Related papers: DROP: Dimensionality Reduction Optimization for Ti…

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand…

In order to process efficiently ever-higher dimensional data such as images, sentences, or audio recordings, one needs to find a proper way to reduce the dimensionality of such data. In this regard, SVD-based methods including PCA and…

Poor scaling of dynamics simulations with number of dimensions is currently a major limiting factor in the simulation of photochemical processes. In this work, we investigate ways to reduce the dimensionality of many-atom systems with a…

High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these…

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…

Fine-tuning large-scale pre-trained models is inherently a resource-intensive task. While it can enhance the capabilities of the model, it also incurs substantial computational costs, posing challenges to the practical application of…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

Model merging is to combine fine-tuned models derived from multiple domains, with the intent of enhancing the model's proficiency across various domains. The principal concern is the resolution of parameter conflicts. A substantial amount…

This paper proposes a tool for dimension reduction where the dimension of the original space is reduced: a Principal Loading Analysis (PLA). PLA is a tool to reduce dimensions by discarding variables. The intuition is that variables are…

Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…

Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its…

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such…

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

Selecting the appropriate dimensionality reduction (DR) technique and determining its optimal hyperparameter settings that maximize the accuracy of the output projections typically involves extensive trial and error, often resulting in…