text]
  • A Comparative Study on the Effect of Feature Selection on Classification Accuracy
    Available online at www.sciencedirect.com Procedia Technology 1 ( 2012 ) 323 – 327 INSODE 2011 A comparative study on the effect of feature selection on classification accuracy Esra Mahsereci Karabuluta*, Selma Ayşe Özelb, Turgay İbrikçib,c a Gaziantep University, Gaziantep Vocational High School, Şehitkamil/Gaziantep, 27310, Turkey b Çukurova University, Electrical-Electronics Engineering Department, Balcalı/Adana, 01330, Turkey c Çukurova University,Computer Engineering Department, Balcalı/Adana, 01330, Turkey Abstract Feature selection has become interest to many research areas which deal with machine learning and data mining, because it provides the classifiers to be fast, cost-effective, and more accurate. In this paper the effect of feature selection on the accuracy of NaïveBayes, Artificial Neural Network as Multilayer Perceptron, and J48 decision tree classifiers is presented. These classifiers are compared with fifteen real datasets which are pre-processed with feature selection methods. Up to 15.55% improvement in classification accuracy is observed, and Multilayer Perceptron appears to be the most sensitive classifier to feature selection. Keywords: feature selection; classification; accuracy; Naïve Bayes; multilayer perceptron 1. Introduction Feature selection is the process of removing redundant or irrelevant features from the original data set. So the execution time of the classifier that processes the data reduces, also accuracy increases because irrelevant features can include noisy data affecting the classification accuracy negatively [1]. With feature selection the understandability can be improved and cost of data handling becomes smaller [2]. Feature selection algorithms are divided into three categories; filters, wrappers and embedded selectors. Filters evaluate each feature independent from the classifier, rank the features after evaluation and take the superior ones [3].
    [Show full text]
  • Deep Learning Feature Extraction Approach for Hematopoietic Cancer Subtype Classification
    International Journal of Environmental Research and Public Health Article Deep Learning Feature Extraction Approach for Hematopoietic Cancer Subtype Classification Kwang Ho Park 1 , Erdenebileg Batbaatar 1 , Yongjun Piao 2, Nipon Theera-Umpon 3,4,* and Keun Ho Ryu 4,5,6,* 1 Database and Bioinformatics Laboratory, College of Electrical and Computer Engineering, Chungbuk National University, Cheongju 28644, Korea; [email protected] (K.H.P.); [email protected] (E.B.) 2 School of Medicine, Nankai University, Tianjin 300071, China; [email protected] 3 Department of Electrical Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailand 4 Biomedical Engineering Institute, Chiang Mai University, Chiang Mai 50200, Thailand 5 Data Science Laboratory, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh 700000, Vietnam 6 Department of Computer Science, College of Electrical and Computer Engineering, Chungbuk National University, Cheongju 28644, Korea * Correspondence: [email protected] (N.T.-U.); [email protected] or [email protected] (K.H.R.) Abstract: Hematopoietic cancer is a malignant transformation in immune system cells. Hematopoi- etic cancer is characterized by the cells that are expressed, so it is usually difficult to distinguish its heterogeneities in the hematopoiesis process. Traditional approaches for cancer subtyping use statistical techniques. Furthermore, due to the overfitting problem of small samples, in case of a minor cancer, it does not have enough sample material for building a classification model. Therefore, Citation: Park, K.H.; Batbaatar, E.; we propose not only to build a classification model for five major subtypes using two kinds of losses, Piao, Y.; Theera-Umpon, N.; Ryu, K.H.
    [Show full text]