Almost Separable Data Aggregation by Layers of Formal Neurons

Information extraction or knowledge discovery from large data sets should be linked to data aggregation process. Data aggregation process can result in a new data representation with decreased number of objects of a given set. A deterministic approach to separable data aggregation means a lesser number of objects without mixing of objects from different categories. A statistical approach is less restrictive and allows for almost separable data aggregation with a low level of mixing of objects from different categories. Layers of formal neurons can be designed for the purpose of data aggregation both in the case of deterministic and statistical approach. The proposed designing method is based on minimization of the of the convex and piecewise linear (CPL) criterion functions

The Shallow and the Deep:A biased introduction to neural networks and old school machine learning

The Shallow and the Deep is a collection of lecture notes that offers an accessible introduction to neural networks and machine learning in general. However, it was clear from the beginning that these notes would not be able to cover this rapidly changing and growing field in its entirety. The focus lies on classical machine learning techniques, with a bias towards classification and regression. Other learning paradigms and many recent developments in, for instance, Deep Learning are not addressed or only briefly touched upon.Biehl argues that having a solid knowledge of the foundations of the field is essential, especially for anyone who wants to explore the world of machine learning with an ambition that goes beyond the application of some software package to some data set. Therefore, The Shallow and the Deep places emphasis on fundamental concepts and theoretical background. This also involves delving into the history and pre-history of neural networks, where the foundations for most of the recent developments were laid. These notes aim to demystify machine learning and neural networks without losing the appreciation for their impressive power and versatility

Efficient piecewise linear classifiers and applications

Supervised learning has become an essential part of data mining for industry, military, science and academia. Classification, a type of supervised learning allows a machine to learn from data to then predict certain behaviours, variables or outcomes. Classification can be used to solve many problems including the detection of malignant cancers, potentially bad creditors and even enabling autonomy in robots. The ability to collect and store large amounts of data has increased significantly over the past few decades. However, the ability of classification techniques to deal with large scale data has not been matched. Many data transformation and reduction schemes have been tried with mixed success. This problem is further exacerbated when dealing with real time classification in embedded systems. The real time classifier must classify using only limited processing, memory and power resources. Piecewise linear boundaries are known to provide efficient real time classifiers. They have low memory requirements, require little processing effort, are parameterless and classify in real time. Piecewise linear functions are used to approximate non-linear decision boundaries between pattern classes. Finding these piecewise linear boundaries is a difficult optimization problem that can require a long training time. Multiple optimization approaches have been used for real time classification, but can lead to suboptimal piecewise linear boundaries. This thesis develops three real time piecewise linear classifiers that deal with large scale data. Each classifier uses a single optimization algorithm in conjunction with an incremental approach that reduces the number of points as the decision boundaries are built. Two of the classifiers further reduce complexity by augmenting the incremental approach with additional schemes. One scheme uses hyperboxes to identify points inside the so-called “indeterminate” regions. The other uses a polyhedral conic set to identify data points lying on or close to the boundary. All other points are excluded from the process of building the decision boundaries. The three classifiers are applied to real time data classification problems and the results of numerical experiments on real world data sets are reported. These results demonstrate that the new classifiers require a reasonable training time and their test set accuracy is consistently good on most data sets compared with current state of the art classifiers.Doctor of Philosoph

Computing on Vertices in Data Mining

The main challenges in data mining are related to large, multi-dimensional data sets. There is a need to develop algorithms that are precise and efficient enough to deal with big data problems. The Simplex algorithm from linear programming can be seen as an example of a successful big data problem solving tool. According to the fundamental theorem of linear programming the solution of the optimization problem can found in one of the vertices in the parameter space. The basis exchange algorithms also search for the optimal solution among finite number of the vertices in the parameter space. Basis exchange algorithms enable the design of complex layers of classifiers or predictive models based on a small number of multivariate data vectors