International Journal of Neural Systems, Vol. 23, No. 5 (2013) 1350020 (18 pages) c World Scientific Publishing Company DOI: 10.1142/S0129065713500202 ASSESSMENT OF FEATURE SELECTION AND CLASSIFICATION APPROACHES TO ENHANCE INFORMATION FROM OVERNIGHT OXIMETRY IN THE CONTEXT OF APNEA DIAGNOSIS DANIEL ´ ALVAREZ ∗ , ROBERTO HORNERO and J. V ´ ICTOR MARCOS Biomedical Engineering Group (GIB ), University of Valladolid Paseo Bel´ en 15, 47011, Valladolid, Spain ∗ [email protected]NIELS WESSEL Cardiovascular Physics, Humboldt-Universit¨ at zu Berlin Robert Koch Platz 4, 10115, Berlin, Germany [email protected]THOMAS PENZEL and MARTIN GLOS Center of Sleep Research, Charit´ e Universit¨ atsmedizin Berlin Chariteplatz 1, 10117, Berlin, Germany [email protected]F ´ ELIX DEL CAMPO Department of Pneumology Hospital Universitario P´ ıo del R´ ıo Hortega Dulzaina 2, 47013, Valladolid, Spain [email protected]Accepted 3 May 2013 Published Online 2 July 2013 This study is aimed at assessing the usefulness of different feature selection and classification method- ologies in the context of sleep apnea hypopnea syndrome (SAHS) detection. Feature extraction, selection and classification stages were applied to analyze blood oxygen saturation (SaO 2 ) recordings in order to simplify polysomnography (PSG), the gold standard diagnostic methodology for SAHS. Statistical, spectral and nonlinear measures were computed to compose the initial feature set. Principal component analysis (PCA), forward stepwise feature selection (FSFS) and genetic algorithms (GAs) were applied to select feature subsets. Fisher’s linear discriminant (FLD), logistic regression (LR) and support vec- tor machines (SVMs) were applied in the classification stage. Optimum classification algorithms from each combination of these feature selection and classification approaches were prospectively validated on datasets from two independent sleep units. FSFS + LR achieved the highest diagnostic performance using a small feature subset (4 features), reaching 83.2% accuracy in the validation set and 88.7% accuracy in the test set. Similarly, GAs + SVM also achieved high generalization capability using a small number of input features (7 features), with 84.2% accuracy on the validation set and 84.5% accuracy in the test set. Our results suggest that reduced subsets of complementary features (25% to 50% of total features) and classifiers with high generalization ability could provide high-performance screening tools in the context of SAHS. Keywords : Sleep apnea hypopnea syndrome; oximetry; blood oxygen saturation; feature selection; princi- pal component analysis; stepwise selection; genetic algorithms; Fisher’s discriminant; logistic regression; support vector machines. 1350020-1
This study is aimed at assessing the usefulness of different feature selection and classification method-ologies in the context of sleep apnea hypopnea syndrome (SAHS) detection. Feature extraction, selectionand classification stages were applied to analyze blood oxygen saturation (SaO2) recordings in orderto simplify polysomnography (PSG), the gold standard diagnostic methodology for SAHS. Statistical,spectral and nonlinear measures were computed to compose the initial feature set. Principal componentanalysis (PCA), forward stepwise feature selection (FSFS) and genetic algorithms (GAs) were appliedto select feature subsets. Fisher’s linear discriminant (FLD), logistic regression (LR) and support vec-tor machines (SVMs) were applied in the classification stage. Optimum classification algorithms fromeach combination of these feature selection and classification approaches were prospectively validated ondatasets from two independent sleep units. FSFS +LR achieved the highest diagnostic performance usinga small feature subset (4 features), reaching 83.2% accuracy in the validation set and 88.7% accuracy inthe test set. Similarly, GAs+ SVM also achieved high generalization capability using a small number ofinput features (7 features), with 84.2% accuracy on the validation set and 84.5% accuracy in the test set.Our results suggest that reduced subsets of complementary features (25% to 50% of total features) andclassifiers with high generalization ability could provide high-performance screening tools in the contextof SAHS.
The sleep apnea hypopnea syndrome (SAHS) isa respiratory disorder characterized by frequentbreathing cessations (apneas) or partial collapses(hypopneas) during sleep. These respiratory eventslead to deep oxygen desaturations, blood pressureand heart rate acute changes, increased sympa-thetic activity and cortical arousals.1 Daytime hyper-somnolence, neurocognitive dysfunction, metabolicderegulation and/or cardiovascular and cerebrovas-cular diseases could affect people having undiagnosedSAHS.1,2 Common epidemiological data reflects ahigh SAHS prevalence in western countries: 1% to5% of adult men and 2% of women. However, recentstudies suggest that 20% of adults have at least mildSAHS and 7% of adults have moderate-to-severeSAHS.3 Unlike its high prevalence and negative influ-ence in the quality of life, it is estimated that 90%of cases in men and 98% of cases in women may beundiagnosed for many years.2
The gold standard method for SAHS diag-nosis is in-hospital, technician-attended overnightpolysomnography (PSG).4 However, this method-ology is labor-intensive, expensive and time-consuming,4 which has led to large waiting lists,delaying diagnosis and treatment.5 Thus, there isa great demand on new techniques aimed at sim-plifying the standard procedure and/or reducingthe number of PSGs needed.6 The main alterna-tives to PSG focus on developing automated analysisusing a reduced set of cardiorespiratory-derived sig-nals. Blood oxygen saturation (SaO2) from overnightoximetry provides relevant information to detectapneas, it can be easily recorded ambulatory and itis less expensive and highly reliable.6 However, thereis still a great demand on new studies to improve theusefulness of SaO2 in SAHS diagnosis.7
Several studies applied multivariate analysis toassist in SAHS detection.8–11 Multivariate adap-tive regression splines8 and stepwise linear regres-sion9 have been used to classify subjects from con-ventional oximetric indexes. Discriminant analysis,logistic regression and neural networks have alsobeen applied in the context of SAHS.10–12 However,few studies applied feature selection before classifi-cation, which could improve diagnostic performance.
