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Full-Text Articles in Data Science

Modeling Cyber Situational Awareness Through Data Fusion, Evan L. Raulerson Mar 2013

Modeling Cyber Situational Awareness Through Data Fusion, Evan L. Raulerson

Theses and Dissertations

Cyber attacks are compromising networks faster than administrators can respond. Network defenders are unable to become oriented with these attacks, determine the potential impacts, and assess the damages in a timely manner. Since the observations of network sensors are normally disjointed, analysis of the data is overwhelming and time is not spent efficiently. Automation in defending cyber networks requires a level of reasoning for adequate response. Current automated systems are mostly limited to scripted responses. Better defense tools are required. This research develops a framework that aggregates data from heterogeneous network sensors. The collected data is correlated into a single …


Hyperspectral Image Classification Using A Spectral-Spatial Sparse Coding Model, Ender Oguslu, Guoqing Zhou, Jiang Li, Lorenzo Bruzzone (Ed.) Jan 2013

Hyperspectral Image Classification Using A Spectral-Spatial Sparse Coding Model, Ender Oguslu, Guoqing Zhou, Jiang Li, Lorenzo Bruzzone (Ed.)

Electrical & Computer Engineering Faculty Publications

We present a sparse coding based spectral-spatial classification model for hyperspectral image (HSI) datasets. The proposed method consists of an efficient sparse coding method in which the l1/lq regularized multi-class logistic regression technique was utilized to achieve a compact representation of hyperspectral image pixels for land cover classification. We applied the proposed algorithm to a HSI dataset collected at the Kennedy Space Center and compared our algorithm to a recently proposed method, Gaussian process maximum likelihood (GP-ML) classifier. Experimental results show that the proposed method can achieve significantly better performances than the GP-ML classifier when training data …


Divad: A Dynamic And Interactive Visual Analytical Dashboard For Exploring And Analyzing Transport Data, Tin Seong Kam, Ketan Barshikar, Shaun Jun Hua Tan Nov 2012

Divad: A Dynamic And Interactive Visual Analytical Dashboard For Exploring And Analyzing Transport Data, Tin Seong Kam, Ketan Barshikar, Shaun Jun Hua Tan

Research Collection School Of Computing and Information Systems

The advances in location-based data collection technologies such as GPS, RFID etc. and the rapid reduction of their costs provide us with a huge and continuously increasing amount of data about movement of vehicles, people and goods in an urban area. This explosive growth of geospatially-referenced data has far outpaced the planner’s ability to utilize and transform the data into insightful information thus creating an adverse impact on the return on the investment made to collect and manage this data. Addressing this pressing need, we designed and developed DIVAD, a dynamic and interactive visual analytics dashboard to allow city planners …


Maximizing Network Lifetime On The Line With Adjustable Sensing Ranges, Amotz Bar-Noy, Ben Baumer Feb 2012

Maximizing Network Lifetime On The Line With Adjustable Sensing Ranges, Amotz Bar-Noy, Ben Baumer

Statistical and Data Sciences: Faculty Publications

Given n sensors on a line, each of which is equipped with a unit battery charge and an adjustable sensing radius, what schedule will maximize the lifetime of a network that covers the entire line? Trivially, any reasonable algorithm is at least a 1/2-approximation, but we prove tighter bounds for several natural algorithms. We focus on developing a linear time algorithm that maximizes the expected lifetime under a random uniform model of sensor distribution. We demonstrate one such algorithm that achieves an average-case approximation ratio of almost 0.9. Most of the algorithms that we consider come from a family based …


Parsing The Relationship Between Baserunning And Batting Abilities Within Lineups, Ben S. Baumer, James Piette, Brad Null Jan 2012

Parsing The Relationship Between Baserunning And Batting Abilities Within Lineups, Ben S. Baumer, James Piette, Brad Null

Statistical and Data Sciences: Faculty Publications

A baseball team's offensive prowess is a function of two types of abilities: batting and baserunning. While each has been studied extensively in isolation, the effects of their interaction is not well understood. We model offensive output as a scalar function f of an individual player's batting and baserunning profile z. Each of these profiles is in turn estimated from Retrosheet data using heirarchical Bayesian models. We then use the SimulOutCome simulation engine as a method to generate values of f(z) over a fine grid of points. Finally, for each of several methods of taking the extra base, we graphically …


