Abstract
Aim:
To develop an automatic magnetic resonance (MR) brain classification that can assist physicians to make a diagnosis and reduce wrong decisions.
Method:
This article investigated the binary particle swarm optimization (BPSO) approach and proposed its three new variants: BPSO with mutation and time-varying acceleration coefficients (BPSO-MT), BPSO with mutation (BPSO-M), and BPSO with time-varying acceleration coefficients (BPSO-T). We first extracted wavelet entropy (WE) features from both approximation and detail sub-bands of eight-level decomposition. Afterwards, we used the proposed BPSO-M, BPSO-T, and BPSO-MT to select features. Finally, the selected features were fed into a probabilistic neural network (PNN).
Results:
The proposed BPSO-MT performed better than BPSO-T and BPSO-M. It finally selected two features of entropies of the following two sub-bands (V1, D1). The proposed system “WE + BPSO-MT + PNN” yielded perfect classification on Data160 and Data66. In addition, it yielded 99.53% average accuracy for the Data255, over 10 repetitions of k-fold stratified cross validation (SCV), higher than state-of-the-art approaches.
Conclusions:
The proposed method is effective for MR brain classification.
Background
Magnetic resonance imaging (MRI) is a popular tool for human body imaging. It is basically a noninvasive technique that provides superior resolution for soft tissues within the brain [52] to traditional computed tomography (CT) [5], ultrasound [1], positron emission tomography (PET) [16], etc.
To develop an easy and swift diagnosis based on brain magnetic resonance (MR) images [14] remains a hot topic in both academic and industrial fields [32, 35, 44]. Traditional manual methods are either tedious or time-consuming, expensive, or irreproducible, as the MR data are commonly enormous. This causes scholars to try to develop an automatic computer-aided diagnosis (CAD) method [2, 39, 62].
The literature shows that a wide variety of automatic methods have been proposed for brain MR image classification. Chaplot et al. [4] were the forerunners to use discrete wavelet transform (DWT) to extract the approximation coefficients and employed both a self-organizing map (SOM) neural network and a support vector machine (SVM) for classification. Wang and Wu [41] presented to use a feed-forward neural network (FNN) to solve the task, that is to make decisions on a given MR brain image as to whether it is healthy or pathological. El-Dahshan et al. [10] employed three-level DWT coefficients and then reduced them by the classical feature reduction technique: principal component analysis (PCA). They utilized two classifiers: artificial neural network (ANN) and K-nearest neighbors (KNN). Dong et al. [9] further suggested a relatively new method, the scaled conjugate gradient (SCG). Das et al. [6] combined ripplet transform (RT) and PCA. They combined the least square method and a support vector machine and termed it LS-SVM. They performed a 5×5 cross validation test, which offered excellent accuracies. Zhang and Wu [50] utilized a kernel support vector machine (KSVM). They used three new kernels: a radial basis function, a homogeneous polynomial, and an inhomogeneous polynomial. Zhang et al. [56] suggested to use particle swarm optimization (PSO) to train the KSVM. El-Dahshan et al. [11] used the feedback pulse-coupled neural network to preprocess the MR images, the DWT and PCA to extract and reduce features, and the ANN to detect pathological brains from normal brains. Wang et al. [42] distinguished Alzheimer’s disease (AD) from healthy controls, by structural MR images by the KSVM decision tree. A five-fold cross validation showed their method yielded 80% accuracy. Zhou et al. [63] utilized wavelet entropy (WT) from MR brain images. They utilized a naive Bayes classifier (NBC) as a classifier. Wang et al. [43] utilized the stationary wavelet transform (SWT) to replace traditional DWT. They presented a hybridization of PSO and the artificial bee colony (HPA) algorithm. Nayak et al. [29] proposed to use two-dimensional DWT and AdaBoost with random forests. Zhang et al. [54] employed a discrete wavelet packet transform (DWPT). They also employed Tsallis entropy (TE) and Shannon entropy (SE) to extract features. Finally, a nonparallel SVM, viz. the generalized eigenvalue proximal support vector machine (GEPSVM), was used as the classifier. Yang et al. [47] used wavelet energy to be the features. To train the SVM, they introduced biogeography-based optimization (BBO). Zhang et al. [53] presented a new method to detect AD subjects by a novel 3D eigenbrain analysis method. They achieved 92.36% accuracy. Jayachandran and Sundararaj [18] proposed a multiclass brain tumor classification system, using fuzzy logic-based hybrid KSVM. Zhang et al. [60] introduced the three-dimensional discrete wavelet transform (3D-DWT) to extract features from volumetric brain MR images. Moeskops et al. [26] used supervised the classification to perform automatic segmentation of MR brain images of preterm infants. Zhang et al. [55] presented a hybridization of BBO and PSO (abbreviated as HBP). Munteanu et al. [27] used proton magnetic resonance spectroscopy (MRS) data in order to detect mild cognitive impairment (MCI) and AD.
