相关论文: Intrinsic dimension of a dataset: what properties …
We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN'07 paper (arXiv:cs/0703125). The main features of our approach are that a high intrinsic dimension of a…
The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID)…
The curse of dimensionality is a phenomenon frequently observed in machine learning (ML) and knowledge discovery (KD). There is a large body of literature investigating its origin and impact, using methods from mathematics as well as from…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set size. Secondly, there is a \emph{related curse} concerned…
Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…
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.…
It is widely believed that natural image data exhibits low-dimensional structure despite the high dimensionality of conventional pixel representations. This idea underlies a common intuition for the remarkable success of deep learning in…
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…
We consider a common measurement paradigm, where an unknown subset of an affine space is measured by unknown continuous quasi-convex functions. Given the measurement data, can one determine the dimension of this space? In this paper, we…
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…
The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…
Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods…
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states:…
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…
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…
It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a "blessing" or a "curse", causing uncomfortable inconsistencies in the literature. We propose that these patterns…
The problem of estimating, from a random sample of points, the dimension of a compact subset $S$ of the Euclidean space is considered. The emphasis is put on consistency results in the statistical sense. That is, statements of convergence…
The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in…
Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such…