There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into a system of ranked taxa: domain, kingdom, phylum, class, etc. Cluster analysis is the formal study of methods and algorithms for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is to find structure in data and is therefore exploratory in nature. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1955. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This speaks to the difficulty in designing a general purpose clustering algorithm and the ill-posed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semi-supervised clustering, ensemble clustering, simultaneous feature selection during data clustering, and large scale data clustering.

Data clustering: 50 years beyond K-means

The practice of classifying objects according to perceived similarities is the basis for much of science. Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms in to taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and methods for grouping objects according to measured or perceived intrinsic characteristics. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes cluster analysis (unsupervised learning) from discriminant analysis (supervised learning). The objective of cluster analysis is to simply find a convenient and valid organization of the data, not to establish rules for separating future data into categories.

/pdf/data-clustering-50-years-beyond-k-means-2sd3ukqpur.pdf

Data Clustering: 50 Years Beyond K-means

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

/pdf/computer-vision-algorithms-and-applications-25dn6wu83j.pdf

Computer Vision: Algorithms and Applications

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

This paper is the nal report of an undergraduate honors thesis project advised by Prof Dennis Hejhal of the School of Mathematics University of Minnesota The main pur pose of this project is to examine the analytic properties of certain quantum mechanical particles in Lobachevsky space The results were obtained on vectorized CRAY serial supercomputers a CRAY CPU T D massively parallel system and a K CPU mas sively parallel system CM located in University of Minnesota Using complex arithmetic we have successfully determined numerous Fourier coe cients for certain types of holo morphic modular forms including the Ramanujan function Our experiments involve both arithmetic and non arithmetic groups The treatment of the latter is new Analyzing the output data enables us to experimentally justify a number of properties Finally a veri cation of a Central Limit Theorem for automorphic functions on Hecke Groups was attempted and very promising results have been obtained Analytic Number Theory Complex Variable and Supercomputers

Analytic Number Theory, Complex Variable and Supercomputers

This chapter describes WBIIS (Wavelet-Based Image Indexing and Searching), an image indexing and retrieval algorithm with partial-sketch image-searching capability for large image databases. We developed WBIIS in 1996 as a first step in image retrieval using wavelets [142]. The SIMPLIcity system (Chapter 8), another wavelet-based image indexing and searching system, has been developed to address the limitations of the WBIIS system.

Wavelet-Based Image Indexing and Searching

Numerical precipitation prediction plays a crucial role in weather forecasting and has broad applications in public services including aviation management and urban disaster early warning systems. However, Numerical Weather Prediction (NWP) models are often constrained by a systematic bias due to coarse spatial resolution, lack of parametrizations and limitations of observation and conventional meteorological models, including constrained sample size and long-tail distribution. To address these issues, we present a data-driven deep learning model, named the Ordinal Distribution Autoencoder (ODA), which principally includes a Precipitation Confidence Network and a combinatorial network that contains two blocks, i.e., a Denoising Autoencoder block and an Ordinal Distribution Regression block. As an expert-free model for bias correction of precipitation, it can effectively correct numerical precipitation prediction based on meteorological data from the European Centre for Medium- Range Weather Forecasts (ECMWF) and SMS-WARMS, an NWP model used in East China. Experiments in the two NWP models demonstrate that, compared with several classical machine learning algorithms and deep learning models, our proposed ODA generally performs better in bias correction.

Robust Precipitation Bias Correction Through an Ordinal Distribution Autoencoder

HCIndex: a Hilbert-Curve-based clustering index for efficient multi-dimensional queries for cloud storage systems

Parameter estimation is a key computational issue in all statistical image modeling techniques. In this paper, we explore a computationally efficient parameter estimation algorithm for multi-dimensional hidden Markov models. 2-D HMM has been applied to supervised aerial image classification and comparisons have been made with the first proposed estimation algorithm. An extensive parametric study has been performed with 3-D HMM and the scalability of the estimation algorithm has been discussed. Results show the great applicability of the explored algorithm to multi-dimensional HMM based image modeling applications.

James Z. Wang

Papers

Analytic Number Theory, Complex Variable and Supercomputers

Wavelet-Based Image Indexing and Searching

Robust Precipitation Bias Correction Through an Ordinal Distribution Autoencoder

HCIndex: a Hilbert-Curve-based clustering index for efficient multi-dimensional queries for cloud storage systems

Parameter estimation of multi-dimensional hidden Markov models - a scalable approach