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Subspace clustering is a classical technique that has been widely used for human motion segmentation and other related tasks. However, existing segmentation methods often cluster data without guidance from prior knowledge, resulting in…

In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance…

Clinical outcome prediction from high-dimensional data is problematic in the common setting where there is only a relatively small number of samples. The imbalance causes data overfitting, and outcome prediction becomes computationally…

We search for the best fit in Frobenius norm of $A \in {\mathbb C}^{m \times n}$ by a matrix product $B C^*$, where $B \in {\mathbb C}^{m \times r}$ and $C \in {\mathbb C}^{n \times r}$, $r \le m$ so $B = \{b_{ij}\}$, ($i=1, \dots, m$,~…

Scaling recommendation models into large recommendation models has become one of the most widely discussed topics. Recent efforts focus on components beyond the scaling embedding dimension, as it is believed that scaling embedding may lead…

In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…

Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards…

Multi-scale deep neural networks (MscaleDNNs) with downing-scaling mapping have demonstrated superiority over traditional DNNs in approximating target functions characterized by high frequency features. However, the performance of…

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…

In this paper, we address the problem of measuring and analysing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: the sensation of the stimulus is evaluated via relative judgments…

Unsupervised Deep Distance Metric Learning (UDML) aims to learn sample similarities in the embedding space from an unlabeled dataset. Traditional UDML methods usually use the triplet loss or pairwise loss which requires the mining of…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

With the recent development of technology, wireless sensor networks (WSN) are becoming an important part of many applications. Knowing the exact location of each sensor in the network is very important issue. Therefore, the localization…

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…

We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating…

We consider the \emph{exact} error correction of a noisy Euclidean distance matrix, EDM, where the elements are the squared distances between $n$ points in $R^d$. For our problem we are given two facts: (i) the embedding dimension, $d$,…

In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…

We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces…

Distance metric learning (DML) is to learn the embeddings where examples from the same class are closer than examples from different classes. It can be cast as an optimization problem with triplet constraints. Due to the vast number of…

Estimating causal treatment effects in observational settings is frequently compromised by selection bias arising from unobserved confounders. While traditional econometric methods struggle when these confounders are orthogonal to…