The process of performing smart computations in the big data and cloud computing environment is considered to be highly essential in spite of its complexity and cost. The method of Fully Homomorphic encryption is considered to be the effective approach that provides the option of working with the encrypted form of sensitive data in order to preserve high confidentiality that concentrates on deriving benefits from cloud computing capabilities. In this paper, a Hybrid Improved Zhou and Wornell’s inspired Fully Homomorphic Encryption (HIZWFHE) Scheme is proposed for securing big data computation, when they are outsourced to cloud service. This HIZWFHE scheme is potent in encrypting integer vectors that permit the computation of big data represented in the contextual polynomial form in the encrypted form with a bounded degree of limits. This HIZWFHE scheme is determined to be highly applicable and suitable and applicable in cloud big data computation in which the learning process of low dimensional representations is of high concern.