Random projections as regularizers: learning a linear discriminant from fewer observations than dimensions

We prove theoretical guarantees for an averaging-ensemble of randomly projected Fisher linear discriminant classifiers, focusing on the casewhen there are fewer training observations than data dimensions. The specific form and simplicity of this ensemble permits a direct and much more detailed analysis than existing generic tools in previous works. In particular, we are able to derive the exact form of the generalization error of our ensemble, conditional on the training set, and based on this we give theoretical guarantees which directly link the performance of the ensemble to that of the corresponding linear discriminant learned in the full data space. To the best of our knowledge these are the first theoretical results to prove such an explicit link for any classifier and classifier ensemble pair. Furthermore we show that the randomly projected ensemble is equivalent to implementing a sophisticated regularization scheme to the linear discriminant learned in the original data space and this prevents overfitting in conditions of small sample size where pseudo-inverse FLD learned in the data space is provably poor. Our ensemble is learned from a set of randomly projected representations of the original high dimensional data and therefore for this approach data can be collected, stored and processed in such a compressed form. We confirm our theoretical findings with experiments, and demonstrate the utility of our approach on several datasets from the bioinformatics domain and one very high dimensional dataset from the drug discovery domain, both settings in which fewer observations than dimensions are the norm

Linear Maximum Margin Classifier for Learning from Uncertain Data

In this paper, we propose a maximum margin classifier that deals with uncertainty in data input. More specifically, we reformulate the SVM framework such that each training example can be modeled by a multi-dimensional Gaussian distribution described by its mean vector and its covariance matrix -- the latter modeling the uncertainty. We address the classification problem and define a cost function that is the expected value of the classical SVM cost when data samples are drawn from the multi-dimensional Gaussian distributions that form the set of the training examples. Our formulation approximates the classical SVM formulation when the training examples are isotropic Gaussians with variance tending to zero. We arrive at a convex optimization problem, which we solve efficiently in the primal form using a stochastic gradient descent approach. The resulting classifier, which we name SVM with Gaussian Sample Uncertainty (SVM-GSU), is tested on synthetic data and five publicly available and popular datasets; namely, the MNIST, WDBC, DEAP, TV News Channel Commercial Detection, and TRECVID MED datasets. Experimental results verify the effectiveness of the proposed method.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence. (c) 2017 IEEE. DOI: 10.1109/TPAMI.2017.2772235 Author's accepted version. The final publication is available at http://ieeexplore.ieee.org/document/8103808

Generalizing, Decoding, and Optimizing Support Vector Machine Classification

The classification of complex data usually requires the composition of processing steps. Here, a major challenge is the selection of optimal algorithms for preprocessing and classification. Nowadays, parts of the optimization process are automized but expert knowledge and manual work are still required. We present three steps to face this process and ease the optimization. Namely, we take a theoretical view on classical classifiers, provide an approach to interpret the classifier together with the preprocessing, and integrate both into one framework which enables a semiautomatic optimization of the processing chain and which interfaces numerous algorithms

Feature Subset Selection in Intrusion Detection Using Soft Computing Techniques

Intrusions on computer network systems are major security issues these days. Therefore, it is of utmost importance to prevent such intrusions. The prevention of such intrusions is entirely dependent on their detection that is a main part of any security tool such as Intrusion Detection System (IDS), Intrusion Prevention System (IPS), Adaptive Security Alliance (ASA), checkpoints and firewalls. Therefore, accurate detection of network attack is imperative. A variety of intrusion detection approaches are available but the main problem is their performance, which can be enhanced by increasing the detection rates and reducing false positives. Such weaknesses of the existing techniques have motivated the research presented in this thesis. One of the weaknesses of the existing intrusion detection approaches is the usage of a raw dataset for classification but the classifier may get confused due to redundancy and hence may not classify correctly. To overcome this issue, Principal Component Analysis (PCA) has been employed to transform raw features into principal features space and select the features based on their sensitivity. The sensitivity is determined by the values of eigenvalues. The recent approaches use PCA to project features space to principal feature space and select features corresponding to the highest eigenvalues, but the features corresponding to the highest eigenvalues may not have the optimal sensitivity for the classifier due to ignoring many sensitive features. Instead of using traditional approach of selecting features with the highest eigenvalues such as PCA, this research applied a Genetic Algorithm (GA) to search the principal feature space that offers a subset of features with optimal sensitivity and the highest discriminatory power. Based on the selected features, the classification is performed. The Support Vector Machine (SVM) and Multilayer Perceptron (MLP) are used for classification purpose due to their proven ability in classification. This research work uses the Knowledge Discovery and Data mining (KDD) cup dataset, which is considered benchmark for evaluating security detection mechanisms. The performance of this approach was analyzed and compared with existing approaches. The results show that proposed method provides an optimal intrusion detection mechanism that outperforms the existing approaches and has the capability to minimize the number of features and maximize the detection rates

Knowledge modeling of phishing emails

This dissertation investigates whether or not malicious phishing emails are detected better when a meaningful representation of the email bodies is available. The natural language processing theory of Ontological Semantics Technology is used for its ability to model the knowledge representation present in the email messages. Known good and phishing emails were analyzed and their meaning representations fed into machine learning binary classifiers. Unigram language models of the same emails were used as a baseline for comparing the performance of the meaningful data. The end results show how a binary classifier trained on meaningful data is better at detecting phishing emails than a unigram language model binary classifier at least using some of the selected machine learning algorithms

Personalized large scale classification of public tenders on hadoop

Ce projet a été réalisé dans le cadre d’un partenariat entre Fujitsu Canada et Université Laval. Les besoins du projets ont été centrés sur une problématique d’affaire définie conjointement avec Fujitsu. Le projet consistait à classifier un corpus d’appels d’offres électroniques avec une approche orienté big data. L’objectif était d’identifier avec un très fort rappel les offres pertinentes au domaine d’affaire de l’entreprise. Après une séries d’expérimentations à petite échelle qui nous ont permise d’illustrer empiriquement (93% de rappel) l’efficacité de notre approche basé sur l’algorithme BNS (Bi-Normal Separation), nous avons implanté un système complet qui exploite l’infrastructure technologique big data Hadoop. Nos expérimentations sur le système complet démontrent qu’il est possible d’obtenir une performance de classification tout aussi efficace à grande échelle (91% de rappel) tout en exploitant les gains de performance rendus possible par l’architecture distribuée de Hadoop.This project was completed as part of an innovation partnership with Fujitsu Canada and Université Laval. The needs and objectives of the project were centered on a business problem defined jointly with Fujitsu. Our project aimed to classify a corpus of electronic public tenders based on state of the art Hadoop big data technology. The objective was to identify with high recall public tenders relevant to the IT services business of Fujitsu Canada. A small scale prototype based on the BNS algorithm (Bi-Normal Separation) was empirically shown to classify with high recall (93%) the public tender corpus. The prototype was then re-implemented on a full scale Hadoop cluster using Apache Pig for the data preparation pipeline and using Apache Mahout for classification. Our experimentation show that the large scale system not only maintains high recall (91%) on the classification task, but can readily take advantage of the massive scalability gains made possible by Hadoop’s distributed architecture