This paper introduces the R package spca, which provides a computational framework for least squares sparse principal component analysis (LS-SPCA). Unlike other SPCA methods, LS-SPCA generates uncorrelated sparse principal components (sPCs) that effectively maximize the explained variance while maintaining strong correlations with standard principal components (PCs). The framework also includes more computationally efficient variants that produce mildly correlated sPCs, which often have lower cardinality while explaining equal or greater variance than the LS-SPCA optimal sPCs. The spca package is built on an efficient C++ backend for matrix computations, with distinct engines for tall and fat matrices, and a flexible R frontend. The user interface offers several options for computing sPCs, such as deciding whether sparsification should stop when a threshold for cumulative variance explained or R2 with the PCs is reached, and choosing between simple forward selection, stepwise forward selection, or backward elimination for variable selection. In addition to the print(), summary(), and plot() methods, the package includes tools for comparing different "spca" solutions, grouping sparse loadings, and representing foreign SPCA solutions as "spca" objects. This article demonstrates with real datasets the use of the package in a typical LS-SPCA workflow and briefly contrasts LS-SPCA with conventional SPCA solutions . Then it compares different LS-SPCA solutions obtained from the dataset. Finally, the performance of spca on large tall and fat matrices is discussed, showing that spca offers a computationally efficient alternative for computing interpretable sPCs.

This paper compares different methods for forecasting the term structure of U.S. and European zero-coupon government bonds using both traditional econometric and Machine Learning (ML) approaches. We compare classical models (e.g., Dynamic Nelson-Siegel (DNS) and Principal Component Analysis (PCA)) with different Neural Network (NN) architectures, including those inspired by the classical models, on the U.S. Treasury market and bonds issued by the European Central Bank (ECB). To enhance predictive performance, macroeconomic variables are incorporated. The findings for both markets are separately analyzed and compared. To this end, we propose a robust model evaluation framework combining statistical accuracy metrics - such as RMSE, MAE, and directional accuracy - with the economic relevance of a quantitative bond trading strategy. Results show that NNs consistently outperform traditional models in both forecasting accuracy and portfolio performance. For the U.S., the most effective approach is a direct-forecasting NN that incorporates DNS factors to reduce the dimensionality of zero-rate data and an Autoencoder (AE) to extract macroeconomic features, while for Europe, the optimal model is a factor-based NN using PCA-derived zero-rate factors without the integration of macroeconomic variables. Overall, the paper demonstrates how combining traditional modeling approaches with modern ML techniques and evaluation can improve yield curve forecasts and support applications in fixed-income portfolio construction.

Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on variables and does not account for differences in variable importance, which may lead to unstable performance in highly noisy or structurally complex settings. We propose SP-SPCA, a method that introduces a single equilibrium parameter into the regularization framework to adaptively adjust variable penalties. This modification of the L2 penalty provides flexible control over the trade-off between sparsity and explained variance while maintaining computational efficiency. Simulation studies show that the proposed method consistently outperforms standard sparse principal component methods in identifying sparse loading patterns, filtering noise variables, and preserving cumulative variance, especially in high-dimensional and noisy settings. Empirical applications to crime and financial market data further demonstrate its practical utility. In real data analyses, the method selects fewer but more relevant variables, thereby reducing model complexity while maintaining explanatory power. Overall, the proposed approach offers a robust and efficient alternative for sparse modeling in complex high-dimensional data, with clear advantages in stability, feature selection, and interpretability

Collecting multiple types of data on the same set of subjects is common in modern scientific applications including, genomics, metabolomics, and neuroimaging. Joint and Individual Variance Explained (JIVE) seeks a low-rank approximation of the joint variation between two or more sets of features captured on common subjects and isolates this variation from that unique to eachset of features. We develop an expectation-maximization (EM) algorithm to estimate a probabilistic model for the JIVE framework. The model extends probabilistic principal components analysis to multiple data sets. Our maximum likelihood approach simultaneously estimates joint and individual components, which can lead to greater accuracy compared to other methods. We apply ProJIVE to measures of brain morphometry and cognition in Alzheimer's disease. ProJIVE learns biologically meaningful courses of variation, and the joint morphometry and cognition subject scores are strongly related to more expensive existing biomarkers. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Code to reproduce the analysis is available on our GitHub page.

