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[References: 17 tit.]

This paper proposes optimal clustering (OC) for magnetic induction (MI) communication-based 3-D Non-Conventional Wireless Sensor Networks (3-D Non-Conv WSNs) leveraging compressive sensing (CS) and principal component analysis (PCA) with and without consideration of relay node. These WSNs are resource constrained with limited energy reserves. OC for 3-D media is performed using analytical modeling to minimize the energy consumption in the network. Clustering efficacy is further improved by applying the CS and PCA data compression techniques. The performance of the proposed model is evaluated in terms of energy efficiency and network lifetime for three different media (viz., sea water, dry soil, and sedimentary wet rock) by considering three different positions of base station (BS) (viz., center, lateral mid point, and outside of sensing held). Furthermore, from the results, we observed that our proposed techniques save energy up to 84.37% for all base station (BS) positions.