After analyzing the above methods, we found most of them performed DWT or its variants for brain MR images. This will lead to a problem that the wavelet coefficients will cost a mass of computer memory. Saritha et al. [34] were the forerunner to introduce a new wavelet-entropy (WE) feature in abnormal brain detection. They then utilized spider-web plots (SWP) with the aim of discarding redundant features, which greatly reduced the feature number to only three. They finally employed the probabilistic neural network (PNN) for classification and achieved 100% accuracy, better than existing methods.
However, three problems arise in their work. (1) How do SWP influence the classification results? Our past work [51] suggested that removing SWP yielded the same classification performance. (2) Can the features be reduced further? We found they only consider the approximation coefficients; hence, in this study, we suggested to consider both approximation coefficients and detail coefficients, and proposed a novel feature selection (FS) method to determine the best feature subset. In our experiments, we demonstrated that we used only two features (the least among all publications) while obtaining 100% classification accuracy. (3) Their work was tested over a 75-image dataset, so how does the algorithm perform over a larger dataset? To answer this, we used three different datasets in this study.
The structure of the article is organized in follows: the following contains the materials used in this study, this is followed by the methodology. The next section presents the experiment results and gives the discussions. The final section concludes the article with future directions. The explanation of acronyms used is appended at the end of this article.
Materials
Three commonly used benchmark datasets use sizes of 66 images, 160 images, and 255 images. We abbreviated them as Data66, Data160, and Data255, respectively. Any user can download these data from the website of Medical School of Harvard University. Figure 1 offers samples of brain MR images.
Sample of MR brains. MS, Multiple sclerosis; HD, Huntington’s disease.
The cost of predicting abnormal to normal is heavy. The treatments of patients may be delayed. Nevertheless, predicting normal to abnormal is remediable by other diagnostic means. We solve this cost sensitivity (CS) problem by adjusting the class distribution by intentionally picking up more abnormal brains than normal ones.
Methodology
Saritha et al. [34] proposed a method that used only three features while yielding 100% classification accuracy. It is one of the best algorithms for MR brain classification. Their method “WE + SWP + PNN” is listed in Table 1. For details, the readers can refer to their work.
Pseudocode of Saritha’s work.
| Algorithm 1: Saritha’s method (WE + SWP + PNN) | |
|---|---|
| Step 1 | Acquire the image or data |
| Step 2 | Choose the proper wavelet for analysis |
| Step 3 | Obtain the entropy of the wavelet decompositions |
| Step 4 | Construct the spider-web plots (SWP) |
| Step 5 | Calculate areas of SWP |
| Step 6 | Perform statistical analysis of the areas |
| Step 7 | Classify using PNN with suitable areas as feature set |
The difference between our work and Saritha’s work lie in two major points. First, we not only consider detailed coefficients but also approximation coefficients, while Saritha et al. [34] only considered the latter. Second, we proposed a novel advanced FS method to select the optimal feature, while Saritha et al. [34] used SWP.
Wavelet entropy
As is known, the famous DWT is a signal processing tool that used the dyadic scales and positions for multilevel and multiresolution analyses [12]. In addition, entropy is traditionally a statistical measure of randomness, which was then redefined as an uncertainty measure for the information content of a system with the definition of S=-Σpjlog2(pj), where j represents the gray value of reconstructed coefficient, and pj the corresponding probability.
In this study, we performed an eight-level db4 wavelet and thus obtained 25 WE features [54] for each MR brain image. Table 2 shows the decomposition components of both Saritha’s method and our method. Note that the feasible combination should be 2N for a total set of N features; hence, we need to pick up an optimal solution from the 225=33,554,432 types of combination. A feasible solving technique is proposed below.
