The K-Means clustering using LLoyd's algorithm is an iterative approach to
partition the given dataset into K different clusters. The algorithm assigns
each point to the cluster based on the following objective function
\[\ \min \Sigma_{i=1}^{n}||x_i-\mu_{x_i}||^2\] The serial algorithm involves
iterative steps where we compute the distance of each datapoint from the
centroids and assign the datapoint to the nearest centroid. This approach is
essentially known as the expectation-maximization step. Clustering involves
extensive computations to calculate distances at each iteration, which
increases as the number of data points increases. This provides scope for
parallelism. However, we must ensure that in a parallel process, each thread
has access to the updated centroid value and no racing condition exists on any
centroid values. We will compare two different approaches in this project. The
first approach is an OpenMP flat synchronous method where all processes are run
in parallel, and we use synchronization to ensure safe updates of clusters. The
second approach we adopt is a GPU based parallelization approach using OpenACC
wherein we will try to make use of GPU architecture to parallelize chunks of
the algorithm to observe decreased computation time. We will analyze metrics
such as speed up, efficiency,time taken with varying data points, and number of
processes to compare the two approaches and understand the relative performance
improvement we can get.

K-Means 聚类使用 LLoyd 算法是一种迭代方法，将给定数据集分成 K 个不同的簇；本文将比较并分析两种不同的方法，一种是基于 OpenMP 的平坦同步方法，另一种是基于 GPU 的并行化方法，通过比较结果测量性能改进。