Quantum dimensionality reduction by linear discriminant analysis

Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and classification. In this paper, we present quantum algorithm circuit to efficiently perform linear discriminant analysis (LDA) dimensionality reduction. Firstly, the presented improves existing LDA avoid error caused by irreversibility between-class scatter matrix $S_B$ in original algorithm. Secondly, circuits are proposed obtain target state corresponding low-dimensional data. Compared with best-known classical algorithm, (QLDADR) has exponential acceleration on number $M$ vectors quadratic speedup $D$ space, when dataset projected onto polylogarithmic space. Moreover, obtained our can be used submodule other tasks. It practical application value make that free from disaster dimensionality.