In the present study, feature extraction, selec-tion and classification procedures were carried
out to analyze SaO2 recordings. Signal processingtechniques were applied to compose an initial featureset: statistical, spectral and nonlinear measures werecomputed to obtain as much information as possi-ble from oximetry. At this point, we hypothesizedthat an exhaustive analysis of the search space bymeans of variable selection could provide furtherknowledge on SaO2 dynamics. Dimensionality reduc-tion and feature selection techniques could be veryuseful to derive a smaller but optimal subset forclassification purposes. There are many potentialbenefits of variable selection after feature extrac-tion13,14: simplifying data representation, reducingmeasurement, storage and computational require-ments, avoiding redundant and noisy information,selecting complementary features and defying thecurse of dimensionality to improve classificationaccuracy. Feature subset selection methodologies areessentially divided into wrapper, filter and embed-ded methods.14,15 Wrapper methods use a classifierof interest to score subsets of variables according totheir predictive power, whereas filter methods selectsubsets of variables as a pre-processing stage inde-pendent of the predictor. Finally, embedded methodsintegrate variable selection into the learning machinetraining process. Additionally, feature constructionand dimensionality reduction techniques are a differ-ent and useful approach when the number of vari-ables is not too large and time and computationalcost is not a concern.14,16 Filter, wrapper and embed-ded techniques select features in the original space,which makes new subsets easy to interpret. On theother hand, feature construction approaches selectvariables in a transformed space, providing a moreefficient representation of patterns. However, newfeatures could not have clear physical meaning.17 Inthe present study, three different approaches wereassessed for feature selection: conventional princi-pal component analysis (PCA),18 forward stepwisefeature selection (FSFS)19 and genetic algorithms(GAs).20 Additionally, three classifiers were used toinvestigate classification performance: Fisher’s lineardiscriminant (FLD),13 logistic regression (LR)18 andsupport vector machines (SVMs).21 Previous stud-ies already applied these feature selection algorithmsin different contexts, such as image processing,22
signal monitoring,23,24 structural monitoring25,26 ormodel optimization.27–29 Similarly, FLD and LR are
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conventional classifiers extensively assessed in manyfields11,13,30,31 and SVMs are optimal state-of-the-art classifiers widely applied in different contexts,such as fMRI data analysis,31 document classifica-tion,32 biomedical signal processing33,34 or motorpump faults detection.35
The goal of this study is to assess the useful-ness of these algorithms for feature selection andclassification in the context of SAHS diagnosis. Wehypothesized that a prospective evaluation of differ-ent feature subsets from oximetry could provide fur-ther knowledge on SaO2 dynamics. Thus, we wantedto test if the proposed classification schemes will besuitable for applying at another sleep laboratory. Toachieve this goal, oximetric recordings from two inde-pendent sleep units were analyzed.
2. DataSet
Subjects under study were recruited from twoindependent sleep units: the “Rıo Hortega Hos-pital” (RHH) from Valladolid (Spain) and the“Philipps University Hospital” (PUH) from Marburg(Germany). First, a population set composed of 249consecutive subjects (191 males and 58 females) wasstudied, with a mean ± standard deviation (SD) ageof 52.2± 13.5 years and an average body mass index(BMI) of 29.9± 4.9 kg/m2. All subjects were derivedto the sleep unit of the RHH due to a suspicion of suf-fering from SAHS. This population set was dividedinto training set and validation set. Table 1 shows thedemographic and clinical characteristics of the popu-lation groups. The training set was used to composeoptimum feature subsets from oximetric features andbuild the classifiers, whereas the validation set wassubsequently used to assess their performance. Inorder to test whether proposed classification schemeswill fit recordings from another sleep laboratory,optimum classifiers were further assessed on an inde-pendent test set. The Marburg subset (71 recordings)of the SIESTA database from the PUH was used. Inthis dataset, healthy subjects with no sleep distur-bances composed the control group, whereas patientswith a positive diagnosis of SAHS from PSG com-posed the SAHS-positive group. Table 2 shows thedemographic and clinical features of this population.
The standard apnea–hypopnea index (AHI) fromPSG was used to diagnose SAHS. Apnea was definedas a drop in the airflow signal greater than or equal
Table 1. Demographic and clinical features of the pop-ulation from the RHH sleep unit.
to 90% from baseline lasting at least 10 s, whereashypopnea was defined as a drop greater than or equalto 50% during at least 10 s accompanied by a desatu-ration greater than or equal to 3% and/or an arousal.Subjects with an AHI ≥ 10 events per h (e/h) werediagnosed as suffering from SAHS. Regarding thepopulation under study from the RHH, a positivediagnosis of SAHS was confirmed in 165 patients.
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The training set from the RHH was composed of148 patients (48 SAHS-negative and 100 SAHS-positive), whereas the validation set was composedof 101 patients (36 SAHS-negative and 65 SAHS-positive). Every subject contributed one PSG studyeach (7.2± 0.6 h of recording, mean±SD). On theother hand, nocturnal PSG was carried out duringtwo consecutive nights at the PUH sleep unit. Inthe test set from the PUH, 50 PSG studies from26 healthy subjects composed the control group (24subjects contributed two recordings each and twosubjects contributed one recording each), whereas21 PSG studies from 11 SAHS-positive patientscomposed the SAHS-positive group (10 patients con-tributed two recordings each and 1 patient con-tributed with a single recording).
All SaO2 recordings from PSG were saved to sep-arate files and processed offline to compose the initialoximetric feature set. SaO2 was recorded at a sam-pling rate of 1Hz. SaO2 signals presented zero sam-ples at the beginning of the acquisition process anddrops to zero due to patient movements along therecording time. An automatic signal pre-processingstage was carried out to remove these artifacts.
3. Methodology
Our methodology was divided into three stages: fea-ture extraction, feature selection and classification.A total of 16 features composed the initial featureset from oximetry, which was the input to the subse-quent feature selection stage. Three feature selectionalgorithms were evaluated: PCA, FSFS and GAs.Three classifiers were applied to assess classificationperformance in the third stage: FLD, LR and SVMs.Therefore, nine different classification schemes wereproposed: PCA+FLD, PCA+LR, PCA+SVM,FSFS +FLD, FSFS +LR, FSFS +SVM, GAs +FLD, GAs +LR and GAs +SVM. Training and adouble testing process were carried out. The trainingset was used to perform feature selection and com-pose classifiers, where a number of optimum featuresubsets were automatically selected. Every optimumclassifier from each proposed classification schemawas subsequently assessed on two test sets: a valida-tion group from the same sleep unit as the trainingset and a test set from an independent sleep unit.Figure 1 shows a block diagram to illustrate thismethodology.