Model Individualization For Real-Time Operator Functional State Assessment, Guangfan Zhang, Roger Xu, Wei Wang, Aaron A. Pepe, Feng Li, Jiang Li, Frederick Mckenzie, Tom Schnell, Nick Anderson, Dean Heitkamp Jan 2012

Model Individualization For Real-Time Operator Functional State Assessment, Guangfan Zhang, Roger Xu, Wei Wang, Aaron A. Pepe, Feng Li, Jiang Li, Frederick Mckenzie, Tom Schnell, Nick Anderson, Dean Heitkamp

Electrical & Computer Engineering Faculty Publications

Proper assessment of Operator Functional State (OFS) and appropriate workload modulation offer the potential to improve mission effectiveness and aviation safety in both overload and under-load conditions. Although a wide range of research has been devoted to building OFS assessment models, most of the models are based on group statistics and little or no research has been directed towards model individualization, i.e., tuning the group statistics based model for individual pilots. Moreover, little emphasis has been placed on monitoring whether the pilot is disengaged during low workload conditions. The primary focus of this research is to provide a real-time engagement …


Real-Time Anomaly Detection In Full Motion Video, Glenn Konowicz,, Jiang Li, Donnie Self (Ed.) Jan 2012

Real-Time Anomaly Detection In Full Motion Video, Glenn Konowicz,, Jiang Li, Donnie Self (Ed.)

Electrical & Computer Engineering Faculty Publications

Improvement in sensor technology such as charge-coupled devices (CCD) as well as constant incremental improvements in storage space has enabled the recording and storage of video more prevalent and lower cost than ever before. However, the improvements in the ability to capture and store a wide array of video have required additional manpower to translate these raw data sources into useful information. We propose an algorithm for automatically detecting anomalous movement patterns within full motion video thus reducing the amount of human intervention required to make use of these new data sources. The proposed algorithm tracks all of the objects …


Contributions Of Financial Sector Reforms And Credit Supply To Nigerian Agricultural Sector (1978-2009), Anthony O. Onoja, M. E. Onu, S. Ajodo-Ohiemi Dec 2011

Contributions Of Financial Sector Reforms And Credit Supply To Nigerian Agricultural Sector (1978-2009), Anthony O. Onoja, M. E. Onu, S. Ajodo-Ohiemi

CBN Journal of Applied Statistics (JAS)

This study analyzed the trends and pattern of institutional credit supply to agriculture during pre- and post-financial reforms along with their determinants. It then compared the effects of reform policies on access to institutional credits in Nigerian agricultural sector before and after the reforms (1978 - 1985; and 1986 -2009). Relying mainly on time series data from CBN and NBS, it used ordinary least squares method (linear, semi-log and double log) to model the determinants of banking sector lending to the agricultural sector during the review period. The models were subjected to several econometric tests before accepting one. Chow test …


Determinants Of Foreign Reserves In Nigeria: An Autoregressive Distributed Lag Approach, David Irefin, Baba N. Yaaba Dec 2011

Determinants Of Foreign Reserves In Nigeria: An Autoregressive Distributed Lag Approach, David Irefin, Baba N. Yaaba

CBN Journal of Applied Statistics (JAS)

On global scale, central banks’ holdings of foreign reserves have escalated sharply in recent years. World international reserves holdings have risen significantly from US$1.2 trillion in 1995 to nearly US$10.0 trillion in June 2011. Dominant among these reserves are concentrated in the hands of few countries. Ten major holders of foreign reserves are mostly from Asia. Oil exporting countries in Africa and the Middle East are not left out in this trend. Nigeria’s foreign reserves rose from US$5.5 billion in 1999 to US$62.40 billion in July 2008, making Nigeria the twenty-fourth largest reserves holder in the world. This pace of …


Effects Of Exchange Rate Movements On Economic Growth In Nigeria, Eme O. Akpan, Johnson A. Atan Dec 2011

Effects Of Exchange Rate Movements On Economic Growth In Nigeria, Eme O. Akpan, Johnson A. Atan

CBN Journal of Applied Statistics (JAS)

This study investigates the effect of exchange rate movements on real output growth in Nigeria. Based on quarterly series for the period 1986 to 2010, the paper examines the possible direct and indirect relationship between exchange rates and GDP growth. The relationship is derived in two ways using a simultaneous equations model within a fully specified (but small) macroeconomic model. A Generalised Method of Moments (GMM) technique was explored. The estimation results suggest that there is no evidence of a strong direct relationship between changes in exchange rate and output growth. Rather, Nigeria’s economic growth has been directly affected by …