Decomposition components extracted from an eight-level decomposition.
| Level | Saritha’s method | Our method |
|---|---|---|
| 1 | A1 | (H1, D1, V1) |
| 2 | A2 | (H2, D2, V2) |
| … | … | … |
| 7 | A7 | (H7, D7, V7) |
| 8 | A8 | (H8, D8, V8, A8) |
Feature selection
FS explores the combination spaces to find the optimal feature combination. Generally speaking, there are three categories of FS (See Table 3). One is the traditional exponential algorithms, which evaluated enormous subsets, the number of which will grow in an exponential way when the dimension grows. The typical algorithm is exhaustive search. Another category is the sequential methods. They removed or added features one by one; however, those algorithms have a deficiency of being trapped in local minima. The third are the metaheuristics algorithms that incorporate randomness to the search so as to guarantee it escapes from local minima points. Two typical algorithms are simulated annealing (SA) and genetic algorithm (GA).
Summary of state-of-the-art algorithms of feature selection (FS).
| Category | Typical methods |
|---|---|
| Exponential | Exhaustive research, beam search, branch and bound |
| Sequential | Plus-l minus-r selection, sequential backward selection, sequential forward selection, bidirectional search, sequential floating selection |
| Metaheuristics | Random generation, simulated annealing, particle swarm optimization, genetic algorithm, ant colony optimization |
Nevertheless, both GA and SA have two problems. (1) They are sensitive to initial populations. (2) The search procedure costs lengthy time [19, 21]. To alleviate these two problems, PSO was proposed to be a naive metaheuristic, biologically inspired by the swarming behavior of ants, fish, birds, bees, etc. PSO is proposed initially to solve continuous problems. Recently, its variant, the binary PSO (BPSO), was presented by scholars to extend its ability to solve discrete problems.
Encoding
Binary encoding was used in the way that every candidate was represented by a particle, associated with two characteristics (velocity v and position x). For the ith particle, the two characteristics were in the form of
Here, N denotes the problem dimension, and i the particle index. For the FS problem, the xij describes the status of corresponding jth feature: selected or not. Figure 2 illustrates a six-dimensional FS problem, where an ith particle xi=[0, 1, 0, 0, 1, 1] suggests the corresponding 2nd, 5th, and 6th features are selected.
A six-dimensional feature selection (FS) problem.
Particle swarm optimization
PSO evaluates the fitness functions of the whole swarm in each step. The vi of ith particle is updated by the positions of the two best particles [13, 20, 58]: (1) the optimal position that a particle had traveled (pB) and (2) the optimal position the neighbors of ith particle had traveled so far (nB). When the whole swarm is treated as a neighborhood area, the neighborhood becomes the global best and is accordingly called “gB”. From above we can deduce the updated equations as
Here, rand() is a random number generator whose values fall within the range of [0, 1]. The rand() are performed when they occur. c is termed the “inertia weight” [30, 38, 61]. If c is less than 1, the particle favors exploitation over exploration; else if c is larger than 1, the particle favors exploration over exploitation.
The parameters a1 and a2 are non-negative constants named as “acceleration coefficients” [3, 37, 40]. The positions of the particle swarm are changed according to formulas (3) and (4). They will become close to each other from various directions. The PSO ran through these processes iteratively until the termination criterion was met [15, 48]. Note that vmax (the maximum velocity) should be determined beforehand, with the aim of keeping the optimizers within a reasonable range [33].
Binary particle swarm optimization
The BPSO initializes the velocities and positions of the swarm randomly [22],
The positions xij for each variable was calculated by
Here, S(.) denotes the logistic function, by which it serves as the probability distribution for the position xij,
The velocities vij are iteratively updated by Equation (3). From an empirical point, the value S(vmax) should be <1, which increases the chance to produce new solutions [25, 57].
Unlike traditional PSO, the positions of BPSO are within the Hamming space (a set of all 2N binary strings with length of N) [31]. Therefore, divergence will not occur due to the limited string length. Nevertheless, the premature convergence may exist. To solve it, the maximum velocity vmax is important.
Two improvements
With the aim of improving the diversity of BPSO, we proposed a mutation operator as
where rmut represents the chance of random mutation. Each chromosome is mutated with a probability rmut, after position properties are updated by (7). rmut is commonly assigned with a value of 1/N, which suggests that one bit in each candidate will be flipped on average.
