1 Introduction

It has been demonstrated earlier that the increased breast density is prominent indicator for the growth of breast cancer. It is the most common life threatening form of cancer that is found in women [7, 92, 93]. For the experienced radiologists, especially in cases of dense mammogram if masses are present in the center area (i.e. the area where glandular ducts are prominent) detection of breast abnormalities is really a tedious work. In routine clinical practice, during screening mammography the radiologist may find that sometimes in a dense tissue when the lesion is not visible there are chances that the lesion is present and is masked behind the dense tissue. So it is highly recommended that if the prediction for that suspicious case is dense (B-III or B-IV) then such cases must be double screened for the presence of masked lesions.

Fundamentally, different breast tissues reflect different intensity i.e. fatty tissue represented as dark region while dense tissues represented as brighter region on digitized screen film mammographic images [51, 96]. The brief description of Breast Imaging-Reporting and data system (BIRADS) density classes and the sample digitized film screen mammogram (SFM) images of each class, randomly taken from the Digital database for screening mammography (DDSM) dataset [36] are shown in Fig. 1.

Fig. 1
figure 1

Sample of digitized screen film mammograms of BIRADS breast density class taken from DDSM dataset belonging to (a) BIRADS-I: B-I, (b) BIRADS-II: B-II, (c) BIRADS-III: B-III and (d) BIRADS-IV: B-IV

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1.1 Hierarchical classification system

It is worth mentioning that the designing of computer-aided diagnosis system, hierarchical approach has been extensively used in studies [4, 32, 53, 69, 79, 80] which yields the prominent results. The hierarchical approach for the design of 4-class breast density classification system is shown in Fig. 2.

Fig. 2
figure 2

Hierarchical approach for the design of 4-class breast density classification system

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In the Fig. 3 it has been observed that classifier-1 is used to classify the input test ROI into C 1 /other class. If the test ROI is predicted as other class, it is inputted to the second classifier for classification into C 2 /other class-2. If the test ROI is predicted as belonging to other class-2, it is inputted to the third classifier for the classification into C 3 /C 4 .

Fig. 3
figure 3

Approaches used for the design of breast density classification systems. Note: STBAs: Segmented tissue based approaches, RBAs: ROI based approaches. Benchmark dataset#: MIAS, DDSM

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There are few advantages of hierarchical classification approach (a) less number of classifiers required with respect to multiclass classifier (for 4-class classification problem six binary classifiers required in OAO approach however only three binary classifiers are required in hierarchical approach), (b) possibility to go stepwise from the general classification problem, i.e. fatty (B-I) versus other class, to more particular classification problem i.e. B-II versus dense and B-III versus B-IV class.

Therefore in the present work hierarchical framework for the classification of breast density is used. It provides the possibility to go stepwise from the general classification problem, i.e. B-I/other class, classification problem which is the identification of B-I breast density class with hierarchical framework of classifiers. In the similar manner next level of classification frameworks classify the B-II)/dense class {B-III, B-IV} and further move on for B-III/B-IV breast density class.

2 Literature review

From the study conducted in past it has been observed that the breast density classification systems have been designed for (1) 2-class (fatty tissue/dense tissue) breast density class, (2) 3-class (fatty tissue/fatty glandular tissue/dense tissue) breast density class and (3) 4-class BIRADS (fatty tissue/some fibroglandular tissue/hetero-geneously dense tissue/extremely dense tissue) breast density classes. The classification of these approaches is shown in Fig. 3.

The broad study of the literature demonstrate that the breast density classification system using SFMs can be designed using (1) segmented tissue based approaches (STBAs) [11, 12, 18, 30, 42, 52, 60, 65, 67, 68, 70] and (2) fixed size region of interest (ROI) based approaches (RBAs) [35, 39, 59]. It is well known that STBAs require additional steps viz. eliminating the background and removing the pectoral muscle. Due to these additional steps STBAs are more time consuming and complex in comparison to the RBAs.

After the depth study of literature it has been observed that most of the studies for 4-class breast density classification using SFMs carried on benchmark dataset i.e. (a) Mammographic image analysis society (MIAS) [11, 18, 65, 67, 68, 70], (b) DDSM [11, 12, 52, 67, 68] and (c) self collected mammograms by individual research group [30, 35, 39, 42, 59, 60]. It is worth mentioning that the DDSM dataset contains images which are already labeled according to BIRADS density standard by the experts, however in case of MIAS dataset as well as in case of datasets collected by authors the images have been labeled according to BIRADS standard by the participating radiologists.

