Tuesday, September 11, 2007
Monday, September 10, 2007
Types of Learning
ANN Classification is an example of Supervised Learning. Known class labels help indicate whether the system is performing correctly or not. This information can be used to indicate a desired response, validate the accuracy of the system, or be used to help the system learn to behave correctly.
Clustering is an example of Unsupervised Learning where the class labels are not presented to the system that is trying to discover the natural classes in a dataset. Clustering often fails to find known classes because the distinction between the classes can be obscured by the large number of features (genes) which are uncorrelated with the classes.
Sunday, September 9, 2007
- The neocognitron, proposed by Fukushima (1980), is a hierarchical multi layered neural network capable of robust visual pattern recognition through learning.
- The lowest stage is the input layer consisting of two-dimensional array of cells, which correspond to photo receptors of the retina.
- The retina is a multi-layered sensory tissue that lines the back of the eye.
- It contains millions of photoreceptors that capture light rays and convert them into electrical impulses. These impulses travel along the optic nerve to the brain where they are turned into images.
- There are two types of photoreceptors in the retina: rods and cones. The retina contains approximately 6 million cones. The cones are contained in the macula, the portion of the retina responsible for central vision
- Cones function best in bright light and allow us to appreciate color.
- There are approximately 125 million rods. They are spread throughout the peripheral retina and function best in dim lighting.
- The rods are responsible for peripheral and night vision.
Wednesday, September 5, 2007
A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively
Eykhoff (1974) defined a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'.
Examples of mathematical models
Model of rational behavior for a consumer. In this model we assume a consumer faces a choice of n commodities labelled 1,2,...,n each with a market price p1, p2,..., pn. The consumer is assumed to have a cardinal utility function U (cardinal in the sense that it assigns numerical values to utilities), depending on the amounts of commodities x1, x2,..., xn consumed. The model further assumes that the consumer has a budget M which she uses to purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn). The problem of rational behavior in this model then becomes an optimization problem, that is:
Classification of mathematical models
Mathematical models can be classified in several ways, some of which are described below.
1.Linear vs. nonlinear: Mathematical models are usually composed by variables, which are abstractions of quantities of interest in the described systems, and operators that act on these variables, which can be algebraic operators, functions, differential operators, etc. If all the operators in a mathematical model present linearity, the resulting mathematical model is defined as linear. A model is considered to be nonlinear otherwise. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model.
2.Deterministic vs. probabilistic (stochastic): A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables. Therefore, deterministic models perform the same way for a given set of initial conditions. Conversely, in a stochastic model, randomness is present, and variable states are not described by unique values, but rather by probability distributions.
3.Static vs. dynamic: A static model does not account for the element of time, while a dynamic model does. Dynamic models typically are represented with difference equations or differential equations
4.Discrete and continuous Models:Discrete networks(with discrete values) and continuous network (with continuous values)