Related papers: Optimized Cartesian $K$-Means

Computational optical imaging (COI) systems have enabled the acquisition of high-dimensional signals through optical coding elements (OCEs). OCEs encode the high-dimensional signal in one or more snapshots, which are subsequently decoded…

Approximate K nearest neighbor (AKNN) search is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations…

High dimensionality, i.e. data having a large number of variables, tends to be a challenge for most machine learning tasks, including classification. A classifier usually builds a model representing how a set of inputs explain the outputs.…

Zeroth-order optimization addresses problems where gradient information is inaccessible or impractical to compute. While most existing methods rely on first-order approximations, incorporating second-order (curvature) information can, in…

Hashing is at the heart of large-scale image similarity search, and recent methods have been substantially improved through deep learning techniques. Such algorithms typically learn continuous embeddings of the data. To avoid a subsequent…

Most natural language processing tasks can be formulated as the approximated nearest neighbor search problem, such as word analogy, document similarity, machine translation. Take the question-answering task as an example, given a question…

Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…

Sequence classification algorithms, such as SVM, require a definition of distance (similarity) measure between two sequences. A commonly used notion of similarity is the number of matches between $k$-mers ($k$-length subsequences) in the…

In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…

High-dimensional Nearest Neighbor (NN) search is central in multimedia search systems. Product Quantization (PQ) is a widespread NN search technique which has a high performance and good scalability. PQ compresses high-dimensional vectors…

We introduce a new variant of the nearest neighbor search problem, which allows for some coordinates of the dataset to be arbitrarily corrupted or unknown. Formally, given a dataset of $n$ points $P=\{ x_1,\ldots, x_n\}$ in high-dimensions,…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an…

Product measures of dimension $n$ are known to be concentrated in Hamming distance: for any set $S$ in the product space of probability $\epsilon$, a random point in the space, with probability $1-\delta$, has a neighbor in $S$ that is…

With explosive growth of data volume and ever-increasing diversity of data modalities, cross-modal similarity search, which conducts nearest neighbor search across different modalities, has been attracting increasing interest. This paper…

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder…

In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time…

In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In…

We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances…

Clustering is a useful data exploratory method with its wide applicability in multiple fields. However, data clustering greatly relies on initialization of cluster centers that can result in large intra-cluster variance and dead centers,…