An unsupervised approach to feature discretization and selection

Many learning problems require handling high dimensional datasets with a relatively small number of instances. Learning algorithms are thus confronted with the curse of dimensionality, and need to address it in order to be effective. Examples of these types of data include the bag-of-words representation in text classification problems and gene expression data for tumor detection/classification. Usually, among the high number of features characterizing the instances, many may be irrelevant (or even detrimental) for the learning tasks. It is thus clear that there is a need for adequate techniques for feature representation, reduction, and selection, to improve both the classification accuracy and the memory requirements. In this paper, we propose combined unsupervised feature discretization and feature selection techniques, suitable for medium and high-dimensional datasets. The experimental results on several standard datasets, with both sparse and dense features, show the efficiency of the proposed techniques as well as improvements over previous related techniques.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Feature Discretization with Relevance and Mutual Information Criteria

Feature discretization (FD) techniques often yield adequate and compact representations of the data, suitable for machine learning and pattern recognition problems. These representations usually decrease the training time, yielding higher classification accuracy while allowing for humans to better understand and visualize the data, as compared to the use of the original features. This paper proposes two new FD techniques. The first one is based on the well-known Linde-Buzo-Gray quantization algorithm, coupled with a relevance criterion, being able perform unsupervised, supervised, or semi-supervised discretization. The second technique works in supervised mode, being based on the maximization of the mutual information between each discrete feature and the class label. Our experimental results on standard benchmark datasets show that these techniques scale up to high-dimensional data, attaining in many cases better accuracy than existing unsupervised and supervised FD approaches, while using fewer discretization intervals.

Markovian versus non-Markovian stochastic quantization of a complex-action model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

COMPRESSIVE QUANTIZATION FOR SCALABLE CLOUD RADIO ACCESS NETWORKS

With the proliferation of new mobile devices and applications, the demand for ubiquitous wireless services has increased dramatically in recent years. The explosive growth in the wireless traffic requires the wireless networks to be scalable so that they can be efficiently extended to meet the wireless communication demands. In a wireless network, the interference power typically grows with the number of devices without necessary coordination among them. On the other hand, large scale coordination is always difficult due to the low-bandwidth and high-latency interfaces between access points (APs) in traditional wireless networks. To address this challenge, cloud radio access network (C-RAN) has been proposed, where a pool of base band units (BBUs) are connected to the distributed remote radio heads (RRHs) via high bandwidth and low latency links (i.e., the front-haul) and are responsible for all the baseband processing. But the insufficient front-haul link capacity may limit the scale of C-RAN and prevent it from fully utilizing the benefits made possible by the centralized baseband processing. As a result, the front-haul link capacity becomes a bottleneck in the scalability of C-RAN. In this dissertation, we explore the scalable C-RAN in the effort of tackling this challenge. In the first aspect of this dissertation, we investigate the scalability issues in the existing wireless networks and propose a novel time-reversal (TR) based scalable wireless network in which the interference power is naturally mitigated by the focusing effects of TR communications without coordination among APs or terminal devices (TDs). Due to this nice feature, it is shown that the system can be easily extended to serve more TDs. Motivated by the nice properties of TR communications in providing scalable wireless networking solutions, in the second aspect of this dissertation, we apply the TR based communications to the C-RAN and discover the TR tunneling effects which alleviate the traffic load in the front-haul links caused by the increment of TDs. We further design waveforming schemes to optimize the downlink and uplink transmissions in the TR based C-RAN, which are shown to improve the downlink and uplink transmission accuracies. Consequently, the traffic load in the front-haul links is further alleviated by the reducing re-transmissions caused by transmission errors. Moreover, inspired by the TR-based C-RAN, we propose the compressive quantization scheme which applies to the uplink of multi-antenna C-RAN so that more antennas can be utilized with the limited front-haul capacity, which provide rich spatial diversity such that the massive TDs can be served more efficiently.