Fig. 1. System block diagram of the proposed method-ology for feature extraction, selection and classification.
3.1. Feature extraction stage
Oximetric recordings were parameterized by meansof 16 features from 4 feature subsets: time domainstatistics, frequency domain statistics, conventionalspectral measures and nonlinear features. All fea-tures were computed for each whole overnightrecording.
3.1.1. Time domain statistics
The amplitude (%) of each SaO2 signal was used tocompute the normalized histogram. First to fourth-order statistical moments were computed36:
(i) Arithmetic mean (M1t), which is a measure ofthe central tendency of the data distribution:
M1t ≡ E[x] = µ =1N
N∑n=1
xn. (1)
(ii) Variance (M2t), which quantifies the amountof dispersion in data, assigning higher values tohigher variation:
M2t ≡ E[(x − µ)2] = σ2
=1
N − 1
N∑n=1
(xn − µ)2. (2)
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(iii) Skewness (M3t), which is a measure of symme-try in the data distribution. Large negative val-ues suggest skewness (asymmetry) to the leftwhile relatively large positive values suggestskewness to the right:
M3t =1σ3
E[(x − µ)3], (3)
where σ is the SD.(iv) Kurtosis (M4t), which quantifies the peaked-
ness, i.e. the frequency of data in the middleof the distribution. Positive peakedness suggestslarge concentration of probability in the centeraround µ accompanied by relative long tails,while negative values indicate relatively shorttails:
M4t =1σ4
E[(x − µ)4]. (4)
3.1.2. Frequency domain statistics
The power spectral density (PSD) of each oximet-ric recording was estimated by applying the Welch’smethod. A 512-sample Hanning window with 50%overlap and 1024-points discrete Fourier transformwere used. The following statistics were computed:
(i) First to fourth-order moments (M1f–M4f)in the frequency domain.36 The amplitude(W/Hz) of the PSD function at each single spec-tral component was used to obtain the normal-ized histogram.
(ii) Median frequency (MF), which is defined as thespectral component which comprises 50% of thetotal signal power37:
0.50.5fS∑
fj=0Hz
PSD(fj) =MF∑
fj=0Hz
PSD(fj). (5)
(iii) Spectral entropy (SE), which is a disorder quan-tifier related to the flatness of the spectrum37:
SE = −∑
j
pj ln(pj), (6)
where pj is the normalized value of the PSD ateach frequency component:
pj =PSD(fj)∑0.5fs
fj=0 Hz PSD(fj). (7)
3.1.3. Conventional spectral features
The frequency band from 0.014 to 0.033 Hz proposedby Zamarron et al. was parameterized. A significantpower increase linked with suffering from SAHS wasfound in this frequency band.38 The following mea-sures were computed:
(i) Total spectral power (PT ), which is computedas the total area under the PSD.
(ii) Peak amplitude (PA) in the apnea frequencyband, which is the local maximum of the spec-tral content in the apnea frequency range 0.014–0.033Hz.
(iii) Relative power (PR), which is the ratio of thearea enclosed under the PSD in the apnea fre-quency band to the total signal power.
3.1.4. Nonlinear features
Linear methods cannot capture all the informationfrom biological signals due to their nonlinearities andnonstationary behavior.39–42 Therefore, nonlinearmeasures of irregularity, variability and complexitywere applied to obtain additional and complemen-tary information from SaO2 dynamics.30,43,44
(i) Sample entropy (SampEn), which is a nonlin-ear measure of irregularity in time series, withlarger values corresponding to more irregulardata45:
SampEn(m, r, N) = − ln[
Am(r)Bm(r)
], (8)
where Am and Bm are the average number of(m)-length and (m + 1)-length segments Xm(i)(1 ≤ i ≤ N − m + 1) with d[Xm(i), Xm(j)] ≤r(1 ≤ j ≤ N − m, j �= i), respectively, and
d[Xm(i), Xm(j)]
= maxk=0,...,m−1
(|x(i + k) − x(j + k)|). (9)
(ii) Central tendency measure (CTM ), which is anonlinear measure of variability from second-order difference plots, assigning larger values tolower variability46,47:
CTM =1
N − 2
N−2∑i=1
δ(di), (10)
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where
δ(di) =
1 if [(x(i + 2) − x(i + 1))2
+ (x(i + 1) − x(i))2]1/2 < ρ
0 otherwise
.
(11)
(iii) Lempel–Ziv complexity (LZC ), which is a non-linear measure of complexity linked with therate of new subsequences and their repetitionalong the original sequence.48,49 The complex-ity counter c(n) is increased every time a newsubsequence is encountered:
LZC =c(n)b(n)
, (12)
where b(n) is a normalization parameter.48
3.2. Pre-processing stage
Units used to measure input variables or changes inscale of measurement can influence the performanceof classifiers.13,50 Therefore, standardizing each fea-ture by subtracting its mean and dividing by its SDis a common practice in the context of pattern recog-nition.50,51 A linear re-scaling of each individual vari-able was carried out to obtain a zero mean and unitvariance distribution for each input feature:
xk(i) =xraw
k (i) − xk
σxk
, k = 1, . . . , p, (13)
where xk(i) is the standardized value for sample i offeature k, xraw
k (i) is the original raw value for samplei of feature k, xk is the mean value of feature k andσxk
is its SD.