2.1 Study carried out on benchmark DDSM dataset

After the extensive study of the literature it has been observed that the most of the studies carried out on benchmark DDSM dataset is using STBAs [11, 12, 67, 68]. The brief description of studies carried out for 4-class breast density classification on DDSM dataset is given in Table 1. It is worth observing that the only one study is based on RBAs [52]. The maximum classification accuracy obtained for DDSM dataset is 84.7% using the STBA [11]. The study [11] carried out on 500 digitized SFMs taken from DDSM dataset which is comprised of 125 mammograms of each class. The segmentation of breast region is performed using global thresholding method and polynomial approach proposed by Ferrari at el. [30] is used for removal of pectoral muscle. Appearance based and edge based features are extracted for each segmented mammograms and support vector machine is used for classification purpose. In this study 499 samples are used for training purpose and 1 image is tested 500 times and 84.7% classification accuracy is observed.

Table 1 Studies carried out for 4-class breast density classification
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In study [52] the authors have attempted 4-class breast density classification using RBA on 480 digitized SFMs taken from DDSM dataset. The fixed size of ROIs i.e. 128 × 128 pixels are cropped from center location of each breast (i.e. just behind the nipple) and wavelet texture features are computed using the haar compact support wavelet filter. The study reports the accuracy of 73.7% using SVM classifier. From the literature study it may be noted that the study [52] can be only directly related to present work as it has been carried out on DDSM dataset using RBA.

2.2 Study carried out on benchmark MIAS dataset

In the literature few studies [11, 18, 65, 67, 68, 70] have been carried out on benchmark MIAS dataset for 4-class breast density classification as the images have been labeled according to BIRADS standard by the participating radiologists. It is worth observing that most of the studies conducted on using STBAs [11, 18, 67, 68, 70] and only few studies are conducted using RBAs. The maximum accuracy of 95.4% has been achieved by using STBA on studies carried out on MIAS dataset [11]. In study [11] 322 SFMs are taken. Whole breast region is segmented using global thresholding method and polynomial approach proposed by Ferrari at el. [30] is used for removal of pectoral muscle. The extracted features are based on edges and intensity appearance and used classifier is support vector machine.

The maximum accuracy achieved on MIAS dataset using the RBAs is 79.2% reported in study [65]. In this study ROI of fixed size i.e. 512 × 384 pixels are cropped from 322 digitized SFMs. The 7 intensity based and 17 GLCM texture features (for the angle 0°, 45°, 90° and 135° at inter-pixels distance 1,3,5 and 7) are extracted for each ROI. Naïve Bayes probabilistic classifier is used for the characterization between BIRADS density class. The summary of studies carried out for 4-class breast density classification on MIAS dataset is reported in Table 1.

2.3 Study carried out on self collected mammograms by individual research group

It is also found that the few studies were carried out on self collected mammograms by individual research group [35, 39, 42, 59, 60]. It is worth observing that the most of the studies carried out on self collected mammograms by individual research group are based on STBAs. The maximum classification accuracy obtained on self collected dataset is 80.0% consisting of 80 mammograms [39]. The summary of studies carried out for 4-class breast density classification on self collected by different research group dataset is reported in Table 1.

In the present work, a hybrid hierarchical framework for classification of breast density is designed which is consisting of five hierarchical classifiers i.e. 3 PCA-kNN, 3 PCA-PNN, 3 PCA-ANN, 3 PCA-NFC and 3 PCA-SVM classifiers have been proposed. Further, the best performing individual classifiers at each node are clubbed together in a hierarchical framework to design hybrid hierarchical framework for classification of breast density using digitized screen film mammograms. Various texture parameters including 11 first-order statistics (FOS) features, 13 GLCMmean features, 5 Gy level difference statistics (GLDS) features, 11 Gy level run length matrices (GLRLM) features, 30 Laws’3 features, 75 Laws’ 5 features, 30 Laws’7 features, 75 Laws’9 features and 42 2-D Gabor wavelet transform (GWT) features are computed from extracted each fixed size of ROIs i.e. 128 × 128 pixels from center area of the breast (i.e. the area where glandular ducts are prominent). Finally, a combined feature set consisting of 292 features is inputted to Principal component analysis (PCA) for feature space dimensionality reduction. The resultant feature vector is fed to the classification module.

