Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors

This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in absolute frequencies of the outcomes of N identical von Neumann projective measurements performed on N identically prepared three-level systems. Various small values of N as well as the large-N limit are considered. Two kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; the other represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. In a companion paper the case of measurement data consisting in average values, and an additional prior studied by Slater, are considered.Comment: 23 pages, 14 figures. V2: Added an important note concerning cylindrical algebraic decomposition and thanks to P B Slater, corrected some typos, added reference

Deep Hashing for Image Similarity Search

Hashing for similarity search is one of the most widely used methods to solve the approximate nearest neighbor search problem. In this method, one first maps data items from a real valued high-dimensional space to a suitable low dimensional binary code space and then performs the approximate nearest neighbor search in this code space instead. This is beneficial because the search in the code space can be solved more efficiently in terms of runtime complexity and storage consumption. Obviously, for this method to succeed, it is necessary that similar data items be mapped to binary code words that have small Hamming distance. For real-world data such as images, one usually proceeds as follows. For each data item, a pre-processing algorithm removes noise and insignificant information and extracts important discriminating information to generate a feature vector that captures the important semantic content. Next, a vector hash function maps this real valued feature vector to a binary code word. It is also possible to use the raw feature vectors afterwards to further process the search result candidates produced by binary hash codes. In this dissertation we focus on the following. First, developing a learning based counterpart for the MinHash hashing algorithm. Second, presenting a new unsupervised hashing method UmapHash to map the neighborhood relations of data items from the feature vector space to the binary hash code space. Finally, an application of the aforementioned hashing methods for rapid face image recognition

A weighted regional voting based ensemble of multiple classifiers for face recognition.

Face recognition is heavily studied for its wide range of application in areas such as information security, law enforcement, surveillance of the environment, entertainment, smart cards, etc. Competing techniques have been proposed in computer vision conferences and journals, no algorithm has emerged as superior in all cases over the last decade. In this work, we developed a framework which can embed all available algorithms and achieve better results in all cases over the algorithms that we have embedded, without great sacrifice in time complexity. We build on the success of a recently raised concept - Regional Voting. The new system adds weights to different regions of the human face. Different methods of cooperation among algorithms are also proposed. Extensive experiments, carried out on benchmark face databases, show the proposed system's joint contribution from multiple algorithms is faster and more accurate than Regional Voting in every case. --P. ix.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b180553