Supervised neighborhood graph construction for semi-supervised classification

Locality Preserving Projection (LPP) is a typical method of neighbor graph based dimensionality reduction algorithm. So, graph construction plays a key role on the performance of LPP. The original samples were transformed into their vectorial form by the traditional graph construction method before calculate k-nearest neighbors of each samples, which will lost Sample's inner structure information. In this paper, we proposed a new graph construction approach which called Corresponding Block (CB) Based Neighbor Graph Construction Method, and we named the so constructed graph as Corresponding Block Based Graph (CBG). Our new method divided each sample matrix into several blocks and base on corresponding blocks to determine neighbors of each sample, which can well preserve samples' intrinsic structural information and has the ability of non-uniform illumination immunity in some extent. Then, we incorporate CBG into the state-of-art dimensionality algorithm: LPP, and developed a new algorithm called CBG-LPP. To evaluate CBG-LPP, several experiments were conducted on three well-known face databases and achieved satisfactory results.

Online image search result grouping with MapReduce-based image clustering and graph construction for large-scale photos

Nonlinear data projection based on geodesic distances requires the construction of a neighborhood graph that spans all data points so that the geodesic distance between any pair of data points could be estimated by the graph distance between the pair. This paper proposes an approach for constructing a k-edge connected neighborhood graph. The approach works by repeatedly extracting minimum spanning trees from the complete Euclidean graph of all data points. The constructed neighborhood graph has the following properties: (1) it is k-connected; (2) each point connects to its k-nearest neighbors; (3) if the graph is cut into two partitions, the cut edges contain k-shortest edges between the two partitions. Experiments show that the presented approach works well for clustered data and outperforms the nearest neighbor approaches used in Isomap for evenly distributed data.

Building k-edge-connected neighborhood graph for distance-based data projection

Spectral clustering algorithms rely on graphs where edges are defined based on the similarity between the vertices (data points). The effectiveness and fairness of spectral clustering depend significantly on how the graph is constructed. While automated graph construction methods, which learn graphs from real-valued vector datasets, have demonstrated strong performance in the quality of clustering, fairness concerns still remain. In this work, we introduce a graph construction method that incorporates a new fairness definition—Edge Disparate Impact—into the edge relationships, aiming to produce a fair graph. This approach modifies the optimization process of automated graph construction to account for fairness, resulting in a more equitable graph. Extensive experiments were conducted to compare our method with the latest graph construction techniques and fair spectral clustering algorithms. The results prove that, by using a fair graph for spectral clustering, fairness is improved in the resulting clusters. We also demonstrate that our method outperforms baseline approaches in both fairness and the quality of clustering.

While deep learning is a powerful tool for many applications, there has been only limited research about selection of data for training, i.e., instance selection, which enhances deep learning scalability by saving computational resources. This can be attributed in part to the difficulty of interpreting deep learning models. While some graph-based methods have been proposed to improve performance and interpret behavior of deep learning, the instance selection problem has not been addressed from a graph perspective. In this paper, we analyze the behavior of deep learning outputs by using the K-nearest neighbor (KNN) graph construction. We observe that when a directed KNN graph is constructed, instead of the more conventional undirected KNN, a large number of instances become isolated nodes, i.e., they do not belong to the directed neighborhoods of any other nodes. Based on this, we propose two new instance selection methods, that both lead to fewer isolated nodes, by either directly eliminating them (minimization approach) or by connecting them more strongly to other points (maximization). Our experiments show that our proposed maximization method leads to better performance than random selection and recent methods for instance selection.

This paper proposes a new method of chemical graph construction which is implemented in the chemical structure recognition and correction system ChemInfty (www.inftyproject.org/en/ChemInfty/). The system starts with recognizing the graphical elements of the chemical structure such as lines and characters. In the chemical graph construction phase the validity of the chemical graph is checked to detect inconsistencies. The graph construction starts with an empty chemical graph using only the graphical components. After a solving cycle the system returns a partially solved graph which can be checked for inconsistencies again. This results in a flexible, cycle based and inconsistency-driven graph construction. Furthermore the system introduces semi-automated correction allowing users to interact with the graph-construction cycles.

