The decision-making problems in which there are large numbers of qualitative and quantitative factors involved, the technique of dimensionality reduction plays an important role for simplicity and wider applicability. The impreciseness in the information about these factors are being considered in the neutrosophic perception with the parameters - degree of truth-membership, degree of indeterminacy (neutral) and degree of falsity for a better span of the information. In the present communication, we first propose a technique for finding the threshold value for the information provided in the form of neutrosophic soft matrix. Further, utilizing the proposed definitions of the object-oriented neutrosophic soft matrix and the parameter-oriented neutrosophic soft matrix, we present a new algorithm for the dimensionality reduction process. The proposed algorithm has also been applied in an illustrative example of decision-making problem. Further, a comparative analysis in contrast with the existing methodologies has been successfully presented with comparative remarks and additional advantages.