Exchange Rate Volatility In Nigeria: Consistency, Persistency & Severity Analyses, Babatunde Adeoye, Akinwande A. Atanda Dec 2011

Exchange Rate Volatility In Nigeria: Consistency, Persistency & Severity Analyses, Babatunde Adeoye, Akinwande A. Atanda

CBN Journal of Applied Statistics (JAS)

The adoption of the International Monetary Fund (IMF) Structural Adjustment Programme (SAP) in 1986 resulted in the transition from fixed exchange rate regime to floating exchange rate regime in Nigeria. Ever since, the exchange rate of naira vis-à-vis the U.S dollar has attained varying rates all through different time horizons. On this basis, this study examines the consistency, persistency, and severity (degree) of volatility in exchange rate of Nigerian currency (naira) vis-a-vis the United State dollar using monthly time series data from 1986 to 2008. The standard Purchasing Power Parity (PPP) model was used to analyze the long-run consistency of …


Foreign Private Investment And Economic Growth In Nigeria: A Cointegrated Var And Granger Causality Analysis, F. Z. Abdullahi, S. Ladan, Haruna R. Bakari Dec 2011

Foreign Private Investment And Economic Growth In Nigeria: A Cointegrated Var And Granger Causality Analysis, F. Z. Abdullahi, S. Ladan, Haruna R. Bakari

CBN Journal of Applied Statistics (JAS)

This research uses a cointegration VAR model to study the contemporaneous long-run dynamics of the impact of Foreign Private Investment (FPI), Interest Rate (INR) and Inflation rate (IFR) on Growth Domestic Products (GDP) in Nigeria for the period January 1970 to December 2009. The Unit Root Test suggests that all the variables are integrated of order 1. The VAR model was appropriately identified using AIC information criteria and the VECM model has exactly one cointegration relation. The study further investigates the causal relationship using the Granger causality analysis of VECM which indicates a uni-directional causality relationship between GDP and FDI …


Banking Sector Credit And Economic Growth In Nigeria: An Empirical Investigation, Aniekan O. Akpansung, Sikiru J. Babalola Dec 2011

Banking Sector Credit And Economic Growth In Nigeria: An Empirical Investigation, Aniekan O. Akpansung, Sikiru J. Babalola

CBN Journal of Applied Statistics (JAS)

The paper examines the relationship between banking sector credit and economic growth in Nigeria over the period 1970-2008. The causal links between the pairs of variables of interest were established using Granger causality test while a Two-Stage Least Squares (TSLS) estimation technique was used for the regression models. The results of Granger causality test show evidence of unidirectional causal relationship from GDP to private sector credit (PSC) and from industrial production index (IND) to GDP. Estimated regression models indicate that private sector credit impacts positively on economic growth over the period of coverage in this study. However, lending (interest) rate …


Networks - Ii: A Survey Of Data Management Issues & Frameworks For Mobile Ad Hoc Networks, Noman Islam, Zubair A. Shaikh Jul 2011

Networks - Ii: A Survey Of Data Management Issues & Frameworks For Mobile Ad Hoc Networks, Noman Islam, Zubair A. Shaikh

International Conference on Information and Communication Technologies

Data Management is the execution of a pool of activities on a set of data to conform to the end user data requisitions. MANET is an emerging discipline of computer networks in which a group of roaming hosts spontaneously establishes the network among themselves. The employment of data management in MANET can engender a number of useful applications. However, data management in MANET is a taxing job as it requires deliberation on a number of research issues (e.g. knowledge representation, knowledge discovery, caching, and security etc.). This paper provides a detailed account of the data management problem and its issues, …


Mapsnap System To Perform Vector-To-Raster Fusion, Boris Kovalerchuk, Peter Doucette, Gamal Seedahmed, Jerry Tagestad, Sergei Kovalerchuk, Brian Graff May 2011

Mapsnap System To Perform Vector-To-Raster Fusion, Boris Kovalerchuk, Peter Doucette, Gamal Seedahmed, Jerry Tagestad, Sergei Kovalerchuk, Brian Graff

