Security of Automatic Speaker Verification (ASV) systems against imposters are now focusing on anti-spoofing countermeasures. Under the severe threat of various speech spoofing techniques, ASV systems can easily be'fooled' by spoofed speech which sounds as real as human-beings. As two effective solutions, the Constant Q Cepstral Coefficients (CQCC) and the Scattering Cepstral Coefficients (SCC) perform well on the detection of artificial speech signals, especially for attacks from speech synthesis (SS) and voice conversion (VC). However, for spoofing subsets generated by different approaches, a low Equal Error Rate (EER) cannot be maintained. In this paper, an adaptive weighting based standalone detector is proposed to address the selective detection degradation. The clustering property of the genuine and the spoofed subsets are analysed for the selection of suitable weighting factors. With a Gaussian Mixture Model (GMM) classifier as the back-end, the proposed detector is evaluated on the ASVspoof 2015 database. The EERs of 0.01% and 0.20% are obtained on the known and the unknown attacks, respectively. This presents an essential complementation between the CQCC and the SCC and also promotes the future research on generalized countermeasures.