3.3. Feature selection stage
3.3.1. Principal component analysis
PCA is probably the best-known orthogonal trans-form for variable construction, which has been widelyused as reference methodology for dimensionalityreduction in pattern recognition.16,17 As a variableconstruction technique, PCA is aimed at finding anappropriate transform that maps the pattern vectorx(i) from the original p-dimensional feature space toa new d-dimensional feature space, where d ≤ p.17
When the number of features in the original space islarge, the high correlation between variables understudy becomes a problem in multivariate analysis.In order to avoid this issue, all variables or principal
components from PCA in the new d-dimensionalspace are uncorrelated and mutually orthogonal.13,18
New variables from PCA are linear transforma-tions of the original features in a d-dimensionalspace, providing pattern representation with mini-mum mean-squared error for a given dimension d.17
In the transformed space, new patterns are the pro-jection of the original observations onto the eigen-vectors of the original covariance matrix.13,17 Eacheigenvector accounts for a portion of the total vari-ation of original data and the variance linked witheach eigenvector is represented by its associatedeigenvalue.13,18 The portion of the total variationaccounted for by the eigenvalue λd is given by itsexplained variance (EV ):
EV =λd∑p
k=1 λk. (14)
Regarding dimensionality reduction, PCA is com-monly applied as a filter method to select variablesin the transformed space as a pre-processing stageindependent of the classifier. PCA allows discard-ing the components with lower EV to deal with atransformed space with lower dimension without sig-nificant loss of information.18 The optimum numberof components to accomplish dimensionality reduc-tion can be estimated using some cut-off proportion.In this study, new variables from PCA were rankedaccording to their EV and the average criterion oreigenvalue-one-criterion was used as threshold to fil-ter principal components. According to this rule,the components whose variance (λj , j = 1, . . . , p)exceeds the average variance λ were selected:
λj > λ =p∑
j=1
λj
/p. (15)
In the present study, we applied PCA to the originaldataset of 16 features from oximetry. PCA+FLD,PCA+LR and PCA+ SVM classification schemeswere subsequently built using the principal compo-nents automatically selected.
3.3.2. Forward stepwise feature selection
Sequential forward selection and backward elim-ination algorithms allow exploring the originalp-dimensional feature space looking for a small sub-set that could reasonably describe the original dataand avoiding the need to compute all possible 2p
combinations, which becomes impracticable when p
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is large.19,52 Both forward selection and backwardelimination techniques yield nested subsets of fea-tures, where variables are progressively added intolarger and larger subsets or progressively removingthe least promising ones starting from the completeset of variables, respectively.14 Advantages of bothmethodologies of feature selection are computationalefficiency and robustness against overfitting. On theother hand, their main limitation is that once a vari-able has been included or removed from the subset,there is not a feedback process to modify the inclu-sion or exclusion of previous variables, which couldimprove the information provided by the model.17
Forward stepwise selection and backward stepwiseelimination improve sequential approaches by con-sidering both feature addition and feature deletionat each step.53
Forward and backward stepwise strategies areusually classified as wrapper feature selection meth-ods.14,15 However, they can also be used as anembedded method if the criterion to decide whetheror not to include or exclude a feature is not baseddirectly on the accuracy of a classifier but on anotherobjective function.17 In the present study, we used aforward stepwise classifier-building strategy to findthe simplest feature subset that still significantlyexplains original data.19 Bidirectional FSFS decidesto add or to remove a variable from the currentfeature subset through an iterative process. FSFSselects the strongest variables in the dataset andremoves variables that provide redundant informa-tion in terms of statistical significant differences: ateach iteration, the stepwise method performs a testfor backward elimination followed by a forward selec-tion procedure.19 Different tests of statistical signif-icance are used to compare models differing in onedegree of freedom (1 input variable) depending onthe output of the classifier. FSFS +FLD, FSFS + LRand FSFS +SVM schemes were analyzed in thisstudy. The likelihood ratio test is used when outputvalues can be interpreted as probabilities, such as inLR.19 The output of a SVM can also be mappedto pseudo-probabilities using a logistic function.54
In stepwise linear problems, an F -test is used sincethe errors are assumed to be normally distributed.19
Therefore, the Rao’s R approximate F -test was usedfor FLD.
In FSFS, a new variable is selected if the p-valueassociated to the statistical test was lower than a
significance level αE , which usually varies between0.05 and 0.25.19 Similarly, a variable was removed ifthe p-value was higher than a significance level αR,commonly between 0.20 and 0.9019:
p(step)feature = min(p(step)
j ) < αE → add feature, (16)
p(step)feature = max(p(step)
j ) > αR → remove feature.(17)
The FSFS algorithm stops when all variables fromthe original feature set are selected or when all vari-ables in the model have p-values lower than αR andthe remaining variables have p-values greater thanαE . In the present study, we used the less restrictiveαE = 0.25 and a moderate αR = 0.40 significancethresholds to let the algorithm significantly explorethe original feature space.19
3.3.3. Genetic algorithms
GAs are usually used as optimization schema toefficiently inspect the search space of variables orparameters that govern a model.28,29 They encode apotential solution as a chromosome-like data struc-ture and apply recombination operators on thesestructures.24 A population from a GA optimizationprocedure comprises a group of chromosomes or can-didate solutions that are modified iteratively: A par-ticular group of chromosomes (parents) are selectedfrom an initial population to generate the offspringby means of predefined genetic operations (crossoverand mutation). The offspring replaces chromosomesin the current population based on certain replace-ment strategies.28 The optimization process is car-ried out in cycles called generations.
In this study, GAs were applied as a wrapper fea-ture selection procedure to obtain the optimum inputfeature subset of a classifier in terms of classificationperformance. In this case, an individual or chromo-some from the population is just a combination of apredetermined number of features from SaO2 record-ings.24 While conventional approaches just evaluateand improve a single feature subset, a GA intensivelyanalyzes the whole feature space by modifying andimproving a group of subsets at the same time.
A feature subset in the GA search space is cod-ified with a finite binary sequence, where the kthbit denotes the absence (0) or the presence (1) ofthe kth feature. Each sequence has p bits, wherep is the dimension of the original space, i.e. the
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number of features in the whole set.20 The classi-fication accuracy is used as the objective value, inorder to assess each chromosome performance andto achieve parent selection. A fitness function is usedto map each objective value to a proportional prede-fined fitness interval. In this study, a proportional fit-ness scaling function was used. Additionally, rouletteand tournament schemes were used as parent selec-tion strategies. One-point crossover was applied toproduce offspring: a crossover point is randomlyselected and the portions of both parents beyondthis point are exchanged to form the offspring.28
Uniform mutation was applied to introduce varia-tions into the offspring. In the present study, prob-ability of crossover (Pc) values between 0.5 and 0.9and probability mutation rate (Pm) values between0.01 and 0.09 were used.20 The elite or percentage ofthe best individuals in the old population preservedafter each generation were varied between 0% and25%. A number of realizations were carried out vary-ing the parent selection strategy, Pc, Pm and elite.Each implementation of the GA was run with aninitial population size of 16 individuals during 100generations.24 For each realization, the feature sub-set with the highest accuracy at the last generationwas saved. Finally, the optimum feature subset interms of diagnostic performance was selected. In thisstudy, GAs +FLD, GAs + LR and GAs +SVM clas-sification schemes were assessed.
