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Target decomposition methods from polarimetric Synthetic Aperture Radar (PolSAR) data provides target scattering information. In this regard, several conventional model-based methods use scattering power components to analyze polarimetric SAR data. However, the typical hierarchical process to enumerate power components uses various branching conditions, leading to several limitations. These techniques assume <italic>ad hoc</italic> scattering models within a radar resolution cell. Therefore, the use of several models makes the computation of scattering powers ambiguous. Some common issues of model-based decompositions are related to the compensation of the orientation angle about the radar line of sight and the occurrence of negative power components. We propose a model-free four-component scattering power decomposition that alleviates these issues. In the proposed approach, we use the nonconventional 3-D Barakat degree of polarization to obtain the polarization state of scattered electromagnetic wave. The degree of polarization is used to obtain the even-bounce, odd-bounce, and diffused scattering power components. Along with this, a measure of target scattering asymmetry is also proposed, which is then suitably utilized to obtain the helicity power. All the power components are roll-invariant, nonnegative, and unambiguous. In addition to this, we propose an unsupervised clustering technique that preserves the dominance of the scattering power components for different targets. This clustering technique assists in understanding the importance of diverse scattering mechanisms based on target characteristics. The technique adequately captures the clusters&#x2019; variations from one target to another according to their physical and geometrical properties. In this study, we utilized <italic>L</italic>-, <italic>C</italic>-, and <italic>X</italic>-band full-polarimetric SAR data. We used these three datasets to show the effectiveness of decomposition powers and the natural interpretability of clustering results. The code is available at:&#x00A0;<uri>https://github.com/Subho07/MF4CF</uri>