3 Materials and methods

3.1 Experimental work flow for the design of a hierarchical framework for classification of breast density using digitized screen film mammograms

The experimental work flow followed in this work for the design of a hierarchical framework for classification of breast density using digitized screen film mammograms is shown in Fig. 4.

Fig. 4
figure 4

Experimental work flow for the design of a hierarchical framework for classification of breast density using digitized screen film mammograms

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3.2 Description of image dataset

The image dataset used for this work comprises of 480 mediolateral oblique (MLO) view digitized screen film mammograms taken from DDSM dataset such that (1) 120 mammograms belong to B-I class (2) 120 mammograms belong to B-II class (3) 120 mammograms belong to B-III class and (4) 120 mammograms belong to B-IV class. The DDSM dataset is a standard benchmark dataset which contains four digitized screen film mammographic images for each case, comprising of left/right MLO and left/right cranial-caudal (CC) views. The overlay file of each image contains the expert evaluation of BIRADS breast density [36]. The description of dataset used for this study and its bifurcation into training and testing dataset is shown in Fig. 5.

Fig. 5
figure 5

Description of image dataset and its bifurcation into training and testing dataset

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3.3 ROI extraction module

The study carried by Li et al. [57] verified that the textural variations exhibited by the central region of the breast tissue are significant to account for discrimination between different breast density classes and also according to the participating radiologist the center area (i.e. the area where glandular ducts are prominent) is visualize for the discrimination between different breast density classes. Therefore, in this study ROIs of size 128 × 128 pixels have been cropped from the center area of the breast. The sample images belonging to BIRADS class with respected ROIs is shown in Fig. 6.

Fig. 6
figure 6

Sample images belonging to BIRADS classes with ROIs marked

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3.4 Feature extraction module

From the previous study it has been observed that the statistical texture features [11, 12, 35, 39, 42, 52, 59, 67], Law’s texture features [47, 48, 54] and 2-D Gabor wavelet transform features [1, 13, 14, 22, 23, 26, 38, 55, 71, 83, 97] are extensively used for the designing of CAD system. Accordingly in this work a wide variety of texture features are computed by using FOS features, GLCMmean features [5, 15, 33, 37, 46, 49, 57, 61, 63, 64, 77, 87, 88, 91], GLDS features [19, 29, 45, 49, 73, 86] GLRLM features [21, 25, 49, 75], Laws’ texture energy features [47, 48, 54] and 2-D Gabor wavelet transform (GWT) features [1, 13, 14, 22, 23, 26, 38, 55, 71, 83, 97].

FOS features

In this work a total of 11 first-order statistics features i.e. energy, average grey level, third moments, uniformity, mean, entropy, variance, standard deviation, skewness, kurtosis and smoothness are extracted for each ROI [49, 77].

GLCMmean features

From the exhaustive review of the literature it is observed that the texture features computed using GLCMmean contain significant information to account for variations in texture patterns exhibited by different breast density classes [49, 77]. The GLCMmean for a ROI belonging to a particular breast density class is obtained by using eq. (1).

$$ {GLCM}_{mean, B- I\left( d= i\right)}=\frac{GLCM_{B- I\left({0}^o, d= i\right)}+{GLCM}_{B- I\left({45}^o, d= i\right)}+{GLCM}_{B- I\left({90}^o, d= i\right)}+{GLCM}_{B- I\left({135}^o, d= i\right)}}{4} $$
(1)

In the similar manner GLCM mean,B-II(d = i) , GLCM mean,B-III(d = i) and GLCM mean,B-IV(d = i) are computed by varying the inter-pixel distance ‘d’ = ‘i’ from 1 to 15.

