Related papers: On a Generalization of the Average Distance Classi…
We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data often have the SSE model. We consider a distance-based classifier using eigenstructures for the SSE…
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
A classifier for two or more samples is proposed when the data are high-dimensional and the underlying distributions may be non-normal. The classifier is constructed as a linear combination of two easily computable and interpretable…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…
In this paper we propose the creation of generic LSH families for the angular distance based on Johnson-Lindenstrauss projections. We show that feature hashing is a valid J-L projection and propose two new LSH families based on feature…
The scores of distance-based outlier detection methods are difficult to interpret, making it challenging to determine a cut-off threshold between normal and outlier data points without additional context. We describe a generic…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals,…
Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive…
In this paper, we generalize two criteria, the determinant-based and trace-based criteria proposed by Saranadasa (1993), to general populations for high dimensional classification. These two criteria compare some distances between a new…
This paper deals with clustering methods based on adaptive distances for histogram data using a dynamic clustering algorithm. Histogram data describes individuals in terms of empirical distributions. These kind of data can be considered as…
The most useful data mining primitives are distance measures. With an effective distance measure, it is possible to perform classification, clustering, anomaly detection, segmentation, etc. For single-event time series Euclidean Distance…
Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis,…
The estimation of the generalization error of classifiers often relies on a validation set. Such a set is hardly available in few-shot learning scenarios, a highly disregarded shortcoming in the field. In these scenarios, it is common to…
We consider high-dimensional quadratic classifiers in non-sparse settings. The target of classification rules is not Bayes error rates in the context. The classifier based on the Mahalanobis distance does not always give a preferable…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…