Resolving the Geometric Locus Dilemma for Support Vector Learning Machines

نویسنده

  • Denise M. Reeves
چکیده

Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus of an algebraic equation is the set of points whose coordinates are solutions of the equation. Any given curve or surface must pass through each point on a specified locus. This paper argues that it is impossible to fit random data points to algebraic equations of partially configured geometric loci that reference arbitrary Cartesian coordinate systems. It also argues that the fundamental curve of a linear decision boundary is actually a principal eigenaxis. It is shown that learning principal eigenaxes of linear decision boundaries involves finding a point of statistical equilibrium for which eigenenergies of principal eigenaxis components are symmetrically balanced with each other. It is demonstrated that learning linear decision boundaries involves strong duality relationships between a statistical eigenlocus of principal eigenaxis components and its algebraic forms, in primal and dual, correlated Hilbert spaces. Locus equations are introduced and developed that describe principal eigen-coordinate systems for lines, planes, and hyperplanes. These equations are used to introduce and develop primal and dual statistical eigenlocus equations of principal eigenaxes of linear decision boundaries. Important generalizations for linear decision boundaries are shown to be encoded within a dual statistical eigenlocus of principal eigenaxis components. Principal eigenaxes of linear decision boundaries are shown to encode Bayes’ likelihood ratio for common covariance data and a robust likelihood ratio for all other data.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Comparative Study of Extreme Learning Machines and Support Vector Machines in Prediction of Sediment Transport in Open Channels

The limiting velocity in open channels to prevent long-term sedimentation is predicted in this paper using a powerful soft computing technique known as Extreme Learning Machines (ELM). The ELM is a single Layer Feed-forward Neural Network (SLFNN) with a high level of training speed. The dimensionless parameter of limiting velocity which is known as the densimetric Froude number (Fr) is predicte...

متن کامل

Mining Biological Repetitive Sequences Using Support Vector Machines and Fuzzy SVM

Structural repetitive subsequences are most important portion of biological sequences, which play crucial roles on corresponding sequence’s fold and functionality. Biggest class of the repetitive subsequences is “Transposable Elements” which has its own sub-classes upon contexts’ structures. Many researches have been performed to criticality determine the structure and function of repetitiv...

متن کامل

Application of Artificial Neural Networks and Support Vector Machines for carbonate pores size estimation from 3D seismic data

This paper proposes a method for the prediction of pore size values in hydrocarbon reservoirs using 3D seismic data. To this end, an actual carbonate oil field in the south-western part ofIranwas selected. Taking real geological conditions into account, different models of reservoir were constructed for a range of viable pore size values.  Seismic surveying was performed next on these models. F...

متن کامل

Fault diagnosis in a distillation column using a support vector machine based classifier

Fault diagnosis has always been an essential aspect of control system design. This is necessary due to the growing demand for increased performance and safety of industrial systems is discussed. Support vector machine classifier is a new technique based on statistical learning theory and is designed to reduce structural bias. Support vector machine classification in many applications in v...

متن کامل

Separating Well Log Data to Train Support Vector Machines for Lithology Prediction in a Heterogeneous Carbonate Reservoir

The prediction of lithology is necessary in all areas of petroleum engineering. This means that to design a project in any branch of petroleum engineering, the lithology must be well known. Support vector machines (SVM’s) use an analytical approach to classification based on statistical learning theory, the principles of structural risk minimization, and empirical risk minimization. In this res...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1511.05102  شماره 

صفحات  -

تاریخ انتشار 2015