5. Conclusion

In this chapter, we present a study of spectral clustering based on sparse representation, using two novel weight matrix construction approaches to assess the consistency of two sparse vectors. This construction considers the global information of the solution coefficient vectors of two objects to analyze the similarity between these two objects rather than directly using the sparse coefficients, which only considers local information. Evaluation experiments on realworld data sets show that spectral clustering for high-dimensional data using our novel weight matrix construction exploiting global information outperforms direct k-means and spectral clustering approaches using Gaussian RBF, SIS, l1-directed graph construction and non-negative SIS in five evaluation metrics (CA and NMI).

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These results demonstrate a reliable performance of our algorithm and therefore promise wide applicability in practice. The findings also shed light on developing global solutions theories in the future work.

Figure 2 clearly demonstrates that COS and CSS algorithms outperform other algorithms, and COS is better than CSS on average. CSS obtains the least average value of standard deviation among all seven algorithms. The KM and DGC algorithms have comparable performance, which is usually worse than the other algorithms.