In the present work 13 GLCMmean features are computed. One of the GLCMmean feature i.e. entropy (ENT mean) is computed at inter-pixel distance ‘d’ = 10 by using eq. (2).

$$ {ENT}_{mean\left( d=10\right)}=\left(\frac{ENT_{\left(\theta ={0}^o, d=10\right)}+{ENT}_{\left(\theta ={45}^o, d=10\right)}+{ENT}_{\left(\theta ={90}^o, d=10\right)}+{ENT}_{\left(\theta ={135}^o, d=10\right)}}{4}\right) $$
(2)

In the same manner, remaining 12 GLCMmean texture features (contrastglcm_mean, varianceglcm_mean, angular second momentglcm_mean, correlation, inverse difference moment, information measures of correlation-1, information measures of correlation-2, sum average, sum variance, sum entropy, difference variance, difference entropy) have been computed by varying the inter-pixel distance ‘d’ from 1 to 15. It has been observed that the features extracted at inter-pixel distance d = 10 yielded the maximum classification accuracy. Thus the GLCMmean features computed at inter-pixel distance d = 10 is considered for this study.

GLDS features

In this work a total of 5 GLDS features i.e. contrastglds, homogeneityglds, meanglds, energyglds and entropyglds are extracted for each ROI [49, 77].

GLRLM features

In this work a total of 11 GLRLM features, i.e., emphasisshort_run, emphasislong_run, emphasislow_gray_level_run, emphasishigh_gray_level_run, emphasisshort_run_low_gray_level, emphasislong_run_low_gray_level, emphasisshort_run_high_gray_level, emphasislong_run_high_gray_level, non_uniformitygray_level, non_uniformity_run_length and run_percentage are computed for each ROI [49].

Laws’ texture energy features

In this study, the Laws’ texture energy features [47, 48, 54] have been extracted using 1-D filters of different kernel width, (i.e. 3, 5, 7 and 9). These special filters of different kernel width are used to perform local averaging (L), spot detection (S), edge detection (E), ripple detection (R) and wave detection (W) in an ROI image. The brief description of the Laws’ mask and steps involved to calculate the features are shown in Fig. 7.

Fig. 7
figure 7

Laws’ mask and steps involved to calculate the features

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In this study a total of 210 Laws’ features i.e. 30 Laws’3 features, 75 Laws’5 features, 30 Laws’ 7 features and 75 Laws’9 features are computed for each ROI.

2-D GWT features

In this study, 2-D GWT multi-scale decomposition has been carried out using three magnitude value (0, 1 and 2) and seven directions (22.5°, 45°, 67.5°, 90°, 112.5°, 135° and 157.5°) gives a group of 21 (3 × 7) Gabor wavelet filter bank. The real part of Gabor wavelet filter bank is shown in Fig. 8.

Fig. 8
figure 8

Real part of Gabor wavelet filter bank

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Further, a set of 21 filtered images are obtained after the convolution of ROI with the real part of Gabor filter bank. Each filtered image i.e. feature image represents the texture information at a certain magnitude and direction. Compute two statistics mean and standard deviation from these 21 feature images resulting in a feature vector of length 42. Thus 2-D Gabor feature of length 42 is used for this study.

3.5 Feature space dimensionality reduction module

There might be a possibility that computed texture feature vectors (TFVs) may have redundant features which are correlated to each other thus providing no extra information. The use of redundant features for an efficient classifier design may degrade the performance of the designed system. Therefore the computed TFVs are inputted to dimensionality reduction stage using PCA [2, 28, 40, 50, 72]. In this study, to retain the optimal number of principal components (PCs) for classification task, reduced texture feature vectors have been computed for all classifiers by varying the principal components values from 2 to 15. The steps involved in the implementation of PCA algorithm are given here in Fig. 9.

Fig. 9
figure 9

Steps of PCA algorithm implementation

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3.6 Classification module

The classification module consists of three binary classifiers arranged in a hierarchical framework. These three classifiers provide stepwise classification for the generalized 4-class breast density classification problem. The first classifier is used to classify an unknown test ROI into B-I/other class. If the test ROI is predicted as other class, it is inputted to second classifier for the classification into B-II/dense class. If the test ROI is predicted as belonging to dense class, it is inputted to classifier for the classification into B-III/B-IV class. The generalized block diagram of a hierarchical framework for system is classification of breast density is shown in Fig. 10.