3.4. Feature classification stage
3.4.1. Fisher’s linear discriminant
In a binary (two class) context, FLD performs a lin-ear projection of p-dimensional input data to a one-dimensional space:
y = wT x, (18)
where w is the projection weight matrix whose com-ponents maximize the class separation in the trans-formed space.13 The Fisher criterion can be writtenas follows:
J(w) =wT SBw
wT SW wd, (19)
where SB is the between-class covariance matrix andSW is the total within-class covariance matrix. Dif-ferentiating J(w) with respect to w, the separation ofclasses in the projected space is maximized when13:
w ∝ S−1W (m2 − m1), (20)
where mi is the mean vector of the class i. The pro-jected data can be used to construct a discriminantby choosing a threshold y0 so that we classify a newpoint as belonging to C1 if y(x) ≥ y0 and classify itas belonging to C2 otherwise.
3.4.2. Logistic regression
LR relates a categorical dependent variable Y with aset of input features Xi. For dichotomous problems,input patterns are classified into one of two mutu-ally exclusive categories (SAHS-positive or SAHS-negative in the context of SAHS diagnosis) and theprobability density for the response variable can bemodeled by a Bernoulli distribution18:
f(y | p(d)) = [p(d)]y[1 − p(d)](1−y), (21)
where
p(d) = p(β0 +p∑
i=1
βixi), (22)
models the linear relationship between input featuresXi. The maximum likelihood criterion is used to opti-mize coefficients of the independent input features.18
LR classifiers assign an input vector to the class withthe maximum a posteriori probability value. The LRmodel is expressed as follows18:
ln[
p
1 − p
]= β0 +
p∑i=1
βixi. (23)
3.4.3. Support vector machines
SVMs are binary classifiers that search for theoptimum separating hyperplane between classes.13
The hyperplane is built in a transformed high-dimensional space in order to maximize separation,resulting in the following mapping function:
y(x, w) = wT z + w0, (24)
where x ∈ �p is the input pattern, z = ϕ(x) | z ∈�d, d > p performs the transformation of input datato a high-dimensional space, y is the output of theclassifier and w is the weight vector. w is obtainedby minimizing the following functional21:
Ec(w, ξ) =12‖w‖2 + C
N∑n=1
ξn, (25)
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subject to the constrains
tn(wT zn + w0) ≥ 1 − ξn and ξn ≥ 0
n = 1, . . . , N, (26)
where N is the number of observations in the train-ing set, tn is the target or desired output (+1 forthe positive class and −1 for the negative class), ξn
measures a deviation of a data point xn from theideal condition of separability (nonseparable classes)in the transformed space and C is a regularizationparameter that controls the trade-off between themaximum margin of separation between classes andminimizing the classification error.55 This optimiza-tion problem is commonly reformulated in terms ofLagrange multipliers ηn, so that the weight vector isexpressed as follows:
w =N∑
n=1
ηntnϕ(xn). (27)
Only the support vectors, those for which theirLagrange multipliers are nonzero, contribute to thedefinition of the decision boundary. The output ofthe SVM classifier is expressed in terms of these sup-port vectors as follows21:
y =∑n∈S
ηntnK(xn, x) + w0, (28)
where S is a subset of the indices {1, . . . , N} cor-responding to the support vectors and K(·, ·) rep-resents the inner product kernel function in thetransformed space. In the present study, a linear ker-nel is used. The linear combination of inputs is thesimplest but most useful kernel for SVM classifica-tion in many contexts, such as fMRI data analysis31
or document classification.32 Leave-one-out cross-validation (loo-cv) was carried out in the trainingset to obtain the optimum value of the regularizationparameter C for each SVM classifier. The followingvalues were assessed: 10−4, 10−3, 10−2, . . . , 103, 104.For each value of C, we computed the accuracy ofthe classifier applying loo-cv. The value of C thatachieved the highest accuracy was selected and theclassifier was re-trained using the whole training set.
3.5. Statistical analysis
Matlab R2012a (7.14.0.739) and IBM SPSS Statis-tics 20 were used to implement feature extrac-tion methods and to develop the feature selection
and classification stages. Sensitivity (proportion ofSAHS-positive patients correctly classified), speci-ficity (proportion of SAHS-negative subjects rightlyclassified) and accuracy (the total percentage of sub-jects correctly classified) were computed to quan-tify classification performance. For every classifier, aROC analysis was carried out to obtain its optimumdecision threshold in the training set. This thresholdwas applied on further assessments in the validationand test sets.
4. Results
4.1. Training
Feature extraction was carried out for eachSaO2 recording from the populations under study.Figure 2(a) shows the nocturnal SaO2 profile ofa common SAHS-negative subject and a com-mon SAHS-positive patient from the training set.Figure 2(b) shows the normalized averaged his-togram envelope of recordings in the time domain forthe whole SAHS-negative (dashed black) and SAHS-positive (dotted gray) groups in the training set. Wecan observe that the histogram envelope correspond-ing to the SAHS-negative group showed higher mean,skewness (symmetry) and kurtosis (peakedness) andlower variance in the time domain than that cor-responding to SAHS-positive patients. This agreeswith the fact that recordings from subjects withoutsleep apnea tend to remain constant around 96%,6
i.e. higher mean and peakedness, whereas SAHSpatients show deep desaturations during the night,i.e. higher variability and lower symmetry due to theleft tail of the histogram envelope as a result of lowersaturation values. Figure 2(c) shows the normalizedaveraged PSD for the whole SAHS-negative (dashedblack) and SAHS-positive (dotted gray) groups inthe training set. In the frequency domain, spectralpower of oximetric recordings from SAHS-negativesubjects concentrates on very low frequencies, show-ing lower mean and variance and higher skewnessand kurtosis than SAHS-positive patients due to thecontinuous component (baseline) in the time domainaround 96%. We can observe from Fig. 2(c) thatspectral power of recordings from SAHS-positivepatients spreads in a wider frequency band due tothe repetitive apnea events during the night, lead-ing to higher MF and SE. As a result, PT , PA andPR from SAHS-positive patients were also higher
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(a) (b) (c)
(d) (e) (f)
Fig. 2. Overnight SaO2 profiles for a common SAHS-negative subject and a common SAHS-positive patient (a) from theRHH hospital database and (b) from the PUH database. Average histogram envelopes in the time domain for the wholeSAHS-negative and SAHS-positive group (b) in the training set from the RHH and (e) in the test set from the PUH.Average PSD functions for the whole SAHS-negative and SAHS-positive group (c) in the training set from the RHH and(f) in the test set from the PUH.
