PRISM: A Multi-Metric Framework for Evaluating Sensor Data Reconstruction

PRISM is a benchmark dataset for learning and evaluating unified evaluation metrics for heart rate (HR) imputation. The dataset is constructed from two publicly available physiological datasets, D1NAMO and the BIG IDEAS Lab Glycemic Variability and Wearable Device Data, both containing continuous heart rate recordings collected from wearable sensors. The HR signals were first preprocessed to remove invalid values and ensure continuous time series suitable for imputation experiments. To generate the benchmark dataset, artificial missing segments of 5-minute and 15-minute durations were introduced into complete HR recordings. Each missing segment was independently reconstructed using three statistical imputation techniques: Linear Interpolation, Cubic Interpolation, and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP). This process produces multiple imputed versions of the same HR segment, enabling systematic comparison between original and reconstructed signals. For every imputed segment, five complementary evaluation metrics were computed by comparing the imputed HR values with the corresponding original HR values. These metrics capture both reconstruction accuracy and distributional similarity of the physiological signal. In addition, a Misclassification Rate (MR) was calculated by assigning both the original and imputed HR values to predefined physiological heart rate intervals (10 bpm and 20 bpm bins) and measuring the proportion of incorrectly classified values. The resulting dataset is formulated as a supervised regression dataset, where the five evaluation metrics serve as input features and Misclassification Rate serves as the target variable. The dataset accompanies the FRAM-SHAP framework, where an explainable machine learning model is trained to predict the Misclassification Rate and determine the relative importance of each evaluation metric using SHAP analysis. The learned feature importance values are subsequently used to construct a unified combined evaluation metric for assessing HR imputation quality. However, the dataset itself is model-independent and can be used with any regression or explainable AI method for developing alternative combined evaluation metrics. Dataset Features Each row of the dataset corresponds to a single imputed HR segment. Input Features Root Mean Square Error (RMSE): Measures the magnitude of reconstruction errors while assigning greater penalty to larger deviations between original and imputed HR values. Mean Absolute Error (MAE): Computes the average absolute difference between original and imputed HR values, providing a robust measure of point-wise reconstruction accuracy. Mean Absolute Percentage Error (MAPE): Measures reconstruction error relative to the magnitude of the original HR values, enabling comparison across different heart rate ranges. Cohen's Distance Test (CDT): Measures the statistical similarity between the original and imputed HR signals using a threshold-based statistical distance. Jensen-Shannon Distance (JSD): Quantifies the similarity between the probability distributions of the original and imputed HR values, assessing preservation of the underlying signal distribution. Target Feature Misclassification Rate (MR): The regression target of the dataset. MR represents the proportion of imputed HR values assigned to an incorrect physiological heart rate interval compared with the original HR values. Lower MR values indicate better preservation of the physiological characteristics of the original signal. Dataset Purpose PRISM is intended to provide a standardized benchmark for developing, comparing, and validating combined evaluation metrics for physiological signal imputation. Unlike existing datasets that only report individual evaluation metrics, PRISM formulates the problem as a supervised regression task, enabling researchers to learn the relationship between multiple evaluation metrics and the overall quality of imputation. The dataset can be used to investigate feature importance, develop explainable AI models, construct alternative combined evaluation metrics, and benchmark regression algorithms for evaluation metric fusion. Although developed using HR data, the methodology can be readily extended to other physiological time-series signals and imputation problems. Dataset Organization The dataset is organized on a per-patient and per-imputation-method basis. Each file contains the evaluation metric values generated after applying the FRAM-SHAP preprocessing pipeline to a single patient's heart rate data imputed with a specific imputation technique. D1NAMO Dataset Files corresponding to the D1NAMO dataset follow the naming convention: <PatientID>TempPart_<ImputationMethod>_eval where: <PatientID> denotes the patient identifier (e.g., 1, 2, ..., 9). TempPart indicates the original D1NAMO heart rate recording for that patient. <ImputationMethod> specifies the imputation technique used to reconstruct the artificial missing HR gaps (e.g., linear, cubic, or pchip). eval indicates that the FRAM-SHAP evaluation pipeline has been applied to the imputed data. For example, 1TempPart_cubic_eval.csv contains the heart rate data of Patient 1 from the D1NAMO dataset after artificial gaps have been imputed using Cubic Interpolation, with the FRAM-SHAP framework applied to each imputed segment to compute the five evaluation metrics (RMSE, MAE, MAPE, CDT, and JSD) together with the corresponding Misclassification Rate (MR). BIG IDEAS Dataset Files corresponding to the BIG IDEAS Lab Glycemic Variability and Wearable Device Data follow the naming convention: HR_<PatientID>_<ImputationMethod>_eval where: HR_<PatientID> identifies the patient (e.g., HR_01, HR_02, ..., HR_16). <ImputationMethod> denotes the imputation technique applied to reconstruct the missing HR segments. eval indicates that the FRAM-SHAP evaluation pipeline has been executed on the imputed data. For example, HR_01_pchip_eval.csv contains the heart rate data of Patient 1 from the BIG IDEAS dataset after missing segments have been imputed using PCHIP interpolation, with the FRAM-SHAP pipeline subsequently applied to generate the five evaluation metrics and the corresponding Misclassification Rate for every imputed HR segment. Each file therefore, represents the complete set of regression samples for one patient and one imputation technique, making it straightforward to perform patient-wise analyses, compare different imputation methods, or aggregate data across patients and datasets Dataset Archives The dataset is provided as two compressed archives, each corresponding to a different definition of the Misclassification Rate (MR) target variable. combined training dataset with distribution size 10.zip contains all patient files where the Misclassification Rate is computed using 10 bpm physiological heart rate intervals. In this version, both the original and imputed HR values are categorized into 10 bpm bins (e.g., <60, 60–70, 70–80, …, 150–160, >160 bpm). The target variable (MR) represents the proportion of imputed values assigned to an incorrect 10 bpm interval. combined training dataset with distribution size 20.zip contains the same patient files and evaluation metrics, but the Misclassification Rate is computed using 20 bpm physiological heart rate intervals. Here, HR values are categorized into broader 20 bpm bins (e.g., <60, 60–80, 80–100, …, 140–160, >160 bpm), resulting in a different target variable while keeping the input evaluation metrics unchanged. Both archives contain the same directory structure, patient organization, and evaluation features. The only difference between the two versions is the definition of the Misclassification Rate (MR) target, allowing researchers to investigate how the choice of physiological distribution interval influences regression performance, feature importance, and the resulting combined evaluation metric.