Mining Breast Cancer Classification Rules from Mammograms

1 Introduction

Breast cancer is a leading cause of cancer death in women; however, effective methods to prevent its occurrence are lacking. Moreover, it ranked first among all causes of death in 2011, representing 28% of all cases in Taiwan [23]. However, there is evidence that early detection accompanied with early treatment can increase the survival chances of patients. Thus, early detection is critical for improving breast cancer prognosis. Recent research has emerged on the mechanisms that may contribute to breast cancer [29], suggesting new avenues for cancer control strategy. Nonetheless, mammography screening continues to be a key strategy and has been used as such for decades [35]. Basic information for this detection pertains chiefly to microcalcifications or masses that become visible in mammographic X-ray images.

According to the representations of breast cancer in mammograms, lesions can be classified as space-occupying lesions and microcalcifications (CALC). Space-occupying lesions are further divided into three types: masses, architectural distortion (ARCH), and asymmetry (ASYM). Among them, masses and ARCH are the typical signal characteristics of breast cancer. On the basis of the shape and boundary characteristics, masses can further be divided into speculated masses (SPIC), circumscribed masses (CIRC), and other masses (MISC) [9, 26].

Breast calcifications are deposits of calcium inside the breast tissue. They appear widespread in the breast, and most women have a few on their mammograms at some time, more commonly after menopause [15]. Two major types of calcifications exist depending on the size: macrocalcifications and microcalcifications. Whereas macrocalcifications are nearly always non-cancerous and require neither an additional follow-up nor a biopsy, microcalcifications should be diagnosed after further examinations. Microcalcifications are tiny specks of calcium deposits with an average diameter of 0.3 mm in individual calcifications, and can be scattered throughout the mammary gland or appear in clusters. The size, shape, and distribution of microcalcifications vary. Figure 1 shows typical examples of microcalcification and space-occupying lesions.

Figure 1:

Typical Examples of (A) Microcalcification and (B–F) Space-Occupying Lesions.

2 Background

Space-occupying lesions are defined as groups of cells appearing with varying density (bright regions surrounded by a darker homogeneous background); however, their boundaries are often blurred and difficult to identify. Therefore, the detection of space-occupying lesions on mammograms is difficult. Cheng et al. [4] discussed methods for the automated detection and classification of masses and compared their advantages and disadvantages. They reported that the average sensitivity of radiologists in breast cancer screening is only approximately 75%. However, the performance would be improved if computer-aided detection (CAD) were applied to locate abnormalities. Kom et al. [14] presented an algorithm for the detection of suspicious masses from mammographic images. The algorithm was tested on a database of 61 mammograms, on which masses had previously been marked by experienced radiologists. The results showed that a sensitivity of 95.91% was achieved for mass detection.

Suliga et al. [27] proposed a Markov random field (MRF)-based technique for the automatic detection and classification of masses, which are typically among the first symptoms analyzed in the early diagnosis of breast cancer. The presented MRF model was shown to be an efficient tool for mammogram processing. Kozegar et al. [16] implemented two steps for detecting masses. The first step was to extract suspicious regions from the mammograms through an adaptive thresholding technique. Second, an ensemble classifier was applied to reduce false-positive rates. Experimental results showed that the proposed mass detection algorithm outperformed other competing methods. Oliver et al. [20] provided additional details after reviewing existing methods for automatically detecting and segmenting masses in mammograms.

Because microcalcifications appear as small bright spots within the inhomogeneous background of a mammogram, detecting them is a difficult task. Papadopoulos et al. [22] examined the effect of an image enhancement processing stage and the parameter tuning of a CAD system for the detection of microcalcifications in mammograms. They tested five image enhancement algorithms. The optimal performance for two mammographic data sets was achieved for local range modification (A_ZMIAS = 0.932/A_ZNIJ = 0.915) and the wavelet-based linear stretching (A_ZMIAS = 0.926/A_ZNIJ = 0.904) method. Oliver et al. [21] used local features extracted from a bank of filters for the automatic detection of microcalcifications and clusters in mammographic images. The experimental evaluation was performed on receiver-operating curve (ROC) analysis for microcalcification detection, and on free-response OC analysis for cluster detection, resulting in the sensitivity of > 80% for a single false-positive cluster per image.