than conventional spectral measures from the SAHS-negative group. Finally, common oximetric record-ings in the time domain plotted in Fig. 2(a) showmarked changes in the SaO2 profile due to recur-rent desaturations during the night in SAHS-positivepatients, leading to higher irregularity (Samp-En), variability (lower CTM ) and complexity (LZC )than non-SAHS subjects. This trend was also presentin the test set, although some differences betweenpatient groups from both sleep units under study(RHH versus PUH) can be seen both in time andfrequency domains. Figure 2(d) shows the SaO2 pro-file of a normal subject and a SAHS patient fromthe PUH database, whereas Figs. 2(e) and 2(f) showthe normalized averaged histograms and PSDs forthe whole normal (dashed black) and SAHS-positive(dotted gray) groups in this test set. Differencesbetween databases agree with heterogeneity of popu-lation commonly derived to sleep units. Additionally,
the histogram envelope in the time domain of thenormal group from the PUH shows a marked peak,higher than that corresponding to the RHH. This isdue to the fact that the dataset from the PUH is com-posed of non-SAHS subjects with lower average AHIthan SAHS-negative patients from the RHH. Simi-larly, the PSD of the SAHS-positive group from thePUH show higher power increase in the apnea fre-quency band than SAHS-positive patients from theRHH due to the fact that, on average, they havehigher SAHS severity.
PCA, FSFS and GAs were applied for fea-ture selection in the training set and a numberof FLD, LR and SVM classifiers were composed.Table 3 shows principal components from PCA inthe training set ranked in decreasing order of theirEV. The three first consecutive principal compo-nents were selected according to the average cri-terion. Table 4 summarizes the performance of
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Table 3. Explained variance for each principalcomponent from PCA in the training set.
feature selection and classification schemes understudy. Regarding PCA dimensionality reduction,PCA+ LR achieved the highest diagnostic accuracyin the training set (90.5%), while PCA+FLD andPCA+ SVM achieved similar but lower performancethan LR (83.8% and 84.5%, respectively). Simi-larly, FSFS + LR also achieved the highest accu-racy (91.9%) after bidirectional feature selection inthe training set. A reduced LR model composedof 4 features was built. FSFS +FLD (8 features)and FSFS + SVM (5 features) achieved slightlylower performance (90.5% and 87.8%, respectively).
Table 4. Optimum feature subsets for each feature selection and classification methodology and their performance inthe training set.
Algorithm n Features Se Sp Ac
PCA +FLD 3 3 principal components 80.0 91.7 83.8PCA +LR 3 3 principal components 92.0 87.5 90.5PCA +SVM 3 3 principal components 81.0 91.7 84.5
Exhaustive feature selection by means of evolution-ary algorithms built more complex classifiers com-posed of a larger number of features, ranging from 7to 15 variables. GAs +LR also obtained the highestdiagnostic accuracy in the training set (96.6% using14 and 15 features). GAs +FLD (7 and 9 features)and GAs + SVM (7 and 8 features) yielded to lowerperformances in the training set (93.2% and 86.5%,respectively).
4.2. Validation and testing
Each feature selection and classification schemawas prospectively assessed. Optimum classifiers wereevaluated on two independent test sets from differ-ent sleep units. Table 5 summarizes the performanceassessment of the proposed methodology. The accu-racy of optimum classifiers from PCA significantlydecreased, with accuracies ranging from 71.3% to81.2% in the validation set and 40.9% to 54.9% inthe test set. Similarly, the FSFS +FLD classifiercomposed of 8 features achieved 78.2% accuracy inthe validation set and 57.8% accuracy in the testset. On the other hand, optimum classifiers fromFSFS +LR and FSFS +SVM schemes showed lowerperformance decrease. The LR model composed of4 features achieved 83.2% accuracy in the validationset and 88.7% accuracy in the test set, whereas theSVM classifier with 5 input features achieved 82.2%accuracy in the validation set and 80.3% accuracyin the test set from the PUH sleep unit. Optimumclassification schemes from GAs showed different
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Table 5. Diagnostic performance assessment of optimum feature subsets from each feature selection and classificationmethodologies in the validation set and in the test set from an independent sleep unit.
Validation set (RHH) Test set (PUH)
Algorithm n Features Se Sp Ac Se Sp Ac
PCA +FLD 3 First 3 principal components 66.2 80.6 71.3 52.4 44.0 46.5PCA +LR 3 First 3 principal components 92.3 61.1 81.2 100.0 36.0 54.9PCA +SVM 3 First 3 principal components 67.7 80.6 72.3 28.6 46.0 40.9
performance depending on the classifier. GAs + LRachieved moderate to high accuracies in the valida-tion set, ranging from 68.3% (15 features) to 85.2%(14 features), but extremely low performance in thetest set, with accuracies ranging from 29.6% (15 fea-tures) to 31.0% (14 features). GAs + FLD achievedunbalanced accuracies in the validation set, rangingfrom 39.6% (9 features) to 81.2% (7 features), andmoderate performance in the test set, with accu-racies ranging from 66.2% (9 features) to 60.6%(7 features). On the other hand, GAs +SVM pro-vided higher performance and more stable classifiers,leading to 84.2% accuracy (7 and 8 features) in thevalidation set, and accuracies ranging from 81.7%(8 features) to 84.5% (7 features) in the test set.
5. Discussion
This study assessed the usefulness of 9 feature selec-tion and classification schemes to enhance informa-tion from SaO2 oximetric recordings in the contextof SAHS diagnosis. An initial feature set composedof 16 features was developed to characterize SaO2
dynamics. A filter-based selection approach fromvariable construction (PCA), an embedded featureselection approach (FSFS) and a wrapper method-ology for exhaustive analysis of the feature space(GAs) were applied. FLD, LR and SVM classifiers
were involved on each feature selection methodology.Optimum classification schemes from the training setwere subsequently assessed in datasets from differentsleep units.
