Accelerating Non-Negative Matrix Factorization on Embedded FPGA with Hybrid Logarithmic Dot-Product Approximation

Non-negative matrix factorization (NMF) is an ef-fective method for dimensionality reduction and sparse decom-position. This method has been of great interest to the scien-tific community in applications including signal processing, data mining, compression, and pattern recognition. However, NMF implies elevated computational costs in terms of performance and energy consumption, which is inadequate for embedded applications. To overcome this limitation, we implement the vector dot-product with hybrid logarithmic approximation as a hardware optimization approach. This technique accelerates floating-point computation, reduces energy consumption, and preserves accuracy. To demonstrate our approach, we employ a design exploration flow using high-level synthesis on an embedded FPGA. Compared with software solutions on ARM CPU, this hardware implementation accelerates the overall computation to decompose matrix by $5.597\times$ and reduces energy consumption by $69.323\times$. Log approximation NMF combined with KNN(k-nearest neighbors) has only 2.38% decreasing accuracy compared with the result of KNN processing the matrix after floating-point NMF on MNIST. Further on, compared with a dedicated floating-point accelerator, the logarithmic approximation approach achieves $3.718\times$ acceleration and $8.345\times$ energy reduction. Compared with the fixed-point approach, our approach has an accuracy degradation of 1.93% on MNIST and an accuracy amelioration of 28.2% on the FASHION MNIST data set without pre-knowledge of the data range. Thus, our approach has better compatibility with the input data range.