Zhang and Gao [33] presented a novel procedure for detecting microcalcification clusters in mammograms that involves image enhancing, feature selection, and supervised learning. The primary contribution of their method is the combination of subspace learning algorithms and the twin support vector machine (SVM). The proposed approach has been evaluated through numerous experiments. Chen et al. [3] used a topological structure over a range of scales in graphical form to classify microcalcification clusters in mammograms. The experimental results showed that the classification accuracy was as high as 96%, and the ROC area was as high as 0.96. Zhang et al. [34] applied mathematical morphology and the SVM to detect microcalcification clusters. They obtained a high level of detection precision and substantially reduced the number of false-positive object regions.

Several studies on microcalcification and space-occupying-lesion detection have been performed. For example, Arodz et al. [1] used the AdaBoost and SVM algorithms to detect suspicious anomalies. The AdaBoost algorithm has an accuracy of 76% for all lesion types and 90% for masses under ideal conditions. Hu et al. [10] developed an adaptive global thresholding segmentation algorithm for detecting suspicious lesions in mammograms. Their experimental results indicated that the algorithm had a sensitivity of 91.3% and 0.71 false-positives per image. Kendall et al. [13] detected anomalies in screening mammograms by using two-dimensional (2D) discrete wavelet transforms, statistical features, and naïve Bayesian classifiers. After a series of tests, the proposed approach resulted in 100% sensitivity and up to 79% specificity for abnormalities. For detecting and classifying suspicious lesions, Veena and Jayakrishna [28] developed a systematic scheme that consists of a back-propagation neural network (BPNN), wavelet transform, and window-based adaptive thresholding. Experimental results showed that the approach yields good detection and classification results. Table 1 lists the summary of studies related to the detection of masses, microcalcifications, and suspicious lesions in mammograms.

Studies present limits because of the specificity of the detected microcalcification, the characteristics of the extracted space-occupying lesions (e.g., size, shape, and number), or the procedure used for detection. Considering these drawbacks, this study proposes a CAD system for analyzing mammograms. The database used to develop our system was provided by the Mammographic Image Analysis Society (mini-MIAS). After selecting the region of interest (ROI), we determined three distinct features: the shape, spatial, and spectral domain features. In addition, we used the structural equation model (SEM) to calculate relations between features and the breast tissue type, lesion class, and tumor severity. Finally, the decision tree (DT) and classification and regression tree (CART) was applied to frame computer-aided breast cancer diagnosis rules. Figure 2 shows a diagram of the proposed method.

Figure 2:

Diagram of the Proposed Method.

The main contributions of the current study are as follows:

• A novel method for analyzing irregularities in mammograms that consists of SEM, DT, and CART is proposed.

• Several computer-aided diagnosis rules are generated to aid radiologists in classifying abnormal lesions and in classifying tumor severity.

• Two practical data sets, namely mini-MIAS and Digital Database for Screening Mammography (DDSM), are used to develop and evaluate the proposed approach.

The remainder of this article is organized as follows: Section 2 details the materials and methods used in the article; Section 3 presents an analysis of the experimental results as well as a discussion; and, lastly, Section 4 offers a conclusion.

3 Materials and Methods

3.1 Data Set

The data set used in this study was provided by the MIAS (mini-MIAS). In the data set, X-ray films have been digitized using a Joyce-Lobel scanning microdensitometer with a resolution of 50 μm × 50 μm, 8-bit word, and the original images have a size of 1024 × 1024 pixels. The mammographic images were obtained from 161 subjects. Both right and left breast photographs of the subjects are provided, totaling 322 files. Odd (even) file numbers concern the right (left) breast mammogram. Of these files, 207 do not show tumor lesions and are presented as normal mammograms, and the remaining 115 plus 8 (some have two or three abnormal areas) show abnormal mammograms with space-occupying or calcification lesions [26].

