In the process of Data-Driven modeling of the material microstructures, a reduced-order representation is preferred, as it is more manageable from the numerical standpoint. Its main drawback though is the loss of the connection between the parameters of the reduced-order model and the physical properties of the microstructure. We propose a methodology for exploring the intrinsic dimensionality of the multi-scale shape-manifold models of a heterogeneous material and point-out how the representativity of both geometric and spatial features changes depending on snapshot selection. The process is illustrated for an X-ray micro-CT scan of a polymer-ceramic composite microstructure.In the process of Data-Driven modeling of the material microstructures, a reduced-order representation is preferred, as it is more manageable from the numerical standpoint. Its main drawback though is the loss of the connection between the parameters of the reduced-order model and the physical properties of the microstructure. We propose a methodology for exploring the intrinsic dimensionality of the multi-scale shape-manifold models of a heterogeneous material and point-out how the representativity of both geometric and spatial features changes depending on snapshot selection. The process is illustrated for an X-ray micro-CT scan of a polymer-ceramic composite microstructure.In the process of Data-Driven modeling of the material microstructures, a reduced-order representation is preferred, as it is more manageable from the numerical standpoint. Its main drawback though is the loss of the connection between the parameters of the reduced-order model and the physical properties of the microstructure. We propose a methodology for exploring the intrinsic dimensionality of the multi-scale shape-manifold models of a heterogeneous material and point-out how the representativity of both geometric and spatial features changes depending on snapshot selection. The process is illustrated for an X-ray micro-CT scan of a polymer-ceramic composite microstructure.In the process of Data-Driven modeling of the material microstructures, a reduced-order representation is preferred, as it is more manageable from the numerical standpoint. Its main drawback though is the loss of the connection between the parameters of the reduced-order model and the physical properties of the microstructure. We propose a methodology for exploring the intrinsic dimensionality of the multi-scale shape-manifold models of a heterogeneous material and point-out how the representativity of both geometric and spatial features changes depending on snapshot selection. The process is illustrated for an X-ray micro-CT scan of a polymer-ceramic composite microstructure.