Another improvement of time-varying acceleration coefficients (TVAC) technique [36] was introduced, which can augment the global search ability in the initial stage and encourage the local search ability of particles at the end of the search. In order to achieve this goal, TVAC gives more weight to cognitive component and less weight to social component at the former stage, and gives less weight to cognitive component and more weight to social component in the latter stage. Mathematically, TVAC tunes the “acceleration coefficients” a1 and a2 as
where a1i and a1f denote the initial and final values of a1, respectively. a2i and a2f denote the initial and final values of a2, respectively. tmax denotes the number of maximum iteration.
After embedding the two improvements to conventional BPSO, we named this variant the binary particle swarm optimization with mutation and TVAC (BPSO-MT). For fair comparison, we combined only the mutation operator with BPSO and combined only TVAC with BPSO. We then named the two variants the binary particle swarm optimization with mutation (BPSO-M) and the binary particle swarm optimization with TVAC (BPSO-T).
Probabilistic neural network
For the rest, we used PNN, which has gained interest as it yields a probabilistic score for each input. Suppose there are two classes (A and B), we should decide which class the sample x=[x1, …, xN] belongs to [17]. Suppose hA and hB represent the a priori probabilities of instances in classes A and B, respectively, the Bayes decision rule turns to
where lA represents the loss function of the wrong decision that x is in class B when class(x)=A, and the same for lB. The losses are equal to zero for correct corrections [55]. fA and fB are the probability density functions (PDFs) of classes A and B, respectively.
In a simple case that the lA=lB and hA=hB, the classifier predicts a new instance to the class with higher PDF. To embed the Gaussian kernel, the PDF of class A can be expressed as
Here, s is the smoothing factor, TA the number of training samples in class A, and xAj the jth sample in class A.
Figure 3 illustrates the structure of a PNN. Its mathematical expressions are
Structure of probabilistic neural network (PNN).
Here, I denotes the input weight, L the layer weight, fr the radial basis function, and fc the compete function,
The parameter setting of PNN in this article is the same as in the work of Saritha et al. [34].
Statistical setting
Table 4 shows the stratified cross validation (SCV) setting. Following common convention, six-fold and five-fold were used for Data66 and the other two datasets, respectively.
Statistical setting.
| Data | Training | Validation | Total | No. of fold | |||
|---|---|---|---|---|---|---|---|
| A | N | A | N | A | N | ||
| Data66 | 40 | 15 | 8 | 3 | 48 | 18 | 6 |
| Data160 | 112 | 16 | 28 | 4 | 140 | 20 | 5 |
| Data255 | 176 | 28 | 44 | 7 | 220 | 35 | 5 |
A, Abnormal; N, normal.
Implementation
The pseudocode of this proposed methodology is given in Table 5. Compared to Saritha’s method in Table 1, this proposed method uses less procedures and can save computation time. Figure 4 shows the diagram of the proposed system.
Pseudocode of the proposed method.
| Algorithm 2: The proposed method (WE + BPSO-MT + PNN) | |
|---|---|
| Step 1 | Acquire the MR brain image |
| Step 2 | Calculate the eight-level wavelet decomposition |
| Step 3 | Obtain the wavelet entropy values on 25 sub-band coefficients |
| Step 4 | Feature selection by BPSO-MT |
| Step 5 | Output the final classifier constructed by the optimal feature subset and PNN |
Diagram of the proposed system.
Experiments, results, and discussions
Wavelet decomposition
A normal MR brain image is shown in Figure 5A. The one-level and two-level decomposition results are shown in Figure 5B and C, respectively. The high-level decomposition results are not shown, as the approximation coefficients are too small. After this step, we yield a total of 25 sub-bands and corresponding WE values.
Illustration of the discrete wavelet transform (DWT) decomposition result.
BPSO-MT vs. BPSO-M and BPSO-T
We compared the proposed BPSO-MT with the two proposed methods (BPSO-M and BPSO-T). Each algorithm ran 10 times. The maximum, minimum, and mean of the number of the final selected features by different algorithms are listed in Table 6.
BPSO-MT vs. other two proposed methods.
| Algorithm | Maximum | Minimum | Mean |
|---|---|---|---|
| No-FSa | 25 | 25 | 25 |
| BPSO-M (proposed) | 7 | 2 | 4 |
| BPSO-T (proposed) | 5 | 3 | 4 |
| BPSO-MT (proposed) | 4 | 2 | 3 |
aNo-FS represents not implementing any feature selection method.
