Graph Construction from Data using Non Negative Kernel regression (NNK Graphs)

Data driven graph constructions are often used in various applications, including several machine learning tasks, where the goal is to make predictions and discover patterns. However, learning an optimal graph from data is still a challenging task. Weighted $K$-nearest neighbor and $\epsilon$-neighborhood methods are among the most common graph construction methods, due to their computational simplicity but the choice of parameters such as $K$ and $\epsilon$ associated with these methods is often ad hoc and lacks a clear interpretation. We formulate graph construction as the problem of finding a sparse signal approximation in kernel space, identifying key similarities between methods in signal approximation and existing graph learning methods. We propose non-negative kernel regression~(NNK), an improved approach for graph construction with interesting geometric and theoretical properties. We show experimentally the efficiency of NNK graphs, its robustness to choice of sparsity $K$ and better performance over state of the art graph methods in semi supervised learning tasks on real world data

Structure Aware L1 Graph for Data Clustering

In graph-oriented machine learning research, L1 graph is an efficient way to represent the connections of input data samples. Its construction algorithm is based on a numerical optimization motivated by Compressive Sensing theory. As a result, It is a nonparametric method which is highly demanded. However, the information of data such as geometry structure and density distribution are ignored. In this paper, we propose a Structure Aware (SA) L1 graph to improve the data clustering performance by capturing the manifold structure of input data. We use a local dictionary for each datum while calculating its sparse coefficients. SA-L1 graph not only preserves the locality of data but also captures the geometry structure of data. The experimental results show that our new algorithm has better clustering performance than L1 graph