Diagnosis of the cancerous lesions in nano-biomechanics images taken from Firat University Medicine Faculty Pathology Laboratory was investigated using atomic force microscopy method. We used new analysis methods called as Minimum Redundancy Maximum Relevance_Least Square Support Vector Machine (mRMR_LSSVM), Principal Component Analysis_Least Square Support Vector Machine (PCA_LSSVM), Principal Component Analysis_fuzzy k-nearest neighbor (PCA_KNN), Minimum Redundancy Maximum Relevance_fuzzy k-nearest neighbor (mRMR_KNN), Principal Component Analysis_Maximums of Statistical Values/from their Minimum to Maximum Ranking (PCA_MSMMR) and Minimum Redundancy Maximum Relevance Maximums of Statistical Values/from their Minimum to Maximum Ranking (mRMR_MSMMR). In this study, the structure of these methods is formed from three steps, i.e., feature select step, classification step and testing stage. In present study, we used 23 features which are totally obtained 92 (23x4) features by rotating for variety angles (i.e., 0 degrees, 45 degrees, 90 degrees, 135 degrees). The validation of the proposed methods is found with the accuracy rates. These methods are compared with other each. The methods, mRMR_LSSVM and mRMR_KNN, PCA_LSSVM, PCA_MSMMR, mRMR_MSMMR are found to be better than PCA_KNN. Accuracy rates of breast nano-biomechanics images were found 100%, 100%, 92.22%, 92.22%, 75.56% and 94.44% with mRMR_LSSVM, mRMR_KNN, mRMR_MSMMR, PCA_LSSVM, PCA_KNN and PCA_MSMMR respectively.