Results in Table 6 show that among 10 runs, BPSO-M obtains the maximum feature number of 7, minimum number of 2, and mean number of 4; the BPSO-T obtains the maximum number of 5, minimum number of 3, and mean number of 4; and the BPSO-MT obtains the maximum number of 4, minimum number of 2, and mean number of 3. Therefore, we can conclude that mutation operator offers variability to the population, so the BPSO-M can find the global minimal value, but it fails in the robustness. The BPSO-T is more robust than BPSO-M; however, it cannot reach the global minimal value. The BPSO-MT combines the advantages of both BPSO-M and BPSO-T, so it finally not only obtains the global optimal result but also obtains the least mean values (more robust than BPSO-M and BPSO-T).
BPSO-MT vs. other heuristics methods
In the third experiment, we compared the best proposed method, BPSO-MT, with other five heuristics methods, including GA [8], PSO [59], restarted SA (RSA) [49], ant colony optimization (ACO) [46], and BPSO [24]. Parameter setting is the same as above and the results are listed in Table 7.
Number of selected features (10 runs).
| Algorithm | Maximum | Minimum | Mean |
|---|---|---|---|
| No-FSa | 25 | 25 | 25 |
| GA [8] | 10 | 4 | 7 |
| RSA [49] | 14 | 6 | 9 |
| ACO [46] | 8 | 3 | 6 |
| PSO [59] | 5 | 3 | 4 |
| BPSO [24] | 5 | 3 | 4 |
| BPSO-MT (proposed) | 4 | 2 | 3 |
aNo-FS represents not implementing any feature selection method.
We can find from Table 7 that the proposed “BPSO-MT” method yields the least features among all algorithms with the maximum of 4, minimum of 2, and mean of 3. The BPSO and PSO yield the same results with the maximum feature number of 5, minimum of 3, and mean of 4. The ACO selects six features on average with the maximum of 8 and minimum of 3. The GA selected seven features on average with the maximum of 10 and minimum of 4. The RSA performs worst with the maximum feature number of 14, minimum of 6, and mean of 9.
Selected features
The two most important features obtained by BPSO-MT are the entropies over (V1, D1). The selected features of all other algorithms are listed in Table 8. Here, GA, RSA, PSO, and BPSO-MT find the same number of least features among 10 runs. The proposed BPSO-MT finds a two-feature combination of (V1, D1). Nevertheless, ACO and BPSO find different combinations among 10 runs. The ACO selects at least three features among 10 runs, they are either (H1, V1, D1) or (H2, V1, D1). The BPSO selects two different 3-feature combinations of (H1, V1, D1) and (V1, D1, A1) among 10 runs.
Selected features (the least of 10 runs).
| Algorithm | Least-feature combination(s) | No. of least features |
|---|---|---|
| No-FS | H1–H7, V1–V7, D1–D7, A1–A8 | 25 |
| GA [8] | (H2, V2, H1, A1) | 4 |
| RSA [49] | (H2, V2, H1, V1, D1, A1) | 6 |
| ACO [46] | (H1, V1, D1) | 3 |
| (H2, V1, D1) | ||
| PSO [59] | (H1, V1, D2) | 3 |
| BPSO [24] | (H1, V1, D1) | 3 |
| (V1, D1, A1) | ||
| BPSO-MT (proposed) | (V1, D1) | 2 |
Comparing the BPSO and PSO results in Table 8, we can find that BPSO finds two best solutions while PSO only finds one best solution. It suggests that BPSO have better exploration ability than PSO. The reason is because initialized and updated positions of the former method are coherent with the binary properties of the problem, while the latter does not consider the binary characteristics of the positions. The most important result in Table 8 is that the proposed BPSO-MT yields a two-feature combination of (V1, D1). The number of selected features of BPSO-MT is only two, less than all existing methods. This proves again the superiority of the proposed BPSO-MT. Next, we will test the performance of these two features selected by BPSO-MT.
We can conclude that the BPSO-MT performs better than GA, RSA, ACO, PSO, and BPSO with respect to selected features, as it obtains only two (the least) features. The reason may fall in the two improvements we suggested in Section 3.2.4, where we embed the mutation operator and TVAC into the BPSO. The classification of traditional GA, RSA, and ACO does not obtain good results, as they are not designed for binary problem (the FS problem) intentionally.