Fig. 10
figure 10

Generalized block diagram of a hierarchical framework for classification of breast density

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Mapping of higher dimension feature space to lower dimension feature space using principal component analysis algorithm is applied individually before designing each binary classifier. Initially, five different hierarchical frameworks for classification of breast density designed using three PCA-kNN classifiers (shown in Fig. 11), three PCA-PNN classifiers (shown in Fig. 12), three PCA-ANN classifiers (shown in Fig. 13), three PCA-NFC classifiers (shown in Fig. 14) and three PCA-SVM classifiers (shown in Fig. 15.) and. The performance of each binary classifier is evaluated at each node and the best classifiers (yielding the maximum accuracy) at each node are combined in a hierarchical framework for designing the hybrid hierarchical framework (shown in Fig. 16) for classification of breast density.

Fig. 11
figure 11

Block diagram of hierarchical framework for classification of breast density using PCA-kNN classifiers

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Fig. 12
figure 12

Block diagram of hierarchical framework for classification of breast density using PCA-PNN classifiers

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Fig. 13
figure 13

Block diagram of hierarchical framework for classification of breast density using PCA-ANN classifiers

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Fig. 14
figure 14

Block diagram of hierarchical framework for classification of breast density using PCA-NFC classifiers

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Fig. 15
figure 15

Block diagram of hierarchical framework for classification of breast density using PCA-SVM classifiers

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Fig. 16
figure 16

Architecture of proposed hybrid hierarchical framework for classification of breast density for digitized screen film mammograms

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3.6.1 Hierarchical framework for classification of breast density using PCA-kNN classifiers

The kNN classifier is an instance based classifier in which the class of a testing instance is decided by the class of majority from its k nearest neighbors in the training set by calculating the Euclidean distance between neighboring instances [6, 11, 12, 18, 52, 59, 62, 65]. It tries to cluster the instances of feature vector into disjoint classes with an assumption of that the instances of feature vector lying close to each other in feature space represent instance belonging to the same class. The class of an unknown testing instance is selected to be the class of majority of instances among its k-nearest neighbors in the training set. The classification performance is affected by varying the parameter k. In this work, the value of k is optimized by repeated experimentation for classifier design by stepping through by 1 varying from 1 to 10, and if the same performance is achieved for more than one value of k the minimum value of k is considered.

The block diagram of hierarchical framework for classification of breast density using PCA-kNN classifiers is shown in Fig. 11.

3.6.2 Hierarchical framework for classification of breast density using PCA-PNN classifiers

The PNN classifier is a direct continuation of the theory of Bayesian classification estimation of probability density function (PDF). The architecture of PNN classifier comprises of an input layer, pattern layer, summation layer and decision layer. The PNN classification algorithm defines a probability density function (PDF) and optimized kernel width parameter for each class on the basis of training dataset [50]. The width of the radial basis kernel function (RBF) is determined by the spread parameter denoted as S p . In this work, the S p is optimized by repeated experimentation for classifier design by stepping through various values of S p ranging from 1 to 10. The PNN classifier trained with the optimum value of S p is then tested with reduced instances of testing dataset [58, 76, 81]. Instances of feature vectors consisting of optimal number of PCs obtained for the binary classification tasks (i.e. B-I/other class, B-II/dense class and B-III/B-IV) are fed to the input layer of corresponding binary PNN classifiers.

The block diagram of hierarchical framework for classification of breast density using PCA-PNN classifiers is shown in Fig. 12.

3.6.3 Hierarchical framework for classification of breast density using PCA-ANN classifiers

The architecture of ANN classifier comprises of an input layer, hidden layer and output layer. For designing each ANN classifier, corresponding neurons to the output class label is set to 1 and other neurons class label is set to 0, i.e. the learning of each ANN classifier is supervised. Adaptive learning with back-propagation algorithm is used to getting the desired input-output relationship [8, 20, 24, 34, 56, 74, 84, 89, 90, 94, 95, 98]. For the designing of an efficient hierarchical ANN classifier, the trial-and-error procedure was used for the optimization of hidden layer neurons. After the extensive experimentation with different numbers of hidden layer neurons, it was observed that with 10 neurons in hidden layer of ANN-1 to ANN-3 a reasonable tradeoff between convergence and accuracy was obtained.

Instances of feature vectors consisting of optimal number of PCs obtained for the binary classification tasks (i.e. B-I/other class, B-II/dense class and B-III/B-IV) are fed to the input layer of corresponding binary ANN (BNN) classifiers. The Block diagram of hierarchical framework for classification of breast density using PCA-ANN classifiers is shown in Fig. 13.

