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Background: Microarray experiments can simultaneously determine the expression of thousands of genes. Identification of potential genes from microarray data for diagnosis of cancer is important. This study aimed to identify genes for the diagnosis of acute myeloid and lymphoblastic leukemia using a sparse feature selection method. Materials and Methods: In this descriptive study, the expression of 7129 genes of 25 patients with acute myeloid leukemia (AML), and 47 patients with lymphoblastic leukemia (ALL) achieved by the microarray technology were used in this study. Then, the important genes were identified using a sparse feature selection method to diagnose AML and ALL tissues based on the machine learning methods such as support vector machine (SVM), Gaussian kernel density estimation based classifier (GKDEC), k-nearest neighbor (KNN), and linear discriminant classifier (LDC). Results: Diagnosis of ALL and AML was done with the accuracy of 100% using 8 genes of microarray data selected by the sparse feature selection method, GKDEC, and LDC. Moreover, the KNN classifier using 6 genes and the SVM classifier using 7 genes diagnosed AML and ALL with the accuracy of 91.18% and 94.12%, respectively. The gene with the description “Paired-box protein PAX2 (PAX2) gene, exon 11 and complete CDs” was determined as the most important gene in the diagnosis of ALL and AML. Conclusion: The experimental results of the current study showed that AML and ALL can be diagnosed with high accuracy using sparse feature selection and machine learning methods. It seems that the investigation of the expression of selected genes in this study can be helpful in the diagnosis of ALL and AML.

This paper presents an analytical method to estimate the location and number of actual small targets in 2D inverse scattering problems. This method is motivated from the exact maximum likelihood estimation of signal parameters in white Gaussian noise for the linear data model. In the first stage, the method uses the MUSIC algorithm to acquire all possible target locations and in the next stage, it employs an analytical formula that works as a spatial filter to determine which target locations are associated to the actual ones. The ability of the method is examined for both the Born and multiple scattering cases and for the cases of well-resolved and non-resolved targets. Many numerical simulations using both the coincident and non-coincident arrays demonstrate that the proposed method can detect the number of actual targets even in the case of very noisy data and when the targets are closely located. Using the experimental microwave data sets, we further show that this method is successful in specifying the number of small inclusions.

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