Related papers: On pattern classification with weighted dimensions
In recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial…
The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is…
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize…
Data mining research into time series classification (TSC) has focussed on alternative distance measures for nearest neighbour classifiers. It is standard practice to use 1-NN with Euclidean or dynamic time warping (DTW) distance as a straw…
For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…
The k-Nearest Neighbors (kNN) classifier is a fundamental non-parametric machine learning algorithm. However, it is well known that it suffers from the curse of dimensionality, which is why in practice one often applies a kNN classifier on…
The Wasserstein distance provides a notion of dissimilarities between probability measures, which has recent applications in learning of structured data with varying size such as images and text documents. In this work, we study the…
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…
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…
In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying…
The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using of the Manhattan distance and even fractional quasinorms lp (for p less than 1) can help to…
Distance weighted discrimination (DWD) is a linear discrimination method that is particularly well-suited for classification tasks with high-dimensional data. The DWD coefficients minimize an intuitive objective function, which can solved…
There is an increasing body of evidence suggesting that exact nearest neighbour search in high-dimensional spaces is affected by the curse of dimensionality at a fundamental level. Does it necessarily mean that the same is true for k…
Sample weighting is widely used in deep learning. A large number of weighting methods essentially utilize the learning difficulty of training samples to calculate their weights. In this study, this scheme is called difficulty-based…
Very few K-nearest-neighbor (KNN) ensembles exist, despite the efficacy of this approach in regression, classification, and outlier detection. Those that do exist focus on bagging features, rather than varying k or bagging observations; it…
K-Means clustering algorithm is one of the most commonly used clustering algorithms because of its simplicity and efficiency. K-Means clustering algorithm based on Euclidean distance only pays attention to the linear distance between…
Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…