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Summary form only given. Application level multicast approaches have attracted interests in both research and industrial communities. Among various approaches, constructing the overlay multicast tree based on mesh network is very promising for a large multicast group size. This approach is efficient in bandwidth utilization but suffer from high computation overhead. We present a new approach for constructing an overlay multicast tree in a large scale media streaming system using neural networks. The media server first constructs an overlay multicast tree for requests arriving in a relatively short time interval. Then the subsequent requests can join the multicast tree in a distributed way. To utilize the interface bandwidth efficiently, we formulate the original tree construction problem as a balanced multicast tree problem and propose a new SOFM-like neural network algorithm to obtain the solution. For the requests arriving at a later time, the proxy servers process the requests and join the multicast tree using a decentralized prediction based on a multilayered neural network. The tree is kept balanced in the tree joining process by having proxy servers predict the traffic load on its neighbors.