Our results showed that all algorithms fromdifferent feature selection and classification proce-dures reached high performance in the trainingset, with accuracies ranging from 83.8% to 96.6%.In contrast, optimum classification schemes showeddifferent behavior when they were further tested.Regarding results from PCA, significantly lower orunbalanced sensitivity and specificity values werereached in the validation set from the RHH, lead-ing to accuracies ranging from 71.3% to 81.2%. Thediagnostic performance was even lower in the testset from the PUH, with a maximum accuracy of54.9% using a LR classifier. PCA performs featureselection as a pre-processing stage regardless of theclassification method. This is the reason why PCAachieved the lowest performances in the training setand subsequently failed in the validation and testsets independent of the classifier. Optimum clas-sification schemes from GAs showed high depen-dence on the number of selected features. GAs +LRachieved the highest performances in the training setusing high-dimensional feature subsets automaticallyselected. However, extremely unbalanced sensitiv-ity and specificity values were obtained in further
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assessments, especially in the test set from the PUH,with accuracies ranging from 29.6% (15 features) to31.0% (14 features). On the other hand, GAs +SVMprovided higher performance and more stable clas-sifiers using half of the features: 84.5% (7 features)and 81.7% (8 features) in the test set. GAs are opti-mization algorithms aimed at extensively inspectingthe search space in the training set to maximize thefitness function, usually the performance of a classi-fier. SVMs provide high generalization performanceon pattern classification problems.31,55 Indeed, theregularization parameter C controls the trade-offbetween the maximum margin of separation betweenclasses and minimizing the classification error.21,31
Our results suggest that, when low generalizationcapability predictors are used, GAs might build clas-sifiers composed of a high number of features thatoverfit the training set and fail on subsequent assess-ments in different population groups. It is note-worthy that GAs + FLD selected feature subsets ofsimilar size than those from GAs + SVM. However,optimum classifiers from GAs +FLD reached signifi-cantly lower accuracy in the test set. Performancedecrease could be due to the fact that SVMs donot hypothesize any a priori statistical distribu-tion of variables, whereas input features are assumedto have normal distributions and equal covariancematrices when using FLD.31 Similarly, FSFS +FLDachieved unbalanced sensitivity and specificity val-ues and low accuracy in the test set using eight fea-tures. On the contrary, FSFS +LR and FSFS +SVMprovided high performance and balanced classifierswith reduced input feature subsets composed offour and five features, respectively. This agrees withthe aim of forward stepwise selection: features areselected taking into account the amount of infor-mation added to the model, instead of maximizingclassification accuracy on a specific dataset. Usingefficient search strategies instead of “brute force”techniques did not decrease prediction performance.Indeed, our results support previous studies report-ing that greedy search strategies, such as stepwisefeature selection, are computationally advantageousand robust against overfitting.14
Regarding the number of features, the highestand more balanced performances in the validationand test sets were obtained using reduced featuresubsets (25–50% of input features). From FSFS,FSFS + LR and FSFS +SVM schemes selected the
smallest feature subsets: 4 (M2t, M4t, PR, LZC)and 5 (M4t, PA, PR, SampEn, LZC) features, respec-tively. Similarly, GAs +SVM provided 2 models with7 (M2t, M3t, M4t, M2f , M4f , SE, CTM) and 8(M2t, M3t, M4t, M2f , M3f , M4f , SE, CTM) fea-tures that yield to high accuracy both in the val-idation and test sets. Our results suggest that thelarger the number of features, the larger overfittingis on the training set, leading to poor performancein subsequent assessments. Regarding PCA, only thefirst three principal components were selected usingthe average criterion. However, each principal com-ponent is a linear transformation of the original fea-tures, i.e. all 16 features contribute to every newvariable in the transformed space. Thus, informationfrom a large amount of features is used to achievehigh performance in the training set, whereas accu-racy significantly decreases in the validation and testsets.
In order to obtain high-performance classifiers isessential to build an initial feature set that concen-trates as much nonredundant information as possi-ble about the problem under study. Therefore, inthe present research we built an original feature setfrom oximetry composed of metrics from comple-mentary analyses: time versus frequency and linearversus nonlinear. After the feature selection stage,time, spectral and nonlinear features are includedin the optimum feature subsets from FSFS + LR,FSFS +SVM and GAs +SVM, which achieved thehighest accuracies in both test populations. Bothsubsets from the FSFS feature selection approachshare 60–75% of features (three features): a lin-ear statistic in the time domain (M4t), a lin-ear measure in the frequency domain (PR) anda nonlinear measure in the time domain (LZC).These features jointly account for the main char-acteristics of overnight SaO2 profiles of non-SAHSsubjects and the influence of apnea events in therecordings of SAHS-positive patients. M4t mea-sures the peakedness of the data distribution inthe time domain, which is especially high in thecase of SaO2 recordings from non-SAHS subjectsdue to its near-constant behavior. On the otherhand, there is a significant power increase in thefrequency band between 0.014 and 0.033Hz due tothe quasi-periodic components of overnight respira-tory events. PR quantifies the effect of repetitiveapneic episodes on SaO2 recordings in the frequency
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domain. Finally, desaturations of different severitymodify the normal SaO2 profile by adding new pat-terns or subsequences. LZC quantifies to what extentthese desaturations increase the complexity of theSaO2 signal in the time domain. Similarly, subsetsfrom the GAs + SVM schema share 87.5% of features(7 out of 8). Comparing shared optimum featuresfrom both feature selection techniques (FSFS andGAs), we can observe that M4t is present in subsetsfrom both approaches, PR is replaced by SE, whichis also influenced by the presence of additional fre-quency components in the power spectrum due torecurrent apneic events, and the nonlinear measureof complexity LZC is replaced by the nonlinear mea-sure of variability CTM, which also quantifies timedomain changes in the SaO2 profile due to overnightdesaturations. Therefore, our results suggest that asuitable feature selection stage applied to a suitedand balanced initial feature set could detect comple-mentary information and thus increase the diagnos-tic performance of oximetry in the context of SAHSdiagnosis.
