This paper is the first of a series of papers constraining cosmological parameters with weak lensing peak statistics using \sim 450 ~ { } deg ^ { 2 } of imaging data from the Kilo Degree Survey ( KiDS-450 ) .
We measure high signal-to-noise ratio ( SNR : \nu ) weak lensing convergence peaks in the range of 3 < \nu < 5 , and employ theoretical models to derive expected values .
These models are validated using a suite of simulations .
We take into account two major systematic effects , the boost factor and the effect of baryons on the mass-concentration relation of dark matter haloes .
In addition , we investigate the impacts of other potential astrophysical systematics including the projection effects of large scale structures , intrinsic galaxy alignments , as well as residual measurement uncertainties in the shear and redshift calibration .
Assuming a flat \Lambda CDM model , we find constraints for S _ { 8 } = \sigma _ { 8 } ( \Omega _ { m } / 0.3 ) ^ { 0.5 } = 0.746 ^ { +0.046 } _ { -0.107 } according to the degeneracy direction of the cosmic shear analysis and \Sigma _ { 8 } = \sigma _ { 8 } ( \Omega _ { m } / 0.3 ) ^ { 0.38 } = 0.696 ^ { +0.048 } _ { -0.050 } based on the derived degeneracy direction of our high-SNR peak statistics .
The difference between the power index of S _ { 8 } and in \Sigma _ { 8 } indicates that combining cosmic shear with peak statistics has the potential to break the degeneracy in \sigma _ { 8 } and \Omega _ { m } .
Our results are consistent with the cosmic shear tomographic correlation analysis of the same dataset and \sim 2 \sigma lower than the Planck 2016 results .