To avoid the clustering results with the local scaling parameter

i

of self-tuning may be influenced by outliers

and the unstable clustering results from K-means in self-tuning

two true self-adaptive spectral clustering algorithms were proposed.The two spectral clustering algorithms are respectively named as SC_SD(Spectral Clustering based on Standard Deviation) and SC_MD(Spectral Clustering based on Mean Distance).They respectively define the standard deviation of point

i

and the mean distance from point

i

to others

as its radius of neighborhood

then count the number of points in the neighborhood

and use the standard deviation of point

i

in the neighborhood as its local scaling parameter

so as to avoid the influence from outliers to the local scaling parameter

i

of point

i

and the distortion in clustering results of self-tuning.SD_K-medoids are adopted to instead of K-means in self-tuning to avoid the unstable clustering results of K-means

so as to get the true clustering of a dataset.The experimental results on UCI datasets and on synthetic datasets demonstrate that SC_SD and SC_MD can obtain better clustering results than that of traditional spectral clustering algorithm NJW and spectral clustering algorithm self-tuning

and are robust to noises

and has got good scalability.The proposed SC_SD and SC_MD can detect the clustering of a dataset without any given information

and the SC_MD can be used to detect the clustering of a comparable big data.