Dimensionality reduction plays an important role in many machine learning and pattern recognition applications. Linear discriminant analysis (LDA) is the most popular supervised dimensionality reduction technique which searches for the projection matrix that makes the data points of different classes to be far from each other while requiring data points of the same class to be close to each other. In this paper, trace ratio LDA is combined with K-means clustering into a unified framework, in which K-means clustering is employed to generate class labels for unlabeled data and LDA is used to investigate low-dimensional representation of data. Therefore, by combining the subspace clustering with dimensionality reduction together, the optimal subspace can be obtained. Differing from other existing dimensionality reduction methods, our novel framework is suitable for different scenarios: supervised, semi-supervised, and unsupervised dimensionality reduction cases. Experimental results on benchmark datasets validate the effectiveness and superiority of our algorithm compared with other relevant techniques.

中文翻译：

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K-Means聚类降维的通用框架

降维在许多机器学习和模式识别应用中发挥着重要作用。线性判别分析 (LDA) 是最流行的监督降维技术，它搜索投影矩阵，使不同类别的数据点彼此远离，同时要求同一类别的数据点彼此接近。在本文中，迹比LDA与K-means聚类结合成一个统一的框架，其中K-means聚类用于为未标记数据生成类标签，LDA用于研究数据的低维表示。因此，通过将子空间聚类与降维相结合，可以得到最优子空间。与现有的其他降维方法不同，我们的新框架适用于不同的场景：监督、半监督和无监督的降维情况。与其他相关技术相比，基准数据集的实验结果验证了我们算法的有效性和优越性。