There are three types of breast tissues: fatty (F), fatty-glandular (FG), and dense-glandular (DG). Among the 207 normal mammograms, 66 mammograms show fatty tissue, 65 mammograms show glandular tissues, and the remaining 76 show dense tissues. Among the 115 abnormal samples, 40 samples have fatty tissues, 39 samples have glandular tissues, and the remaining 36 have dense tissues. Figure 3 shows the distributions of the types of breast tissues.

Figure 3:

Distributions of Types of Breast Tissues.

The class of abnormal lesions describes the type of lesions and tumor disease. Apart from the normal (NORM) mammograms, the remaining abnormal tumor lesions are divided into six categories: CIRC, SPIC, ARCH, ASYM, CALC, and MISC. Among the 123 abnormal mammograms, 25 mammograms have well-defined/circumscribed masses, 19 mammograms have speculated masses, 19 mammograms have architectural distortion masses, 15 mammograms have asymmetry masses, 30 mammograms have calcifications, and the remaining 15 have other ill-defined masses. The severity of the tumor record type of tumors was examined using a biopsy diagnosis to determine whether the tumors were benign (BENIGN) or malignant (MALIG). There are 69 benign cases and 54 malignant cases. Figure 4 shows the classification of mammographic images. The number of mammograms is mentioned in parentheses.

Figure 4:

Classification of Mammographic Images.

3.4 Spectral Domain Features

The spectral domain features employ the determination of values as the texture unit. The technique is based on a two-level version of the texture spectrum method [19]. First, image pixels are labeled using a step function that records the differences between the central pixel and its neighbors. Pixel values in the neighborhood are multiplied by binomial weights assigned to the corresponding pixels. Finally, the products are summed to obtain the number of the neighborhood.

The information for a pixel can be extracted from a neighborhood of 3 × 3 pixels, which represents the smallest complete unit (with eight directions surrounding the pixel). Texture units thus characterize the local texture for a given pixel and its neighborhood, and the statistics of all of the texture units over the entire image reveal the global texture aspects [8].

With a neighborhood of 3 × 3 pixels, which are denoted by a set of nine elements V= {V₀, V₁, …, V₈}, where V₀ represents the intensity value of the central pixel and V_i denotes the intensity value of the neighboring pixel i, TU is given by TU= {E₀, E₁, …, E₈}, where E_i is determined as follows:

(15)Ei = {0 if Vi < V01 if Vi = V02 if Vi > V0  i = 1,2,…,8. (15)

From equation (15) above, each element can be assigned one of three possible values so the total number of possible texture units for the eight elements can be estimated as 3⁸= 6561. The texture unit number is defined

(16)NTU = ∑i = 18Ei × 3i − 1, (16)

where N_TU varies from 0 to 6560. The set of 6561 texture units corresponds to the relative gray-level relationships between a pixel and its neighbors in all possible directions, i.e., the local texture aspect of a given pixel in accordance with its neighbors.

Moreover, the eight elements can be ordered differently. If they are ordered clockwise as shown in Figure 5, the first element can take eight possible positions from the top left (A) to the middle left (H), and then the 6561 N_TU can be labeled by the above formula under eight different ordering ways (from A to H). Table 4 lists eight spectral domain features, where S(i) is the occurrence of the ith N_TU; P(a, b, c) is the probability of E_a = E_b = E_c; and K(i) is the probability of E_a = E_e, E_b = E_f, E_c = E_g, and E_d = E_h.

Table 4:

Spectral Domain Features.

Features	Expression
Black-white symmetry (BWS)	BWS = 1 − ∑i = 03279[S1(i) − S1(3281 + i)]∑i = 06560S(i)1
Geometric symmetry (GS)	GS = 1 − 14∑j = 14∑i = 06560[Sj(i) − Sj + 4(i)]2 × ∑i = 06560Sj(i)
Degree of direction (DD)	DD = 1 −16∑m = 13∑n = m + 14∑i = 06560[Sm(i) − Sn(i)]2 × ∑i = 06560Sm(i)
Micro horizontal structure (MHS)	MHS = ∑i = 06560[S1(i) × HM(i)]HM(i) = P(a,b,c) × P(e,f,g)
Micro vertical structure (MVS)	MVS = ∑i = 06560[S1(i) × VM(i)]VM(i) = P(a,g,h) × P(c,d,e)
Micro left diagonal structure (MLDS)	MLDS = ∑i = 06560[S1(i) × LDM(i)]LDM(i) = P(a,b,h) × P(d,e,f)
Micro right diagonal structure (MRDS)	MRDS = ∑i = 06560[S1(i) × RDM(i)]RDM(i) = P(b,c,d) × P(f,g,h)
Central symmetry (CS)	CS = ∑i = 06560S1(i) × K(i)2

