中文摘要：

LASSO（Least Absolute Shrinkage and Selection Operator）是1范数和2范数混合学习的一种理论框架，基于LASSO提出了局部保持投影的稀疏回归算法SpLPP及其广义的正则化形式RSpLPP，并从理论上证明了所提模型的收敛性及求解算法，给出了算法的复杂性分析。所提算法同时具有特征选择、降维的特性，在有监督学习、无监督学习两种任务情况下，都可以应用该算法。在人工数据集和真实数据集上进行的大量仿真实验，取得了较好的结果，证明了所提算法的有效性。

英文摘要：

LASSO is a hybrid theoretic learning framework combining both l1 norm and l2 norm.In this paper, a novel sparse learning algorithm, called locality preserving projection with sparsepenalty （SpLPP）, is presented with its regularized version, which two methods perform localitypreserving projection in the LASSO regression framework. The proposed model can be solved inregression framework with Cholesky decomposition, and its convergence is guaranteed in theory,together with its complexity. The proposed algorithms merge feature selection and dimensionalityreduction into one analysis, which indicates that the proposed algorithms can be performed ineither supervised or unsupervised tasks. Experiments on synthetic and real database show thatthe algorithms in this paper are competitive compared with the state of the art methods.