Abstract: Faced with a large number of uncertainties in the financial market, how to rationally choose effective pricing factors and construct a scientific asset pricing system has always been one of the core issues in financial theory research. The method of graph embedding, based on the sparse representation and low rank representation strategies, is used to deeply mine the inherent structure hidden in the data set, and an integrated learning strategy is constructed that can simultaneously reveal the local structure information and global structure information of the data in order to achieve different dimensions of Multi-source data fusion.Based on the theory of CAPM and APT, a quantitative multi-factor portfolio selection model is constructed by integrating learning methods，and the gradient boosting decision Tree method, convolutional neural network, time series and support vector machine are representatively selected to perform combined prediction.It is optimized by the sparse low-rank graph approximation least squares vector regression integration strategy.At the same time, a sparse low-rank model is constructed that can reveal both local and global structural information of the data, thereby learning to obtain a more accurate representation of multi-source data and high-dimensional data in the feature subspace.The empirical results show that the sparse low-rank strategy based on integrated prediction has stronger securities selection ability and higher excess return rate.The non-linear prediction method using machine learning is more conducive to revealing the complex characteristics of financial system. The empirical conclusion has important guiding significance for portfolio management.

Key words: sparse low rank; graph approximate least squares vector regression machine; integrated prediction; multi-factorasset selection