Spectral Graph Optimization for Instance Reduction

Abstract

The operation of instance-based learning algorithms is based on storing a large set of prototypes in the system's database. However, such systems often experience issues with storage requirements, sensitivity to noise, and computational complexity, which result in high search and response times. In this brief, we introduce a novel framework that employs spectral graph theory to efficiently partition the dataset to border and internal instances. This is achieved by using a diverse set of border-discriminating features that capture the local friend and enemy profiles of the samples. The fused information from these features is then used via graph-cut modeling approach to generate the final dataset partitions of border and nonborder samples. The proposed method is referred to as the spectral instance reduction (SIR) algorithm. Experiments with a large number of datasets show that SIR performs competitively compared to many other reduction algorithms, in terms of both objectives of classification accuracy and data condensation.

Sample Reduction Algorithm Based on Classification Contribution

“…However, the existing hybrid methods [14][15][16][17][18][19][20][21][22] still have some disadvantages, such as parameter dependence, high time complexity, difficult to achieve high precision and high reduction rate at the same time.…”

“…In fact, the aggregation method greatly reduces the number of instances and rarely changes the prediction accuracy, while the edition method moderately reduces the number of instances and may change the prediction accuracy to a great extent. In recent years, the hybrid method [14][15][16][17][18][19][20][21][22] which combines the advantages of edition method and Condensation method, has attracted extensive attention. In our work, we mainly focus on hybrid methods.…”

“…Classical hybrid methods include Class boundary preserving algorithm (CBP) [14] and the adaptive threshold-based instance selection algorithm (ATISA) [16]. Many improved hybrid methods [15,[18][19][20][21][22]have also been developed by using new models, innovative theories and optimization algorithms. However, most of the existing hybrid methods [14][15][16][17][18] rely heavily on parameters and are relatively time-consuming, resulting in unstable performance and difficult application.…”

“…Many improved hybrid methods [15,[18][19][20][21][22]have also been developed by using new models, innovative theories and optimization algorithms. However, most of the existing hybrid methods [14][15][16][17][18] rely heavily on parameters and are relatively time-consuming, resulting in unstable performance and difficult application. Although parametric free hybrid methods are proposed [19,20], they are still difficult to achieve high precision and high simplification at the same time.…”

Smoothing graphons for modelling exchangeable relational data

“…friendship linkages in social networks; user-item rating matrices in recommendation systems; and protein-to-protein interactions in computational biology), where exchangeability refers to the phenomenon that the joint distribution over all observed relations remains invariant under node permutations. Techniques for modelling exchangeable relational data include node partitioning to form "homogeneous blocks" [1], [9], [10], graph embedding methods to generate low-dimensional representations [11]- [13], and optimization strategies to minimize prediction errors [14], [15].…”