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Identifying collusion groups using spectral clustering

In an illiquid stock, traders can collude and place orders on a predetermined price and quantity at a fixed schedule. This is usually done to manipulate the price of the stock or to create artificial liquidity in the stock, which may mislead genuine investors. Here, the problem is to identify such group of colluding traders. We modeled the problem instance as a graph, where each trader corresponds to a vertex of the graph and trade corresponds to edges of the graph. Further, we assign weights on edges depending on total volume, total number of trades, maximum change in the price and commonality between two vertices. Spectral clustering algorithms are used on the constructed graph to identify colluding group(s). We have compared our results with simulated data to show the effectiveness of spectral clustering to detecting colluding groups. Moreover, we also have used parameters of real data to test the effectiveness of our algorithm.