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Low-latency data access is becoming an upcoming and increasingly important challenge. The proper placement of data blocks can reduce data travel among distributed storage systems, which contributes significantly to the latency reduction. However, the dominant data placement optimization has primarily relied on prior known data requests or static initial data distribution, which ignores the dynamics of clients' data access requests and networks. The learning technology can help the data center networks (DCNs) learn from historical access information and make optimal data storage decision. Consider a more practical DCNs with fat-tree topology, we utilize a deep-learning technology k-means to help store data blocks and then improve the read and write latency of the DCN, where k is the number of cores in the fat-tree. The evaluation results demonstrate that the average write and read latency of the whole system can be lowered by 33% and 45%, respectively. And the best set of parameter k is analyzed and recommended to provide guidance to the real application, which is equal to the number of cores in the DCNs.