The spectral domain features are also called local binary patterns. Some studies applied them to analyze breast cancers, such as Lladó et al. [18] and Joseph and Balakrishnan [11].

Figure 5:

Eight Possible Positions Associated with the Central Pixel.

3.6 Structural Equation Model

The SEM is a statistical model for testing and estimating causal relations by using a combination of statistical data and qualitative causal assumptions (Figure 6).

Figure 6:

Structural Equation Model.

The general SEM can be represented using the following three matrix equations:

(20)ηm × 1 = Bm × m × ηm × 1 + Γm × n × ξn × 1 × ζm × 1, (20)

(21)Yp × 1 = ΛY(p × m) × ηm × 1 + εp × 1, (21)

(22)Xq × 1 = ΛX(q × n) × ξn × 1 + δq × 1. (22)

An SEM includes two types of latent variables: exogenous and endogenous. Parameters ξ indicate exogenous constructs, which are independent variables in all equations, whereas η denotes endogenous constructs that are dependent variables in at least one equation. Parameter γ represents regression relations between exogenous constructs and endogenous constructs. Parameter β represents regression relations between two endogenous constructs. Typically, in SEM, exogenous constructs are allowed to co-vary freely. Parameter ϕ represents these co-variances. Manifest variables associated with exogenous constructs are labeled X, whereas those associated with endogenous constructs are labeled Y. An SEM includes two separate λ matrices that connect manifest variables with latent variables, one on the X side and the other on the Y side. Parameters δ and ε denote measurement errors, whereas ζ represents the structural error [25].

4 Experimental Design and Analysis

We implemented the proposed method by using Matlab 7.0, Weka 3.7, SPSS 12.0, Lisrel 8.5, and SPM 7.0 (provided by Salford Systems, San Diego, CA, USA) on a personal computer (Intel Core i7, 2.93-GHz CPU, and 3.46 GB RAM). After selecting features by information gain, we obtained the remaining features for shape (FBD, DIFF, AREA, COMPACT, ELONG, PHI2, PHI3, and PHI6) and for spatial (CP_2_90, Intensity_4_90, CP_4_90, Energy_4_90, MP_4_90, Intensity_6_90, CP_6_90, Energy_6_90, and MP_6_90). These features plus the spectral features are then fed into the SEM to establish a structural model.

Figure 7 shows the path model that was fitted using the maximum likelihood method in LISREL to estimate the path parameters; the asterisk indicates 5% significant differences (type I error). The χ² of the SEM was 10,530.57 (p= 0.0) with 546 degrees of freedom. The root mean square error of approximation was 0.24, which indicates that the model was acceptable. For the structure model of the SEM, nine significant paths reached the significance level of 0.05: shape→type (0.18), shape→class (0.05), shape→severity (0.11), spatial→class (0.06), spatial→severity (–0.12), spectral→class (–0.05), spectral→severity (–0.12), type→class (–0.01), and type→severity (–0.03). The value in parentheses is the correlation between latent variables. Therefore, we applied space, spatial, spectral, and type to predict both class and severity.

Figure 7:

Path Model of the Features.

Figure 8 shows the DT tree for predicting the classification of abnormal lesions. AREA, CS, MP_6_90, FBD, BWS, CP_2_90, and PHI6 are shown to play a critical role in rule induction. For instance, if a mammogram ROI is characterized by AREA≤ 10,050, CS> 0.075, MP_6_90 ≤ 0.5655, FBD≤ 16.40, BWS≤ 0.1828, CP_2_90 ≤ 0.9033, it falls into ARCH class with an accuracy of 83.3%. Table 5 lists in summary form the rules and the classification results for lesion class obtained from the constructed tree. Table 6 lists the detailed accuracy by class of DT results for predicting the classification of abnormal lesions. The average accurate rate is 73.64%, and the average ROC area is 0.865.