Previous researchers applied multivariate anal-ysis in the context of SAHS. Using conventionaloximetric indexes based on the number, durationand amplitude of the desaturations, 88.0% sensitiv-ity and 70.0% specificity were reached from step-wise linear regression,9 whereas 90% sensitivity and70% specificity were obtained using multivariateadaptive regression splines.8 Using spectral featuresfrom the high-frequency range, a sensitivity of 82%and a specificity of 84% were obtained with a LRclassifier.10 Higher performance (91.1% sensitivityand 82.6% specificity) was obtained by applyinglinear discriminant analysis to conventional spec-tral features in the apnea frequency band.11 Neu-ral networks have also been applied using clinicaland anthropomorphic features (94.9% sensitivity and64.7% specificity)56 and oximetric features (89.4%sensitivity and 81.4% specificity) as input vari-ables.12 Different approaches of multivariate analysisusing features from nonportable ECG have also beendeveloped in the context of SAHS detection, reach-ing accuracies ranging from 74.4% to 100% usingpopulations with no more than 80 subjects.57–59
Other researchers suggested the use of wavelet fea-tures as inputs to a SVM classifier to assist in SAHSdiagnosis from ECG.60,61 A diagnostic accuracy of92.86% was achieved on a small test set composed of
42 subjects.60 The proposed methodology was alsoassessed on a slightly larger database composed of70 recordings.61 An accuracy of 100% was reachedon a test set with 30 subjects. However, borderlinesubjects were excluded from the study.
Recent studies by our group applied dimension-ality reduction and stepwise feature selection proce-dures before classification.30,62,63 PCA was appliedto a small set of three spectral and three nonlin-ear features.62 First-to-fifth principal componentswere selected and 93.0% accuracy (97.0% sensitiv-ity and 79.3% specificity) was reached on a testset from the same sleep unit. FSFS +LR was pre-viously applied to a larger feature set from oxime-try, reaching 89.7% accuracy (92.0% sensitivity and85.4% specificity) using cross-validation.30 Similarly,FSFS +LR was also applied to a wide feature set(42 features) from single channel airflow and respira-tory rate variability.63 Using cross-validation, 82.4%accuracy was reached by the LR model composedof features automatically selected from both signals.Finally, a preliminary study on the usefulness of GAsfor feature selection in the context of SAHS diagnosisfrom oximetry has been recently carried out.64 A LRmodel composed of six features achieved the high-est accuracy (87.5%) in the test set from the samesleep unit. Nevertheless, these studies tested theirapproaches on populations from the same hospital.In the present research, we analyzed SaO2 datasetsfrom two different sleep units to assess our method-ologies. To our knowledge, this is the first studywhere several complementary feature selection andclassification algorithms are prospectively tested inthe context of SAHS diagnosis from oximetry.
We should take into account some limitationsregarding the general application of our methodol-ogy. Recurrent desaturations during sleep are notexclusive of SAHS. The presence of other disorders,such as asthma, chronic obstructive pulmonary dis-ease (COPD) or obesity-hypoventilation syndromecould influence the performance of methodologiesbased on oximetry alone.4 Regarding this issue, therules of the American Academy of Sleep Medicine(AASM) about the use of portable monitoring asan alternative to PSG were taken into account,which recommend that portable monitoring shouldnot be used in patient groups with significant comor-bid medical conditions, patients suspected of hav-ing other sleeps disorders and for general screening
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of asymptomatic populations.7 Our results suggestthat LR and SVMs classifiers fed with reduced inputfeature subsets provide high performance and sta-ble classifiers across independent populations formdifferent sleep units. However, further analyses areneeded to assess its robustness against commonlimitations of oximetry. Moreover, further work isrequired to test the performance of our methodologyfrom ambulatory portable monitoring at patient’shome. An additional limitation should be taken intoaccount. In the present study, an AHI ≥ 10 e/h wasused as threshold for a positive diagnosis of SAHSin both sleeps units under study. However, there isnot a standardized AHI threshold for SAHS diag-nosis65 and different cut-off points (commonly 5,10 and 15 e/h) have been widely applied. There-fore, further analysis is needed to assess the influ-ence of changes in the diagnostic threshold in orderto generalize our methodology. In addition, SAHS-positive patients are predominant in the training set,which could influence the model design and the per-formance of the classifiers. Finally, additional draw-backs regarding feature selection must be considered.As optimization algorithms, GAs achieved higherperformance in the training set. However, significantunbalanced values of sensitivity and specificity werereached in the validation and the test sets when largefeature subsets are selected. Genetic programming,which is a significant extension of GAs66 could beapplied to further assess the usefulness of evolution-ary algorithms for feature selection in the contextof SAHS diagnosis from oximetry. Moreover, addi-tional feature selection techniques could be appliedto further assess our methodology, such as indepen-dent component analysis, subspace clustering or sim-ulated annealing.
6. Conclusions
In summary, three feature selection approaches(PCA, FSFS and GAs) and three classification algo-rithms (FLD, LR and SVMs) were assessed in thecontext of SAHS diagnosis using populations fromtwo independent sleep units. Optimum classifica-tion schemes from PCA achieved highly unbalancedsensitivity–specificity pairs and poor accuracy bothin the validation and test sets regardless of the classi-fier. Additionally, performance of optimum classifiersfrom GAs significantly decreased when large feature
subsets are selected due to overfitting on the trainingset. On the other hand, FSFS +LR, FSFS +SMVand GAs +SVM classifiers, composed of a reducednumber of features automatically selected, achieveda balanced sensitivity–specificity pair and highaccuracy on populations from both sleep units.Thus, greedy search feature selection strategies andclassifiers with high generalization ability againstoverfitting could be useful to avoid noisy and redun-dant information and to obtain complementary fea-tures in order to enhance SAHS detection fromoximetry.
Acknowledgments
This research was supported in part by the Minis-terio de Economıa y Competitividad and FEDERunder project TEC2011-22987, the Proyecto Cero2011 on Ageing from Fundacion General CSIC, ObraSocial La Caixa and CSIC and project VA111A11-2from Consejerıa de Educacion (Junta de Castillay Leon). D. Alvarez was in receipt of a PIRTUgrant from the Consejerıa de Educacion de la Juntade Castilla y Leon and the European Social Fund(ESF).
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