Adaptive graph construction using data self-representativeness for pattern classification

Graph-based semi-supervised learning (SSL) algorithms have been widely studied in the last few years. Most of these algorithms were designed from unconstrained optimization problems using a Laplacian regularizer term as smoothness functional in an attempt to reflect the intrinsic geometric structure of the data's marginal distribution. Although a number of recent research papers are still focusing on unconstrained methods for graph-based SSL, a recent statistical analysis showed that many of these algorithms may be unstable on transductive regression. Therefore, we focus on providing new constrained methods for graph-based SSL. We begin by analyzing the regularization framework of existing unconstrained methods. Then, we incorporate two normalization constraints into the optimization problem of three of these methods. We show that the proposed optimization problems have closed-form solution. By generalizing one of these constraints to any distribution, we provide generalized methods for constrained graph-based SSL. The proposed methods have a more flexible regularization framework than the corresponding unconstrained methods. More precisely, our methods can deal with any graph Laplacian and use higher order regularization, which is effective on general SSL taks. In order to show the effectiveness of the proposed methods, we provide comprehensive experimental analyses. Specifically, our experiments are subdivided into two parts. In the first part, we evaluate existing graph-based SSL algorithms on time series data to find their weaknesses. In the second part, we evaluate the proposed constrained methods against six state-of-the-art graph-based SSL algorithms on benchmark data sets. Since the widely used best case analysis may hide useful information concerning the SSL algorithms' performance with respect to parameter selection, we used recently proposed empirical evaluation models to evaluate our results. Our results show that our methods outperforms the competing methods on most parameter settings and graph construction methods. However, we found a few experimental settings in which our methods showed poor performance. In order to facilitate the reproduction of our results, the source codes, data sets, and experimental results are freely available.

3D human motion retrieval using graph kernels based on adaptive graph construction

Due to the excellent performance in exploring the structure of low-dimensional subspaces, the low-rank representation (LRR) has recently attracted wide attention of the researchers. However, in most current semi-supervised learning problems based on LRR method, the two steps of graph construction and semi-supervised learning are separated. Therefore, the existing label information cannot be well used to guide the construction of the affinity graph. Thus, these methods cannot guarantee the results are the global optimal solutions. In this paper, we propose a graph regularized low-rank representation for semi-supervised learning, termed as GLRSC. Combing the construction of the affinity graph and the semi-supervised learning, and solving the joint optimization, the proposed GLRSC method can get the global optimal solution. The experimental results on some benchmark datasets show that the effectiveness of the proposed GLRSC method.

Fine‐grained indoor navigation services require obstacle‐level indoor maps to support, but since indoor environments are affected by human activities, resulting in frequent changes in indoor spatial layouts, and indoor environments are easily affected by light and occlusion, the vast majority of indoor maps are at room level, limiting indoor obstacle‐level navigation path planning. To solve this problem, this paper proposes a hierarchy relation graph (HRG) construction method based on RGB‐D. Firstly, the semantic information extraction of indoor scenes and elements is realized by the output transformed PSPNet and YOLO V8 models, and the bounding box of each element is obtained based on YOLO V8. Then an algorithm for determining the hierarchical relationship of indoor elements is proposed, which calculates the correlation between the two elements from both plane and depth dimensions and constructs a HRG of indoor elements based on directed trees. Finally, comparative experiments are designed to validate the proposed method. Experiments showed that the proposed method can construct HRGs in a variety of scenes; the hierarchy relation detection rate is 88.28%; the accuracy of hierarchy relation determination is 73.44%; and the single‐scene HRG can be generated in 3.81 s.

Semi-Supervised Learning (SSL) techniques have become very relevant since they require a small set of labeled data. In this context, graph-based algorithms have gained prominence in the area due to their capacity to exploiting, besides information about data points, the relationships among them. Moreover, data represented in graphs allow the use of collective inference (vertices can affect each other), propagation of labels (autocorrelation among neighbors) and use of neighborhood characteristics of a vertex. An important step in graph-based SSL methods is the conversion of tabular data into a weighted graph. The graph construction has a key role in the quality of the classification in graph-based methods. This paper explores a method for graph construction that uses available labeled data. We provide extensive experiments showing the proposed method has many advantages: good classification accuracy, quadratic time complexity, no sensitivity to the parameter k > 10, sparse graph formation with average degree around 2 and hub formation from the labeled points, which facilitates the propagation of labels.

In this paper, we consider the probability of disconnection of a graph as a measure of network reliability. We compare the vertex and edge failure cases, and then concentrate on the vertex failure case. Optimal graphs are graphs which minimise the probability of disconnection for a given number of vertices and edges when the probability of vertex failure is small. We describe the known results on the construction of optimal regular graphs and present some new results on the construction of optimal nonregular graphs.

Towards Dynamic Self-Training for Scalable Semi-Supervised Learning on Graphs