Figure 8:

Tree of DT for Predicting the Classification of Abnormal Lesions.

Figure 9 shows the CART tree used for classifying the tumor severity. AREA, DD, FBD, COMPACT, BWS, DIFF, GS, and PHI3 clearly play a critical role in rule induction. For example, if a mammogram ROI is characterized by AREA≤ 10,663.50, DD≤ 0.42, and FBD≤ 13.98, it falls into BENIGN class with an accuracy of 84.6%. Table 7 lists the classification rules for tumor severity obtained from the built tree. The average accurate rate is 87.14%. Figure 10 shows the ROC used for classifying tumor severity. The overall area under the curve is 0.9336.

Figure 9:

Tree of CART for Classifying the Tumor Severity.

Figure 10:

ROC for Classifying the Tumor Severity.

To test the performance of the proposed approach, a set of samples was collected from the DDSM database, which contains 2620 cases, including normal images and images with benign and malignant lesions. One hundred benign images and 100 malignant images were randomly selected. Each image has an assessment code between 1 and 5 that is assigned according to the American College of Radiology Breast Imaging and Reporting Data System (ACR Bi-RADS) standard. The distributions of the data are shown in Figure 11. For the lesion severity classification, the average accuracy rate of CART was 82.5%, and the overall area under the ROC curve was 0.844. For the ACR Bi-RADS assessment classification, the average accuracy rate of CART was 65% and the overall area under the ROC curve was 0.69. Although the results were not sufficient compared with those of the mini-MIAS, the accuracy rates of the ACR Bi-RADS assessment classification were acceptable compared with radiologist operations.

Figure 11:

Distributions of DDSM Samples.

Table 8 lists the accuracy and ROC area obtained using the proposed method relative to those obtained by applying other methods to the mini-MIAS and DDSM databases. The methods were naïve Bayes [13], SVM [34], multilayer perception [28], and AdaBoost [1]. The highlighted sections of the table indicate that the proposed approach obtained the classification rules and outperformed other methods when applied to the mini-MIAS database. For the DDSM database, the proposed approach was not the superior classification method. CART and DT provided the classification rules; however, it is difficult to interpret the results obtained using other methods.

Table 8:

Comparison of Accuracy and ROC Area.

Radiologists visually search mammograms for abnormalities; however, the task is repetitive and time consuming. The rules generated in this approach can assist them in detecting mammographic lesions that may indicate the presence of breast cancer. First, radiologists determine an ROI that is then tested using the generated rules. If a suspicious abnormality is detected, then further examination is performed to determine the course of action that may be required. However, CAD acts only as a second reader, and the final decision is made by the radiologist [12, 24]. Moreover, the computational complexity for a new occurrence is constant because the features of the classification rules are determined.

5 Conclusion

Breast cancer is a leading cause of early mortality in women. Mammography is the most effective method for the early detection of breast cancer. Early diagnosis and treatment are crucial to reducing the mortality rate and increasing patients’ lifespan. This article proposed a computer-aided diagnosis system consisting of five main steps. First, the original images are obtained from the mini-MIAS database. Second, after selecting the ROI, we computed three distinct features: the shape, spatial, and spectral domain features. Third, the number of features is reduced by information gain. Fourth, these data are inputted into an SEM to calculate the relationship between features and breast tissue type, lesion class, and tumor severity. Finally, DT and CART are applied to construct a mammogram-based computer-aided breast cancer diagnosis system. The proposed method generates 10 rules for predicting the classification of abnormal lesions with an average accurate rate of 73.64% and average ROC area of 0.865. There are 11 rules for classifying tumor severity with an average accurate rate of 87.14% and average ROC area of 0.934. These rules can help clinicians detect and interpret breast cancer efficiency from mammograms, and thus, improves the quality of medical care.