All Faculty Scholarship for the College of the Sciences

As the availability of geospatial data increases, there is a growing need to match these datasets together. However, since these datasets often vary in their origins and spatial accuracy, they frequently do not correspond well to each other, which create multiple problems. To accurately align with imagery, analysts currently either: 1) manually move the vectors, 2) perform a labor-intensive spatial registration of vectors to imagery, 3) move imagery to vectors, or 4) redigitize the vectors from scratch and transfer the attributes. All of these are time consuming and labor-intensive operations. Automated matching and fusing vector datasets has been a subject …


Semi-Automatic Management Of Knowledge Bases Using Formal Ontologies, Andreas Textor Jan 2011

Semi-Automatic Management Of Knowledge Bases Using Formal Ontologies, Andreas Textor

Theses

This thesis presents an approach that deals with the ever-growing amount of data in knowledge bases, especially concerning knowledge interoperability and formal representation of domain knowledge. There arc multiple issues that must be addressed with current systems. A multitude of different formats, sources and tools exist in a domain, and it is desirable to develop their use further towards a standardised environment. Such an environment should support both the representation and processing of data from this domain, and the connection to other domains, where necessary. In order to manage large amounts of data, it should be possible to perform whatever …


Extreme Data Mining: Inference From Small Datasets, Răzvan Andonie Sep 2010

Extreme Data Mining: Inference From Small Datasets, Răzvan Andonie

All Faculty Scholarship for the College of the Sciences

Neural networks have been applied successfully in many fields. However, satisfactory results can only be found under large sample conditions. When it comes to small training sets, the performance may not be so good, or the learning task can even not be accomplished. This deficiency limits the applications of neural network severely. The main reason why small datasets cannot provide enough information is that there exist gaps between samples, even the domain of samples cannot be ensured. Several computational intelligence techniques have been proposed to overcome the limits of learning from small datasets.

We have the following goals: i. To …


Data Mining: Assessment Of Features Quality Of Class Discrimination Using Arif Index And Its Application To Physiological Datasets, Dr. Muhammad Arif, A. Fida Aug 2009

Data Mining: Assessment Of Features Quality Of Class Discrimination Using Arif Index And Its Application To Physiological Datasets, Dr. Muhammad Arif, A. Fida

International Conference on Information and Communication Technologies

Quality of features determines the maximum achievable accuracy by any arbitrary classifier in pattern classification problem. In this paper, we have proposed an index that can assess the quality of features in discrimination of patterns in different classes. This index is in-sensitive to the complexity of boundary separating different classes if there is no overlap among features of different classes. Proposed index is model free and requires no clustering algorithm to discover the clustering structure present in the feature space. It is only based on the information of local neighborhood of feature vectors in the feature space. This index can …


Data Mining: Analyzing Impact Of Outliers' Detection And Removal From The Test Sample In Blind Source Extraction Using Multivariate Calibration Techniques, S. R. Naqvi, F. Rehman, S. S. Naqvi, A. Amin, I. Qayyum, S. Khan, W. A. Khan Aug 2009

Data Mining: Analyzing Impact Of Outliers' Detection And Removal From The Test Sample In Blind Source Extraction Using Multivariate Calibration Techniques, S. R. Naqvi, F. Rehman, S. S. Naqvi, A. Amin, I. Qayyum, S. Khan, W. A. Khan

International Conference on Information and Communication Technologies

Blind source extraction (BSE) may be an essential but a challenging task where multiple sources are convolved and/or time delayed. In this article we discuss the performance of multivariate calibration techniques that comprise of classical least square (CLS), inverse linear regression (ILS), principal component regression (PCR) and partial least square regression (PLS) in achieving this task in robust speech recognition systems with varying signal-to-noise ratios (SNR). We specifically analyze two methods for identifying and removing outliers from the sample, namely; outlier sample removal (OSR) and descriptor selection (DS) for classical least square and factor Based regression respectively, which results in …


Artificial Intelligence – I: A Two-Step Approach For Improving Efficiency Of Feedforward Multilayer Perceptrons Network, Shoukat Ullah, Zakia Hussain Aug 2009

Artificial Intelligence – I: A Two-Step Approach For Improving Efficiency Of Feedforward Multilayer Perceptrons Network, Shoukat Ullah, Zakia Hussain