Comparison with Saritha’s method
Ten runs of k-fold SCV were carried out on three datasets. Note that true class means abnormal brains, and false class means normal brains. The average accuracy on 10 runs is recorded and listed in Table 9. Here, we can see the proposed “WE + BPSO-MT + PNN” yields higher classification accuracy (100.00% for Data66, 100.00% for Data160, and 99.53% for Data255) than “WE + SWP + PNN” (100.00% for Data66, 99.94% for Data160, and 98.86% for Data255). From the point of feature number, the proposed “WE + BPSO-MT + PNN” only uses two features of (V1, D1), less than the feature number by “WE + SWP + PNN” [34] of 3.
Comparison with Saritha’s method (10 runs).
| Algorithm | Feature number | Data66 | Data160 | Data255 |
|---|---|---|---|---|
| WE + SWP + PNN [34] | 3 | 100.00 | 99.94 | 98.86 |
| WE + BPSO-MT + PNN (proposed) | 2 | 100.00 | 100.00 | 99.53 |
Comparison with other MR brain classification methods
To further demonstrate the effectiveness of this proposed “WE + BPSO-MT + PNN”, we compared with existing different algorithms, such as DWT + SVM [4], DWT + SOM [4], DWT + RBF-SVM [4], DWT + PCA + ANN [10], DWT + PCA + KNN [10], DWT + PCA + SCG [9], RT + PCA + LS-SVM [6], DWT + PCA + SVM [50], DWT + PCA + HPOL-SVM [50], DWT + PCA + IPOL-SVM [50], DWT + PCA + RBF-SVM [50], PCNN + DWT + PCA + ANN [11], WE + NBC [63], SWT + PCA + IABAP-FNN [43], SWT + PCA + ABC-SPSO-FNN [43], SWT + PCA + HPA-FNN [43], DWPT + SE + GEPSVM [54], DWPT + TE + GEPSVM [54], and DWPT + SE + GEPSVM + RBF [54]. The meaning of these abbreviations can be found in Table 11.
From Table 10, we can see the Data66 is too small, which leads to many algorithms obtain 100% accuracy. For the Data160, SWT + PCA + HPA-FNN [43], DWPT + TE + GEPSVM [54], and this proposed WE + BPSO-MT + PNN achieved perfect classification. For the Data255, this proposed “WE + BPSO-MT + PNN” yields the highest accuracy of 99.53% while using the least features of two. The second best algorithm is “SWT + PCA + HPA-FNN” [43] with average accuracy of 99.45%. The third is “RT + PCA + LS-SVM” [6] with average accuracy of 99.39%.
Comparison with other MR brain classification methods.
| Algorithms | Feature number | Run number | Data66 | Data160 | Data255 |
|---|---|---|---|---|---|
| DWT + SVM [4] | 4761 | 5 | 96.15 | 95.38 | 94.05 |
| DWT + SOM [4] | 4761 | 5 | 94.00 | 93.17 | 91.65 |
| DWT + RBF-SVM [4] | 4761 | 5 | 98.00 | 97.33 | 96.18 |
| DWT + PCA + ANN [10] | 7 | 5 | 97.00 | 96.98 | 95.29 |
| DWT + PCA + KNN [10] | 7 | 5 | 98.00 | 97.54 | 96.79 |
| DWT + PCA + SCG [9] | 19 | 5 | 100.00 | 99.27 | 98.82 |
| RT + PCA + LS-SVM [6] | 9 | 5 | 100.00 | 100.00 | 99.39 |
| DWT + PCA + SVM [50] | 19 | 5 | 96.01 | 95.00 | 94.29 |
| DWT + PCA + HPOL-SVM [50] | 19 | 5 | 98.34 | 96.88 | 95.61 |
| DWT + PCA + IPOL-SVM [17] | 19 | 5 | 100.00 | 98.12 | 97.73 |
| DWT + PCA + RBF-SVM [50] | 19 | 5 | 100.00 | 99.38 | 98.82 |
| PCNN + DWT + PCA + ANN [11] | 7 | 10 | 100.00 | 98.88 | 98.24 |
| WE + NBC [63] | 7 | 10 | 92.58 | 91.87 | 90.51 |
| SWT + PCA + IABAP-FNN [43] | 7 | 10 | 100.00 | 99.44 | 99.18 |
| SWT + PCA + ABC-SPSO-FNN [43] | 7 | 10 | 100.00 | 99.75 | 99.02 |
| SWT + PCA + HPA-FNN [43] | 7 | 10 | 100.00 | 100.00 | 99.45 |
| DWPT + SE + GEPSVM [54] | 16 | 10 | 99.85 | 99.62 | 98.78 |
| DWPT + TE + GEPSVM [54] | 16 | 10 | 100.00 | 100.00 | 99.33 |
| DWPT + SE + GEPSVM + RBF [54] | 16 | 10 | 100.00 | 99.88 | 99.33 |
| WE + BPSO-MT + PNN (proposed) | 2 | 10 | 100.00 | 100.00 | 99.53 |
Acronym list.
