Related papers: Dimensionality Invariant Similarity Measure

We design a data-dependent metric in $\mathbb R^d$ and use it to define the $k$-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard $k$-nearest neighbor…

k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has…

Nonparametric learning is a fundamental concept in machine learning that aims to capture complex patterns and relationships in data without making strong assumptions about the underlying data distribution. Owing to simplicity and…

We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…

We propose a novel deep metric learning method. Differently from many works on this area, we defined a novel latent space obtained through an autoencoder. The new space, namely S-space, is divided into different regions that describe the…

Deep Neural Networks(DNN) have excessively advanced the field of computer vision by achieving state of the art performance in various vision tasks. These results are not limited to the field of vision but can also be seen in speech…

Advances in computational power and hardware efficiency have enabled tackling increasingly complex, high-dimensional problems. While artificial intelligence (AI) achieves remarkable results, the interpretability of high-dimensional…

Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…

Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel…

We propose a method for certifying the fairness of the classification result of a widely used supervised learning algorithm, the k-nearest neighbors (KNN), under the assumption that the training data may have historical bias caused by…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

In this note, we present a novel measure of similarity between two functions. It quantifies how the sub-optimality gaps of two functions convert to each other, and unifies several existing notions of functional similarity. We show that it…

Various kinds of k-nearest neighbor (KNN) based classification methods are the bases of many well-established and high-performance pattern-recognition techniques, but both of them are vulnerable to their parameter choice. Essentially, the…

We introduce a class of depth-based classification procedures that are of a nearest-neighbor nature. Depth, after symmetrization, indeed provides the center-outward ordering that is necessary and sufficient to define nearest neighbors. Like…

Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…

An unsupervised learning classification model is described. It achieves classification error probability competitive with that of popular supervised learning classifiers such as SVM or kNN. The model is based on the incremental execution of…

This paper presents an extension and an elaboration of the theory of differential similarity, which was originally proposed in arXiv:1401.2411 [cs.LG]. The goal is to develop an algorithm for clustering and coding that combines a geometric…

We develop a model of perceptual similarity judgment based on re-training a deep convolution neural network (DCNN) that learns to associate different views of each 3D object to capture the notion of object persistence and continuity in our…

The reverse k-nearest neighbor (RkNN) query is an established query type with various applications reaching from identifying highly influential objects over incrementally updating kNN graphs to optimizing sensor communication and outlier…

During the last decades, learning a low-dimensional space with discriminative information for dimension reduction (DR) has gained a surge of interest. However, it's not accessible for these DR methods to achieve satisfactory performance…