Sparse Matrix Format Selection with Multiclass SVM for SpMV on GPU

Abstract

Sparse Matrix-Vector Multiplication (SpMV) kernel dominates the computing cost in numerous scientific applications. Many implementations based on different sparse formats were proposed recently for this kernel on the GPU side. Since the performance of these sparse formats varies significantly according to the sparsity characteristics of the input matrix and the hardware specifications, no one of them can be considered as the best one to use for every sparse matrix. In this paper, we address the problem of selecting the best representation for a given sparse matrix on GPU by using a machine learning approach. First, we present some interesting and easy to compute features for characterizing the sparse matrices on GPU. Second, we use a multiclass Support Vector Machine (SVM) classifier to select the best format for each input matrix. We consider in this paper four popular formats (COO, CSR, ELL, and HYB), but our work can be extended to support more sparse representations. Experimental results on two different GPUs (Fermi GTX 580 and Maxwell GTX 980 Ti) show that we achieved more than 98% of the performance possible with a perfect selection.

Effective Machine Learning Based Format Selection and Performance Modeling for SpMV on GPUs

“…Hence, we remove the cases where COO format is the best format. Similar observation is made by Benatia et al [8], where they avoid the COO format in their study.…”

“…However, this feature set is not sufficient in capturing the spatial patterns associated with sparse matrices. As an example, previous studies [8], [9] have addressed this issue by introducing additional features that are shown in feature set 2. The feature set 2 and 3 requires a scan on the entire matrix resulting in a time complexity of O(nnz) .…”

“…We use SVM and decision-tree based models, as suggested by Benatia et al [8], and Sedaghati et al [9]. We supplement these ML models with multi-layer perceptrons, gradient boosting based models (XGBoost) and ensembles of MLP.…”

“…Benatia et al [8] have proposed a classification technique using multi-class Support Vector Machine (SVM) classifier on manually extracted features. It achieves up to 88% classification accuracy on the four basic formats (COO, CSR, ELL, and HYB) with a dataset of 555 matrices from SuiteSparse [21] on NVIDIA Fermi and Maxwell GPUs.…”

“…Simple ML algorithms such as decision tree and multiclass Support Vector Machine (SVM) classifier have been shown to achieve very good accuracy for format selection [8], [9], and [10]. Deep neural networks (DNNs) such as convolutional neural networks (CNNs) are also starting to be used for the classification problem [11], [12].…”