Two-way threshold-based intelligent water drops feature selection algorithm for accurate detection of breast cancer

Abstract

Breast cancer is one of the common reasons for deaths of women over the globe. It has been found that a Computer-Aided Diagnosis (CAD) system can be designed using X-ray mammograms for early-stage detection of breast cancer, which can decrease the death rate to a large extent. This paper work proposes a novel 2-way threshold-based intelligent water drops IWD “algorithm for feature selection to design an effective and efficient CAD system that can detect breast cancer in early stage. This approach first extracts the local binary patterns in wavelet domain from mammograms and then applies our introduced 2-way threshold-based IWD algorithm to extract most important subset of features from the extracted features set. Two-way thresholding is a technique to find a lower bound and an upper bound on the number of features to be selected in the optimal subset. So, using these threshold values, IWD is capable of producing multiple optimal subsets of features rather than producing a single optimal subset of features. The best subset among the above subsets is then used to train and deploy support vector machine (SVM) to classify new mammograms. The results have shown that the proposed model outperforms many of the existing CAD systems. Further we have compared our introduced feature selection technique with other meta-heuristic features selection techniques such as ant colony optimization, particle swarm optimization, simulated annealing, genetic algorithm, gravitational search algorithm, inclined planes optimization and gray wolf optimization algorithm and found that it outperforms the other feature selection techniques. The accuracy, precision, recall, specificity and F1-score of our proposed framework are measured on MIAS dataset as 99%, 98.7%, 98.123%, 96.2% and 98.4%, respectively, and on DDSM dataset as 97.89%, 96.9%, 96.4%, 94.8% and 96.2%.

Appendices

Appendix A

Acronyms and abbreviations

CAD, Computer-aided diagnosis.

IWD, Intelligent water drops.

LBP, Local binary patterns.

LB, Lower bound.

UB, Upper bound.

SVM, Support vector machine.

ACO, Ant colony optimization.

PSO, Particle swarm optimization.

SA, Simulated annealing.

GA, Genetic algorithm.

GSA, Gravitational search algorithm.

IPO, Inclined planes optimization.

GWO, Gray wolf optimization.

MIAS, Mammographic image analysis society.

DDSM, Digital database for screening mammography.

BCRF, Breast Cancer Research Foundation.

GLCM, Gray-level co-occurrence matrix.

PCA, Principal component analysis.

FNN, Feedforward neural network.

k-NN, k-nearest neighbors.

CS-LBP, Center symmetric-local binary pattern.

FS, Forward selection.

BS, Backward selection.

LDA, Linear discriminant analysis.

HS, Harmony search.

PSOWNN, Particle swarm neural networks.

FFNN, Feed-forward neural network.

DFO, Dragon fly optimization.

RF, Random forest.

ANFIS, Adaptive neurofuzzy interface system.

DWT, Discrete wavelet transform.

HUD, Heuristic undesirability.

TP, True positive.

FP, False positive.

TN, True negative.

FN, False negative.

NB, Naïve bayes.

DT, Decision tree.

RF, Random forest.

ANN, Artificial neural network.

AUC, Area under curve.

ROC, Receiver operating characteristic.

List of variables

• Variables related to feature extraction:

  $g_{i}$: The gray-scale value of neighborhood pixel.

  $g_{c}$: The gray-scale value of the center pixel.

  $P$: Connectivity from the neighborhood pixels.

  $R$: Neighborhood radius for $N$ equally spaced pixels.

• Variables used in IWD algorithm:

  $T^{{{\text{IWD}}}}$: The complete solution.

  $T^{IB}$: Iteration best solution.

  $N_{{{\text{Features}}}}$: Number of final features.

  $N_{{{\text{IWD}}}}$: Number of water drops.

  $\left( {a_{v} ,b_{v} ,c_{v} } \right)$: Variables to update the velocity of the water drops.

  $\left( {a_{s} ,b_{s} ,c_{s} } \right)$: Variables to update the soil of the local path.

  ${\text{MaxIter}}$: Maximum number of iterations.

  ${\text{initSoil}}$: Initial value of the local soil.

  ${\text{initVel}}$: Initial velocity associated with each of the water drop.

  $V_{c}^{{\left( {{\text{IWD}}_{r} } \right)}}$: Feature list visited by each water drop $r$.

  ${\text{initVel}}^{{\left( {{\text{IWD}}_{r} } \right)}}$: Velocity of the water drop $r$.

  ${\text{soil}}^{{\left( {{\text{IWD}}_{r} } \right)}}$: Soil associated with the water drop $r$.

  $\rho_{n}$: Local soil updating parameter.

  $\rho_{{{\text{IWD}}}}$: Global soil updating parameter.

  $\varepsilon_{s}$: Parameter to prevent zero division.

• Variables related to thresholding:

$N_{f}$: Total number of features.

$T_{{{\text{dist}}}}$: Threshold distance.

List of control parameters of various metaheuristic optimization algorithms

Algorithm	Notation of the control parameters	Description
ACO	$m$	Initial number of ants
	$\alpha$	Pheromone exponent
	$\beta$	Heuristic exponent
	$\rho$	Pheromone evaporation factor
	$\tau_{0}$	Initial pheromone value
PSO	$N_{{\text{p}}}$	Number of particles
	${\text{MAX}}_{{{\text{iter}}}}$	Maximum iterations
	$w$	Inertia weight
	$c_{1}$	Cognitive factor
	$c_{2}$	Social factor
SA	${\text{MAX}}_{{{\text{iter}}}}$	Number of iterations
	${\text{MAX}}_{{{\text{const}}}}$	Number of iterations at constant temperature
	$p_{0}$	Initial acceptance probability
	$\delta_{0}$	Minimal difference between solutions
	$T_{0}$	Initial temperature
	$\alpha_{{\text{r}}}$	Reduce factor
GA	$P_{{{\text{size}}}}$	Population size
	${\text{MAX}}_{{{\text{iter}}}}$	Number of iterations
	$F_{{\text{t}}}$	Function tolerance
GSA	$S_{p} \left( {{\text{NP}}} \right)$	Size of the population
	${\text{MAX}}_{{{\text{iter}}}}$	Maximum number of iterations
	$G_{0} ,$ α	Gravitational constants
	$T_{{\text{a}}}$	Total number of agents
GWO	$G_{{\text{p}}}$	Population size
	${\text{MAX}}_{{{\text{iter}}}}$	Number of iterations
	$r_{1} ,r_{2}$	Random vectors
	$\vec{v}$	Coefficient vector
IPO	$c_{1} ,c_{2}$	Constants