## 1 Introduction
More recently, some researchers studied how to synthesize multiple graphs, derived from multiple data sources or multiple modules data, for semi-supervised classification [16]. [PERSON] _et al._[17], [PERSON] and [PERSON] [18], [PERSON] and [PERSON] [19] and [PERSON] _et al._[20] explored different techniques (_i.e._, multiple kernel learning [21], kernel target alignment [22]) to assign different weights to the graphs and then weighted combined these graphs into a composite graph for semi-supervised classification. A number of researchers have applied the random subspace method (RSM) [23] to semi-supervised classification [2,15] and dimensionality reduction [24]. Particularly, [PERSON] _et al._[2] proposed a GSSC method called semi-supervised ensemble classification in subspaces (SSEC in short). SSEC firstly constructs several \(k\)NN graphs in the random subspaces of samples; then, it trains several semi-supervised linear classifiers on these graphs, one classifier for each graph; next, it combines these classifiers into an ensemble classifier for prediction. The empirical study shows that the base classifiers trained on these simple \(k\)NN graphs outperform the classifier trained in the original space, and the ensemble classifier also works better than other graph optimization based semi-supervised classifiers (_i.e._, LNP and RMGT) and some representative ensemble classifiers (_i.e._, Random Forest [25] and Rotation Forest [26]). In this paper, motivated by these observations, we investigate a mixture graph combined by multiple \(k\)NN graphs constructed in the subspaces, and study a semi-supervised classification method on this mixture graph ((semi-supervised classification based on mixture graph SSCMG)). Particularly, SSCMG first constructs multiple \(k\)NN graphs in different random subspaces (like the random subspace scheme in [23]) of samples, and then combines these graphs into a mixture graph. Finally, SSCMG incorporates this mixture graph into GFHF [4], a representative GSSC method, for semi-supervised classification. Since the distance metric is more reliable in the subspace than that in the original space and the mixture graph is constructed in subspaces, the mixture graph is less suffered from the noisy samples and features. Besides, it is able to hold complicated geometric distribution as the diversity of random subspaces. Experimental comparison with other related methods shows that SSCMG not only has higher classification accuracy, but also has wide ranges of effective input parameters. The main difference between SSCMG and aforementioned GFHF, LGC, LNP, RMGT and CGSSL is that SSCMG uses a mixture graph combined by multiple \(k\)NN graphs constructed in the subspaces, whereas the other methods just utilize (or optimize) a single graph alone. SSEC trains several semi-supervised linear classifiers based on \(k\)NN graphs constructed in randomly partitioned subspaces and incorporates these classifiers into an ensemble classifier for prediction. In contrast, SSCMG integrates multiple \(k\)NN graphs constructed in random subspaces into a mixture graph, and then trains one semi-supervised classifier based on the mixture graph. In summary, the main contributions of this paper are summarized as follows: (1) A semi-supervised classification based on mixture graph (SSCMG) method is proposed for high-dimensional data classification; (2) Extensive experimental study and analysis demonstrate that SSCMG achieves higher accuracy and it can be more robust to input parameters than other related methods; (3) Mixture graph works better than the graph optimized by a single \(k\)NN graph alone, and it can be used as a good alternative graph for GSSC methods on high dimensional data. The rest of this paper is structured as follows: Section 2 describes the procedure of GFHF and introduces the construction of mixture graph. In Section 3, extensive experiments are conducted to study the performance and parameter sensitivity of SSCMG. Conclusions and future work are provided in Section 4.