International Conference on Information and Communication Technologies

An artificial neural network has got greater importance in the field of data mining. Although it may have complex structure, long training time, and uneasily understandable representation of results, neural network has high accuracy and is preferable in data mining. This research paper is aimed to improve efficiency and to provide accurate results on the basis of same behaviour data. To achieve these objectives, an algorithm is proposed that uses two data mining techniques, that is, attribute selection method and cluster analysis. The algorithm works by applying attribute selection method to eliminate irrelevant attributes, so that input dimensionality is reduced …


Information Brokerage - A New Approach Using Knowledge Management, Robert Loew Jan 2009

Information Brokerage - A New Approach Using Knowledge Management, Robert Loew

Theses

Traditional knowledge management attempts to store the total enterprise knowledge into IT related structures, but knowledge management strategies should focus also on people and organisations and not just on technology.

This can be addressed in part by communicating knowledge between people, in and across organisations. Such communication focuses on the development and exchange of people’s experience.

This thesis introduces a hybrid knowledge management solution consisting of an automated system that includes people: employees, experts and Knowledge Brokers (KB). The hybrid concept supports the identification of suitable people for certain topics of discussion. Further, it supports the knowledge communication process by …


Object Reuse And Exchange, Michael L. Nelson, Carl Lagoze, Herbert Van De Sompel, Pete Johnston, Robert Sanderson, Simeon Warner, Jürgen Sieck (Ed.), Michael A. Herzog (Ed.) Jan 2009

Object Reuse And Exchange, Michael L. Nelson, Carl Lagoze, Herbert Van De Sompel, Pete Johnston, Robert Sanderson, Simeon Warner, Jürgen Sieck (Ed.), Michael A. Herzog (Ed.)

Computer Science Faculty Publications

The Open Archives Object Reuse and Exchange (OAI-ORE) project defines standards for the description and exchange of aggregations of Web resources. The OAI-ORE abstract data model is conformant with the Architecture of the World Wide Web and leverages concepts from the Semantic Web, including RDF descriptions and Linked Data. In this paper we provide a brief review of a motivating example and its serialization in Atom.


Symbolic Methodology For Numeric Data Mining, Boris Kovalerchuk, Engenii Vityaev Apr 2008

Symbolic Methodology For Numeric Data Mining, Boris Kovalerchuk, Engenii Vityaev

All Faculty Scholarship for the College of the Sciences

Currently statistical and artificial neural network methods dominate in data mining applications. Alternative relational (symbolic) data mining methods have shown their effectiveness in robotics, drug design, and other areas. Neural networks and decision tree methods have serious limitations in capturing relations that may have a variety of forms. Learning systems based on symbolic first-order logic (FOL) representations capture relations naturally. The learned regularities are understandable directly in domain terms that help to build a domain theory. This paper describes relational data mining methodology and develops it further for numeric data such as financial and spatial data. This includes (1) comparing …


Relational Methodology For Data Mining And Knowledge Discovery, Engenii Vityaev, Boris Kovalerchuk Apr 2008

Relational Methodology For Data Mining And Knowledge Discovery, Engenii Vityaev, Boris Kovalerchuk

All Faculty Scholarship for the College of the Sciences

Knowledge discovery and data mining methods have been successful in many domains. However, their abilities to build or discover a domain theory remain unclear. This is largely due to the fact that many fundamental KDD&DM methodological questions are still unexplored such as (1) the nature of the information contained in input data relative to the domain theory, and (2) the nature of the knowledge that these methods discover. The goal of this paper is to clarify methodological questions of KDD&DM methods. This is done by using the concept of Relational Data Mining (RDM), representative measurement theory, an ontology of a …


Ldne: A Program For Estimating Effective Population Size From Data On Linkage Disequilibrium, Robin Waples, Chi Do Jan 2008

Ldne: A Program For Estimating Effective Population Size From Data On Linkage Disequilibrium, Robin Waples, Chi Do

United States Department of Commerce: Staff Publications

LDNE is a program with a Visual Basic interface that implements a recently developed bias correction for estimates of effective population size (Ne) based on linkage disequilibrium data. The program reads genotypic data in standard formats and can accommodate an arbitrary number of samples, individuals, loci, and alleles, as well as two mating systems: random and lifetime monogamy. LDNE calculates separate estimates using different criteria for excluding rare alleles, which facilitates evaluation of data for highly polymorphic markers such as microsatellites. The program also introduces a jackknife method for obtaining confidence intervals that appears to perform better …


Methods And System For Equalizing Data, Jaiganesh Balakrishnan, Richard K. Martin, C. Richard Johnson Jr. Dec 2007

Methods And System For Equalizing Data, Jaiganesh Balakrishnan, Richard K. Martin, C. Richard Johnson Jr.