3.6.4 Hierarchical framework for classification of breast density using PCA-NFC classifiers

The Neuro fuzzy classifier (NFC) is a multilayer feed-forward network comprises of the input layer, membership layer, fuzzification layer, defuzzification layer, normalization layer, and output layer [3, 10, 16, 27, 31, 41, 43, 44, 66, 82, 85]. It is worth mention that fuzzy inference systems are suffers from the learning capability and neural networks have the learning capability. Thus neuro fuzzy classifier (NFC) is the prominent applications of fuzzy inference system and neural network i.e. NFC overcomes the limitations of neural network and fuzzy inference systems. Thus NFC has the capability to learn and represent knowledge according to defined rule and learning ability. In the present study, instances of feature vectors consisting of optimal number of PCs obtained for the binary classification tasks (i.e. B-I/other class, B-II/dense class and B-III/B-IV) are fed to the input layer of corresponding binary NFC classifiers. The block diagram of hierarchical framework for classification of breast density using PCA-NFC classifiers is shown in Fig. 14.

3.6.5 Hierarchical framework for classification of breast density using PCA-SVM classifiers

All three binary SVM classifiers designed for the hierarchical framework for classification of breast density are implemented using LibSVM library [17]. In SVM algorithm, training data is mapped from lower dimensional input features to higher dimensional features. Kernel functions are used for nonlinear mapping of the training data from input space to higher dimensional feature space. In this study, Gaussian radial basis kernel function based SVM classifier (available in LibSVM library) has been used for the design of computerized framework for detection of lesions in dense mammograms.

For designing the classifier, Gaussian radial basis function (RBF) kernel is used. The 10 fold cross validation approach is used to optimize the kernel width γ and regularization parameter C of radial basis function by extensive experiment carried out on training data for the values of γ ∈ {2−12, 2−11,..., 24} and C ∈ {2−4, 2−3 ,…, 215} [9, 34, 55, 78]. The block diagram of hierarchical framework for classification of breast density using PCA-SVM classifiers is shown in Fig. 15.

4 Experiments and results

The 4-class breast density classification task has been considered and hierarchical framework is designed using five classifiers (i.e. PCA-kNN, PCA-PNN, PCA-ANN, PCA-NFC and PCA-SVM) arranged in a hierarchical framework.

The brief details of experiments carried for hierarchical framework for classification of breast density using digitized screen film mammograms is reported in Table 2.

Table 2 Experiments carried for hierarchical framework for classification of breast density using digitized screen film mammograms
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The performance of designed each hierarchical framework at each node is evaluated in terms of accuracy of binary classifier expressed as Acc_Bin_Class, overall classification accuracy expressed as OCA and Individual class accuracy expressed as ICA.

  • Experiment 1: The performance of hierarchical framework for classification of breast density using PCA-kNN classifier is given in Table 3.

Table 3 Performance of hierarchical framework for classification of breast density using PCA-kNN classifiers
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  • Experiment 2: The performance of hierarchical framework for classification of breast density using PCA-PNN classifiers is given in Table 4.

Table 4 Performance of hierarchical framework for classification of breast density using PCA-PNN classifiers
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  • Experiment 3: The performance of hierarchical framework for classification of breast density using PCA-ANN classifiers is given in Table 5.

Table 5 Performance of hierarchical framework for classification of breast density using PCA-ANN classifiers
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  • Experiment 4: The performance of hierarchical framework for classification of breast density using PCA-NFC classifiers is given in Table 6.

Table 6 Performance of hierarchical framework for classification of breast density using PCA-NFC classifiers
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  • Experiment 5 : The performance of hierarchical framework for classification of breast density using PCA-SVM classifiers is given in Table 7.

Table 7 Performance of hierarchical framework for classification of breast density using PCA-SVM classifiers
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The value of OCA is obtained by adding the number of misclassifications obtained at each stage of the hierarchical framework for breast density classification using PCA-NFC classifiers yields minimum i.e. a total of 47 misclassifications consisting of 8, 6, 6, 10, 14 and 3 misclassifications for PCA-NFC1, PCA-NFC2 and PCA-NFC3 classifiers respectively, therefore, OCA for hierarchical framework using PCA-NFC classifiers is {(240–47) / 240} × 100 = {(193 / 240) × 100} = 80.4%.

