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Clustering analysis is one of the critical tasks in machine learning. Traditionally, clustering has been an independent task, separate from outlier detection. Due to the fact that the performance of clustering can be significantly eroded by outliers, a small number of algorithms try to incorporate outlier detection in the process of clustering. However, most of those algorithms are based on unsupervised partition-based algorithms such as k-means. Given the nature of those algorithms, they often fail to deal with clusters of complex, non-convex shapes. To tackle this challenge, we have proposed SSDBCODI, a semi-supervised density-based algorithm. SSDBCODI combines the advantage of density-based algorithms, which are capable of dealing with clusters of complex shapes, with the semi-supervised element, which offers flexibility to adjust the clustering results based on a few user labels. We also merge an outlier detection component with the clustering process. Potential outliers are detected based on three scores generated during the process: (1) reachability-score, which measures how density-reachable a point is to a labeled normal object, (2) local-density-score, which measures the neighboring density of data objects, and (3) similarity-score, which measures the closeness of a point to its nearest labeled outliers. Then in the following step, instance weights are generated for each data instance based on those three scores before being used to train a classifier for further clustering and outlier detection. To enhance the understanding of the proposed algorithm, for our evaluation, we have run our proposed algorithm against some of the state-of-art approaches on multiple datasets and separately listed the results of outlier detection apart from clustering. Our results indicate that our algorithm can achieve superior results with a small percentage of labels.