Dimensionality reduction is vital in many fields, such as computer vision and pattern recognition. This paper proposes an unsupervised dimensionality reduction algorithm based on multi-local linear regression. The algorithm first divides the high-dimensional data into many localities. Under the criterion of local homeomorphism, the continuous dependency relationship of the high-dimensional data is maintained in each locality in the low-dimensional space. At the same time, due to the overlap of locality divisions, that is, each data may belong to multiple localities. Therefore, the algorithm performs a multi-local linear prediction on each target data point, to better capture the internal geometric structure of the data. Finally, to coordinate the predictions of the target data points by each locality, we require that the variance between the predictions of each locality to the same target point should be as small as possible. We perform experiments on synthetic and real datasets. Compared with the existing advanced algorithms, the experimental results show that the proposed algorithm has good feasibility.

降维在许多领域都至关重要，例如计算机视觉和模式识别。本文提出了一种基于多局部线性回归的无监督降维算法。该算法首先将高维数据划分为多个位置。在局部同胚准则下，高维数据在低维空间的每个局部都保持着连续的依赖关系。同时，由于局部划分的重叠，即每个数据可能属于多个局部。因此，该算法对每个目标数据点进行多局部线性预测，以更好地捕捉数据的内部几何结构。最后，为了协调每个地点对目标数据点的预测，我们要求每个位置对同一目标点的预测之间的方差应尽可能小。我们在合成数据集和真实数据集上进行实验。与现有的先进算法相比，实验结果表明该算法具有较好的可行性。