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We consider the Sparse Principal Component Analysis (SPCA) problem under the well-known spiked covariance model. Recent work has shown that the SPCA problem can be reformulated as a Mixed Integer Program (MIP) and can be solved to global…
In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…
Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…
Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…
Federated Learning (FL) faces major challenges in real-world deployments due to statistical heterogeneity across clients and system heterogeneity arising from resource-constrained devices. While clustering-based approaches mitigate…
A wide range of (multivariate) temporal (1D) and spatial (2D) data analysis tasks, such as grouping vehicle sensor trajectories, can be formulated as clustering with given metric constraints. Existing metric-constrained clustering…
Incomplete multi-view spectral clustering generalizes spectral clustering to multi-view data and simultaneously realizes the partition of multi-view data with missing views. For this category of method, K-means algorithm needs to be…
Kernel principal component analysis (kPCA) is a widely studied method to construct a low-dimensional data representation after a nonlinear transformation. The prevailing method to reconstruct the original input signal from kPCA -- an…
This paper presents a new statistical method for clustering step data, a popular form of health record data easily obtained from wearable devices. Since step data are high-dimensional and zero-inflated, classical methods such as K-means and…
Clustering is a well-established technique in machine learning and data analysis, widely used across various domains. Cluster validity indices, such as the Average Silhouette Width, Calinski-Harabasz, and Davies-Bouldin indices, play a…
Composite development indicators used in policy making often subjectively aggregate a restricted set of indicators. We show, using dimensionality reduction techniques, including Principal Component Analysis (PCA) and for the first time…
In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining…
Clustering is the task of gathering similar data samples into clusters without using any predefined labels. It has been widely studied in machine learning literature, and recent advancements in deep learning have revived interest in this…
In many modern statistical problems, the limited available data must be used both to develop the hypotheses to test, and to test these hypotheses-that is, both for exploratory and confirmatory data analysis. Reusing the same dataset for…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…
Giving or recommending appropriate content based on the quality of experience is the most important and challenging issue in recommender systems. As collaborative filtering (CF) is one of the most prominent and popular techniques used for…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
The $k$-principal component analysis ($k$-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications. In statistical settings, the goal of $k$-PCA is to identify a top…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…