Feature selection environment for genomic applications

Background: Feature selection is a pattern recognition approach to choose important variables according to some criteria in order to distinguish or explain certain phenomena (i.e., for dimensionality reduction). There are many genomic and proteomic applications that rely on feature selection to answer questions such as selecting signature genes which are informative about some biological state, e. g., normal tissues and several types of cancer; or inferring a prediction network among elements such as genes, proteins and external stimuli. In these applications, a recurrent problem is the lack of samples to perform an adequate estimate of the joint probabilities between element states. A myriad of feature selection algorithms and criterion functions have been proposed, although it is difficult to point the best solution for each application. Results: The intent of this work is to provide an open-source multiplataform graphical environment for bioinformatics problems, which supports many feature selection algorithms, criterion functions and graphic visualization tools such as scatterplots, parallel coordinates and graphs. A feature selection approach for growing genetic networks from seed genes ( targets or predictors) is also implemented in the system. Conclusion: The proposed feature selection environment allows data analysis using several algorithms, criterion functions and graphic visualization tools. Our experiments have shown the software effectiveness in two distinct types of biological problems. Besides, the environment can be used in different pattern recognition applications, although the main concern regards bioinformatics tasks.

Voice Feature Characteristic in Morbid Obese Population

Morbid obesity is highly prevalent in the Western World, and its consequences present a real public health challenge. Voice alterations can represent one of these consequences and represent an opportunity for interference with therapeutic methods. This particularly features of the individual`s voice was the goal of the present study. A group of 45 adult volunteers of both sexes with a BMI greater than 35 Kg/m(2) was selected among patients of the Obesity Ambulatory of the Digestive Surgery Division. The control group consisted of volunteers matched by sex, age (+/- 1 year), and smoking habits, but with a BMI bellow 30 Kg/m(2). All subjects were submitted to laryngoscopic examination, audio perceptive analysis, and voice acoustics determination. Examinations were always performed by the same doctor, and diagnoses were provided by two different physician specialists in laryngology and voice. Obese individuals exhibit the following modifications in voice feature: hoarseness, murmuring, vocal instability, altered jitter and shimmer, and reduced maximum phonation times as well the presence of voice strangulation at the end of emission. The voices of individuals with morbid obesity are different of the voice of nonobese people and demonstrate significant changes in vocal characteristics.

Claudin-7 down-regulation is an important feature in oral squamous cell carcinoma

Aims: Claudins, a large family of essential tight junction (TJ) proteins, are abnormally regulated in human carcinomas, especially claudin-7. The aim of this study was to investigate claudin-7 expression and alterations in oral squamous cell carcinoma (OSCC). Methods and results: Expression of claudin-7 was analysed in 132 cases of OSCC organized in a tissue microarray. Claudin-7 mRNA transcript was evaluated using real-time polymerase chain reaction and the methylation status of the promoter was also assessed. Claudin-7 was negative in 58.3% of the cases. Loss of claudin-7 protein expression was associated with recurrence (P = 0.019), tumour size (P = 0.014), clinical stage of OSCC (P = 0.055) and disease-free survival (P = 0.015). Down-regulation of the claudin-7 mRNA transcripts was observed in 78% of the cases, in accordance with immunoexpression. Analysis of the methylation status of the promoter region of claudin-7 revealed that treatment of O28 cells (that did not express claudin-7 mRNA transcripts) with 5-Aza-2`-Deoxycytidine (5-Aza-dC) led to the re-expression of claudin-7 mRNA transcript. Conclusion: Loss of claudin-7 expression is associated with important subcellular processes in OSCC with impact on clinical parameters.

The application of adaptive partitioned random search in feature selection problem

Feature selection is one of important and frequently used techniques in data preprocessing. It can improve the efficiency and the effectiveness of data mining by reducing the dimensions of feature space and removing the irrelevant and redundant information. Feature selection can be viewed as a global optimization problem of finding a minimum set of M relevant features that describes the dataset as well as the original N attributes. In this paper, we apply the adaptive partitioned random search strategy into our feature selection algorithm. Under this search strategy, the partition structure and evaluation function is proposed for feature selection problem. This algorithm ensures the global optimal solution in theory and avoids complete randomness in search direction. The good property of our algorithm is shown through the theoretical analysis.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be 'guessed' from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics II. Application to reflection and refraction at a dielectric interface

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.