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In this work, we explore the performance of plasmonic biosensor designs that integrate metamaterials based on machine learning algorithms. The meta-plasmonic biosensors were designed for optimized detection of DNA with a layer of double negative metamaterial modeled by an effective medium. An iterative transfer matrix approach was employed to generate training and test sets of resonance characteristics in the parameter space for machine learning. As a machine learning-based prediction of optical characteristics of a meta-plasmonic biosensor, multilayer perceptron and autoencoder (AE) were used as an algorithm, while the clustering algorithm was constructed by dimensional reduction based on AE and t-Stochastic Neighbor Embedding (t-SNE) as well as k-means clustering. Use of meta-plasmonic structure with analysis based on machine learning has found that enhancement of detection sensitivity by more than 13 times over conventional detection should be achievable with excellent reflectance curves. Further enhancement may be attained by expanding the parameter space.