By visualizing the performance of individual binary classifiers of PCA-kNN, PCA-PNN, PCA-ANN, PCA-NFC and PCA-SVM based on hierarchical framework (shown in Table 3, Table 4, Table 5, Table 6 and Table 7), some interesting facts are observed:

  1. (a).

    For classification between B-I/Other class the maximum accuracy of 96.2% is obtained by using PCA-SVM1 classifier in comparison with 85.0%, 84.5%, 80.4% and 94.1% as obtained by using PCA-kNN1, PCA-PNN1, PCA-ANN1 and PCA-NFC1 classifiers.

  2. (b).

    For further classification of other class instances into B-II/dense class the maximum accuracy of 91.1% is obtained by using PCA-NFC2 classifier in comparison with 90.5%, 87.7%, 72.7% and 88.3% as obtained by using PCA-kNN2, PCA-PNN2, PCA-ANN2 and PCA-SVM2 classifiers respectively.

  3. (c).

    For classification of dense class into B-III/B-IV class the maximum accuracy of 89.1% is obtained by using PCA- kNN3 classifier in comparison with 85.8%, 80.8%, 81.6% and 85.8% as obtained by using PCA-PNN3, PCA-ANN3, PCA-SVM3 and PCA-NFC3 classifiers.

4.1 Comparative analysis

The comparative performance analysis of designed hierarchical frameworks for classification of breast density using various experiments carried out in this work is reported in Table 8.

Table 8 Comparative analysis of performance of designed hierarchical framework for classification of breast density using various experiments
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From Table 8, it can be observed that the PCA-NFC based hierarchical framework performs better in comparison with PCA-kNN, PCA-PNN, PCA-ANN and PCA-SVM based hierarchical framework for 4-class breast density classification. For classification between B-I/other class PCA-SVM1 perform best at PCs value 9. For classification between B-II/dense, PCA-NFC2 is the best at PCs value 7 and for classification between B-III/B-IV, PCA- kNN3 is the best at PCs value 11.

  • Experiment 6: Design of hybrid hierarchical framework for classification of breast density designed the best performing individual classifiers at each node a hierarchical framework

The architecture of the proposed hybrid hierarchical framework for classification of breast density designed the best performing individual classifiers at each node in hierarchical framework is shown in Fig. 16.

The performance obtained for proposed hybrid hierarchical framework for classification of breast density for digitized screen film mammograms is reported in Table 9.

Table 9 Performance obtained by hybrid hierarchical framework for classification of breast density for digitized screen film mammograms
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From Table 9, it has been concluded that the proposed hybrid hierarchical framework yields the maximum OCA value of 84.1% with only 38 misclassifications out of 240 test instances. The proposed hybrid hierarchical framework perform best in comparison to PCA-kNN, PCA-PNN, PCA-ANN, PCA-NFC and PCA-SVM based hierarchical framework for classification of breast density using digitized screen film mammograms. The OCA obtained by hybrid hierarchical framework is 84.1% in comparison with 72.5%, 68.5%, 50.4%, 78.3 and 80.4% as obtained by PCA-kNN, PCA-PNN, PCA-ANN, PCA-NFC and PCA-SVM based hierarchical framework respectively.

5 Conclusion

During the clinical routine screening of mammography expertise observed that the breast lesions are missed in case of dense mammograms. Thus, in this study extensive experimentations have been performed for breast density classification using PCA-kNN, PCA-PNN, PCA-ANN, PCA-NFC and PCA-SVM based hierarchical framework. Among these PCA-NFC based hierarchical framework yielding the OCA value is 80.4% with 47 (47/240) misclassification out 240 test instances. However, it is observed that the hybrid hierarchical framework designed by combination of best binary classifiers at each node yields the OCA value of 84.1% with only 38 (38/240) misclassifications out of 240 test instances. The proposed hybrid hierarchical classification framework perform best in comparison to each of PCA-kNN, PCA-PNN, PCA-ANN, PCA-NFC and PCA-SVM based hierarchical classification framework for breast density classification. The result achieved by the proposed hybrid hierarchical framework for classification of breast density using digitized screen film mammograms is quite promising and indicate its effectiveness to assist radiologists in adequate scheduling of breast lesion treatment in clinical environment.