text: We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, LARS LASSO, and sparse PLS regression, can be performed. Particularly emphasis is placed on simultaneous learning of relevant features from an infinite set of candidates. We first generalize techniques used in all these preceding studies to derive an unifying bounding technique for arbitrary separable functions. We then carefully use this bounding to make block coordinate gradient descent feasible over infinite subgraph features, resulting in a fast converging algorithm that can solve a wider class of sparse learning problems over graph data. We also empirically study the differences from the existing approaches in convergence property, selected subgraph features, and search-space sizes. We further discuss several unnoticed issues in sparse learning over all possible subgraph features.
  @cite_2: Combinatorial chemistry has generated chemical libraries and databases with a huge number of chemical compounds, which include prospective drugs. Chemical structures of compounds can be molecular graphs, to which a variety of graph-based techniques in computer science, specifically graph mining, can be applied. The most basic way for analyzing molecular graphs is using structural fragments, so-called subgraphs in graph theory. The mainstream technique in graph mining is frequent subgraph mining, by which we can retrieve essential subgraphs in given molecular graphs. In this article we explain the idea and procedure of mining frequent subgraphs from given molecular graphs, raising some real applications, and we describe the recent advances of graph mining.
summary: These two existing, popular approaches are based on subgraph features, which are limited to specific type ones only. In contrast, a series of inspiring studies for has been made . These approaches involve automatic selection of relevant features from during the learning process. Triggered by the seminal paper by @cite_2 , it has been shown that we can perform simultaneous learning of not only the model parameters but also relevant subgraph features from all possible subgraphs in several machine-learning problems such as Adaboost , LARS LASSO , sparse partial-least-squares (PLS) regression , sparse principal component analysis (PCA) , and LPBoost . This paper aims to give a coherent and unifying view to understand how these existing methods work well, and then present a more general framework, which is applicable to a wider class of learning problems.