SPINEX_ Symbolic Regression: Similarity-based Symbolic Regression with Explainable Neighbors Exploration

This article introduces a new symbolic regression algorithm based on the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family. This new algorithm (SPINEX_SymbolicRegression) adopts a similarity-based approach to identifying high-merit expressions that satisfy accuracy- and structural similarity metrics. We conducted extensive benchmarking tests comparing SPINEX_SymbolicRegression to over 180 mathematical benchmarking functions from international problem sets that span randomly generated expressions and those based on real physical phenomena. Then, we evaluated the performance of the proposed algorithm in terms of accuracy, expression similarity in terms of presence operators and variables (as compared to the actual expressions), population size, and number of generations at convergence. The results indicate that SPINEX_SymbolicRegression consistently performs well and can, in some instances, outperform leading algorithms. In addition, the algorithm's explainability capabilities are highlighted through in-depth experiments.

SPINEX-TimeSeries: Similarity-based Predictions with Explainable Neighbors Exploration for Time Series and Forecasting Problems

This paper introduces a new addition to the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family, tailored specifically for time series and forecasting analysis. This new algorithm leverages the concept of similarity and higher-order temporal interactions across multiple time scales to enhance predictive accuracy and interpretability in forecasting. To evaluate the effectiveness of SPINEX, we present comprehensive benchmarking experiments comparing it against 18 algorithms and across 49 synthetic and real datasets characterized by varying trends, seasonality, and noise levels. Our performance assessment focused on forecasting accuracy and computational efficiency. Our findings reveal that SPINEX consistently ranks among the top 5 performers in forecasting precision and has a superior ability to handle complex temporal dynamics compared to commonly adopted algorithms. Moreover, the algorithm's explainability features, Pareto efficiency, and medium complexity (on the order of O(log n)) are demonstrated through detailed visualizations to enhance the prediction and decision-making process. We note that integrating similarity-based concepts opens new avenues for research in predictive analytics, promising more accurate and transparent decision making.

SPINEX-Clustering: Similarity-based Predictions with Explainable Neighbors Exploration for Clustering Problems

This paper presents a novel clustering algorithm from the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) algorithmic family. The newly proposed clustering variant leverages the concept of similarity and higher-order interactions across multiple subspaces to group data into clusters. To showcase the merit of SPINEX, a thorough set of benchmarking experiments was carried out against 13 algorithms, namely, Affinity Propagation, Agglomerative, Birch, DBSCAN, Gaussian Mixture, HDBSCAN, K-Means, KMedoids, Mean Shift, MiniBatch K-Means, OPTICS, Spectral Clustering, and Ward Hierarchical. Then, the performance of all algorithms was examined across 51 synthetic and real datasets from various domains, dimensions, and complexities. Furthermore, we present a companion complexity analysis to compare the complexity of SPINEX to that of the aforementioned algorithms. Our results demonstrate that SPINEX can outperform commonly adopted clustering algorithms by ranking within the top-5 best performing algorithms and has moderate complexity. Finally, a demonstration of the explainability capabilities of SPINEX, along with future research needs, is presented.

SPINEX: Similarity-based Predictions with Explainable Neighbors Exploration for Anomaly and Outlier Detection

This paper presents a novel anomaly and outlier detection algorithm from the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family. This algorithm leverages the concept of similarity and higher-order interactions across multiple subspaces to identify outliers. A comprehensive set of experiments was conducted to evaluate the performance of SPINEX. This algorithm was examined against 21 commonly used anomaly detection algorithms, namely, namely, Angle-Based Outlier Detection (ABOD), Connectivity-Based Outlier Factor (COF), Copula-Based Outlier Detection (COPOD), ECOD, Elliptic Envelope (EE), Feature Bagging with KNN, Gaussian Mixture Models (GMM), Histogram-based Outlier Score (HBOS), Isolation Forest (IF), Isolation Neural Network Ensemble (INNE), Kernel Density Estimation (KDE), K-Nearest Neighbors (KNN), Lightweight Online Detector of Anomalies (LODA), Linear Model Deviation-based Detector (LMDD), Local Outlier Factor (LOF), Minimum Covariance Determinant (MCD), One-Class SVM (OCSVM), Quadratic MCD (QMCD), Robust Covariance (RC), Stochastic Outlier Selection (SOS), and Subspace Outlier Detection (SOD), and across 39 synthetic and real datasets from various domains and of a variety of dimensions and complexities. Furthermore, a complexity analysis was carried out to examine the complexity of the proposed algorithm. Our results demonstrate that SPINEX achieves superior performance, outperforms commonly used anomaly detection algorithms, and has moderate complexity (e.g., O(n log n d)). More specifically, SPINEX was found to rank at the top of algorithms on the synthetic datasets and the 7th on the real datasets. Finally, a demonstration of the explainability capabilities of SPINEX, along with future research needs, is presented.