AFIT Patents

A method for equalizing data and systems utilizing the method. The method of this invention for equalizing (by shortening the channel response) data includes minimizing a function of the data and a number of equalizer characteristic parameters, where the function utilizes auto-correlation data corresponding to equalized data. Updated equalizer characteristic parameters are then obtained from the minimization and an initial set of equalizer characteristic parameters. Finally, the received data is processed utilizing the equalizer defined by the minimization. The method of this invention can be implemented in an equalizer and the equalizer of this invention may be included in a …


Distributed Cluster-Based Outlier Detection In Wireless Sensor Networks, Swetha Gali Oct 2007

Distributed Cluster-Based Outlier Detection In Wireless Sensor Networks, Swetha Gali

Electrical & Computer Engineering Theses & Dissertations

Wireless sensor networks find several potential applications in a variety of fields, such as environmental monitoring and control, battlefields, surveillance, smart buildings, human health monitoring, etc. These sensor networks consist of a large number of very tiny, inexpensive, and low power sensor nodes, which are deployed in a variety of harsh environments that may result in the sensor data getting corrupted. It is thus critical to detect and report these abnormal values in the sensor data, in order to have a better understanding of the monitored environment. Detection of the abnormal values is of special interest for the sensor network …


A Day In The Life Of Pubmed: Analysis Of A Typical Day's Query Log, Jorge R Herskovic, Len Y Tanaka, William Hersh, Elmer V Bernstam Mar 2007

A Day In The Life Of Pubmed: Analysis Of A Typical Day's Query Log, Jorge R Herskovic, Len Y Tanaka, William Hersh, Elmer V Bernstam

Faculty, Staff and Student Publications

OBJECTIVE: To characterize PubMed usage over a typical day and compare it to previous studies of user behavior on Web search engines. DESIGN: We performed a lexical and semantic analysis of 2,689,166 queries issued on PubMed over 24 consecutive hours on a typical day. MEASUREMENTS: We measured the number of queries, number of distinct users, queries per user, terms per query, common terms, Boolean operator use, common phrases, result set size, MeSH categories, used semantic measurements to group queries into sessions, and studied the addition and removal of terms from consecutive queries to gauge search strategies. RESULTS: The size of …


Exploration Of Computational Methods For Classification Of Movement Intention During Human Voluntary Movement From Single Trial Eeg, Ou Bai, Peter Lin, Sherry Vorbach, Jiang Li, Steve Furlani, Mark Hallett Jan 2007

Exploration Of Computational Methods For Classification Of Movement Intention During Human Voluntary Movement From Single Trial Eeg, Ou Bai, Peter Lin, Sherry Vorbach, Jiang Li, Steve Furlani, Mark Hallett

Electrical & Computer Engineering Faculty Publications

Objective: To explore effective combinations of computational methods for the prediction of movement intention preceding the production of self-paced right and left hand movements from single trial scalp electroencephalogram (EEG).

Methods: Twelve naïve subjects performed self-paced movements consisting of three key strokes with either hand. EEG was recorded from 128 channels. The exploration was performed offline on single trial EEG data. We proposed that a successful computational procedure for classification would consist of spatial filtering, temporal filtering, feature selection, and pattern classification. A systematic investigation was performed with combinations of spatial filtering using principal component analysis (PCA), independent component analysis …


Dimensionality Reduction Using Non-Linear Principal Components Analysis, Tara Singh Jul 2006

Dimensionality Reduction Using Non-Linear Principal Components Analysis, Tara Singh

Electrical & Computer Engineering Theses & Dissertations

Advances in data collection and storage capabilities during the past decades have led to an information overload in most sciences. Traditional statistical methods break down partly because of the increase in the number of observations, but mostly because of the increase in the number of variables associated with each observation. While certain methods can construct predictive models with high accuracy from high-dimensional data, it is still of interest in many applications to reduce the dimension of the original data prior to any modeling of the data. Patterns in the data can be hard to find in data of high dimensionality, …