We thank the reviewers for their feedback. We will first respond to shared and then to individual comments. Additionally, reviewers 2 and 3 requested clarification regarding the advantages of DCA over other methods. For instance, one could attempt to correlate each neuron's contribution to the DCA subspace with single-neuron Studying the behavior of Kernel DCA is a direction for future studies. Additionally, we found and corrected a minor bug in Figure 1A: the SFA and DCA lines are now blue and red, respectively.

Abstract--Principal Component Analysis (PCA) and K-means constitute fundamental techniques in multivariate analysis. Although they are frequently applied independently or sequentially to cluster observations, the relationship between them, especially when K-means is used to cluster variables rather than observations, has been scarcely explored. This study seeks to address this gap by proposing an innovative method that analyzes the relationship between clusters of variables obtained by applying K-means on transposed data and the principal components of PCA. Our approach involves applying PCA to the original data and K-means to the transposed data set, where the original variables are converted into observations. The contribution of each variable cluster to each principal component is then quantified using measures based on variable loadings. This process provides a tool to explore and understand the clustering of variables and how such clusters contribute to the principal dimensions of variation identified by PCA. We analyze multiple data sets with varying variability structures (USArrests, Iris, Decathlon2) to show that the correspondence between clusters of variables and principal components depends on the data's inherent structure.

Vision-based tactile sensors (VBTSs) are a promising technology for robots, providing them with dense signals that can be translated into an understanding of normal and shear load, contact region, texture classification, and more. However, existing VBTS tactile surfaces make use of silicone gels, which provide high sensitivity but easily deteriorate from loading and surface wear. We propose that polyurethane rubber, used for high-load applications like shoe soles, rubber wheels, and industrial gaskets, may provide improved physical gel resilience, potentially at the cost of sensitivity. To compare the resilience and sensitivity of silicone and polyurethane VBTS gels, we propose a series of standard evaluation benchmarking protocols. Our resilience tests assess sensor durability across normal loading, shear loading, and abrasion. For sensitivity, we introduce model-free assessments of force and spatial sensitivity to directly measure the physical capabilities of each gel without effects introduced from data and model quality. Finally, we include a bottle cap loosening and tightening demonstration as an example where polyurethane gels provide an advantage over their silicone counterparts.

In today's landscape, Mixture of Experts (MoE) is a crucial architecture that has been used by many of the most advanced models. One of the major challenges of MoE models is that they usually require much more memory than their dense counterparts due to their unique architecture, and hence are harder to deploy in environments with limited GPU memory, such as edge devices. MoE offloading is a promising technique proposed to overcome this challenge, especially if it is enhanced with caching and pre-fetching, but prior work stopped at suboptimal caching algorithm and offered limited insights. In this work, we study MoE offloading in depth and make the following contributions: 1. We analyze the expert activation and LRU caching behavior in detail and provide traces. 2. We propose LFU caching optimization based on our analysis and obtain strong improvements from LRU. 3. We implement and experiment speculative expert pre-fetching, providing detailed trace showing its huge potential . 4. In addition, our study extensively covers the behavior of the MoE architecture itself, offering information on the characteristic of the gating network and experts. This can inspire future work on the interpretation of MoE models and the development of pruning techniques for MoE architecture with minimal performance loss.

This study develops a SARIMAX-based prediction system for short-term power outage forecasting during extreme weather events. Using hourly data from Michigan counties with outage counts and comprehensive weather features, we implement a systematic two-stage feature engineering pipeline: data cleaning to remove zero-variance and unknown features, followed by correlation-based filtering to eliminate highly correlated predictors. The selected features are augmented with temporal embeddings, multi-scale lag features, and weather variables with their corresponding lags as exogenous inputs to the SARIMAX model. To address data irregularity and numerical instability, we apply standardization and implement a hierarchical fitting strategy with sequential optimization methods, automatic downgrading to ARIMA when convergence fails, and historical mean-based fallback predictions as a final safeguard. The model is optimized separately for short-term (24 hours) and medium-term (48 hours) forecast horizons using RMSE as the evaluation metric. Our approach achieves an RMSE of 177.2, representing an 8.4\% improvement over the baseline method (RMSE = 193.4), thereby validating the effectiveness of our feature engineering and robust optimization strategy for extreme weather-related outage prediction.