| Abbreviation | Definition |
|---|---|
| (B)PSO(-M)(-T)(-MT) | (Binary) Particle swarm optimization (-mutation) (-TVAC) (-mutation and TVAC) |
| (H)(I)POL | (Homogeneous) (inhomogeneous) Polynomial |
| (S)(T)E | (Shannon) (Tsallis) entropy |
| ABC(-SPSO) | Artificial bee colony (-standard PSO) |
| ANN | Artificial neural network |
| CAD | Computer-aided diagnosis |
| CS | Cost sensitivity |
| DW(P)T | Discrete wavelet (packet) transform |
| FNN | Feed-forward neural network |
| FS | Feature selection |
| GEPSVM | Generalized eigenvalue proximal SVM |
| HPA | Hybridization of PSO and ABC |
| IABAP | Integrated algorithm based on ABC and PSO |
| LS-SVM | Lease-square SVM |
| KNN | K-nearest neighbors |
| MR(I) | Magnetic resonance (imaging) |
| NBC | Naive Bayesian classifier |
| PCA | Principal component analysis |
| PCNN | Pulse-coupled neural network |
| PNN | Probabilistic neural network |
| RBF | Radial basis function |
| RT | Ripplet transform |
| SCG | Scaled conjugate gradient |
| SCV | Stratified cross validation |
| SOM | Self-organizing map |
| SWT | Stationary wavelet transform |
| SVM | Support vector machine |
| TVAC | Time-varying acceleration coefficients |
| WE | Wavelet entropy |
Conclusions and future research
In this work, we proposed a new approach based on Saritha’s method for MR brain image classification. We proposed a novel FS method named as BPSO-MT, in order to find optimal feature combination from the entropy of both approximation and detail sub-bands of eight-level DWT decomposition. The results show that the BPSO-MT yields better results than existing FS methods. Meanwhile, the proposed “WE + BPSO-MT + PNN” method excels existing MR brain classifiers.
Our contributions are the following: (1) We proposed three novel FS methods of BPSO-T, BPSO-M, and BPSO-MT and proved BPSO-MT was the best among all. (2) The proposed system “WE + BPSO-MT + PNN” is superior to state-of-the-art approaches in terms of both classification accuracy and feature number.
In the future, we will test other advanced feature extraction methods, such as fractional wavelet, fractional Fourier entropy [45], and dual-tree complex wavelet transform. Besides, features may be extracted from the reconstruction procedure [7]. To generalize our method to 3D, we may need the help of 3D printing [23].
Acknowledgments
This article was supported by NSFC (51407095, 61503188), Natural Science Foundation of Jiangsu Province (BK20150983, BK20150982), Jiangsu Key Laboratory of 3D Printing Equipment and Manufacturing (BM2013006), Key Supporting Science and Technology Program (Industry) of Jiangsu Province (BE2012201, BE2013012-2, BE2014009-3), Program of Natural Science Research of Jiangsu Higher Education Institutions (15KJB470010, 13KJB460011, 14KJB480004, 14KJB520021), Special Funds for Scientific and Technological Achievement Transformation Project in Jiangsu Province (BA2013058), Nanjing Normal University Research Foundation for Talented Scholars (2013119XGQ0061, 2014119XGQ0080), and Open Fund of Guangxi Key Laboratory of Manufacturing System and Advanced Manufacturing Technology (15-140-30-008K).
Conflict of interest: We have no conflicts of interest to disclose with regard to the subject matter of this article.
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