Breast cancer (BC) is proliferating to a greater extent day to day. Early discovery can help the patient in saving life. Mammography is commonly utilized in diagnosing BC. Mammography classification is the most critical stage as it assists medical professionals in identifying BC. In this paper, a hybrid method accomplishes accurate and precise classification in a timely manner is proposed and tested. In this work a method called, Laplacian Metropolis Hastings Gradient Torgerson Scaling and Optimized (LMHG-TSO) VGG16-based mammogram classification is proposed. The LMHG-TSO VGG16-based mammogram classification method is split into four sections, namely, preprocessing, segmentation, feature selection and finally classification. First, with the raw mammogram images obtained as input is subjected to Laplacian Neighborhood Gabor Filter-based preprocessing for acquiring computationally efficient preprocessed mammogram images. Second watershed segmentation model called Metropolis Hastings Gradient Region is applied to the preprocessed images to obtain precise segmentation results. Next, to minimize dimensionality and reduce loss Torgerson Scaling Sequential Feature Selection model is applied to the segmented preprocessed mammogram images. Finally, Affine Linear Optimized VGG16-based Mammogram Classification model is applied to make distinct classification between three types (i.e., normal, benign and malignant) in an accurate manner. Experimental evaluation is carried out on factors such as precision, recall, training time and classification accuracy for different mammogram images. The reported results prove the efficiency of the suggested method against prevailing stateof-the-art methods.