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PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The…
We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or…
Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
Hough transform is a popular low-level computer vision algorithm. Its computationally effective modification, Fast Hough transform (FHT), makes use of special subsets of image matrix to approximate geometric lines on it. Because of their…
Face recognition is the very significant field in pattern recognition area. It has multiple applications in military and finance, to name a few. In this paper, the combination of the sparse PCA with the nearest-neighbor method (and with the…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite…
In this paper, we propose an efficient numerical scheme for solving some large scale ill-posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited.…
Modern CAPTCHAs rely heavily on vision tasks that are supposedly hard for computers but easy for humans. However, advances in image recognition models pose a significant threat to such CAPTCHAs. These models can easily be fooled by…
Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
Discrete entropy estimation is a classic information theory problem, wherein the average information content of a discrete random variable is estimated from samples alone. Naive approaches, such as the plugin method, fail to account for the…
The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use as an anomaly detection technique. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by…
In this paper, we introduce a new technique that combines two popular methods to estimate uncertainty in object detection. Quantifying uncertainty is critical in real-world robotic applications. Traditional detection models can be ambiguous…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…