Related papers: Data segmentation based on the local intrinsic dim…
Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…
The process of segmenting point cloud data into several homogeneous areas with points in the same region having the same attributes is known as 3D segmentation. Segmentation is challenging with point cloud data due to substantial…
A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…
Extracting an understanding of the underlying system from high dimensional data is a growing problem in science. Discovering informative and meaningful features is crucial for clustering, classification, and low dimensional data embedding.…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
Deep learning algorithms have become the golden standard for segmentation of medical imaging data. In most works, the variability and heterogeneity of real clinical data is acknowledged to still be a problem. One way to automatically…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
This paper reconsiders common benchmarking approaches to nearest neighbor search. It is shown that the concept of local intrinsic dimensionality (LID) allows to choose query sets of a wide range of difficulty for real-world datasets.…
In recent years, convolutional neural networks (CNNs) are used in a large number of tasks in computer vision. One of them is object detection for autonomous driving. Although CNNs are used widely in many areas, what happens inside the…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
Finding valuable training data points for deep neural networks has been a core research challenge with many applications. In recent years, various techniques for calculating the "value" of individual training datapoints have been proposed…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…
Heterogeneous datasets emerge in various machine learning and optimization applications that feature different input sources, types or formats. Most models or methods do not natively tackle heterogeneity. Hence, such datasets are often…
Dimensionality is an important aspect for analyzing and understanding (high-dimensional) data. In their 2006 ICDM paper Tatti et al. answered the question for a (interpretable) dimension of binary data tables by introducing a normalized…
The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered…
Size uniformity is one of the main criteria of superpixel methods. But size uniformity rarely conforms to the varying content of an image. The chosen size of the superpixels therefore represents a compromise - how to obtain the fewest…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…