According to the World Health Organization(WHO), the directing and coordinating authority for health within the United Nations system http://www.who.int/ cancer/en/, from a total of 58 million deaths in 2005, cancer accounts for 7.6 million (or 13%) of all deaths worldwide. This places cancer as one of the leading causes of death in the world, with lung cancer (the main cancer leading to mortality) accounting for 1.3 million deaths per year. Thus the importance of understanding the mechanisms of lung cancer is clear. One approach is through the rapid quantification of the gene expression levels of samples of healthy and diseased lung tissue. This new field blending the knowledge from biologists, computer scientists and mathematicians is known as Bioinformatics and is yielding large quantities of data of a very high dimensional nature that needs to be understood.
The Multi-Objective Approach: A Hybrid Perspective
In order to establish a formulation of the problem based on multi-objective optimization, a set of objective functions has to be specified, representing the corresponding criteria that must be simultaneously satisfied by the solution. The minimization of a measure of similarity information loss between the original and the transformed spaces and a classification error measure over the objects in the new space can be used in a first approximation. Clearly, more requirements can be imposed on the solution by adding the corresponding objective functions. Following a principle of parsimony this paper will consider the use of only two criteria, namely, Sammon’s error (Sammon, J.W., 1969) for the unsupervised case and mean cross-validated classification error with a k-nearest neighbour pattern recognizer for the supervised case.
Key Terms in this Chapter
Unsupervised Algorithm: The true class that an object belongs to is not known to the algorithm hence the algorithm is not supervised by a “teacher”. For example clustering algorithms are unsupervised because each cluster is generated based on the data itself. Although the true class may also be known, it was not used
Multi-objective Algorithm: An optimization algorithm that attempts to find the best solutions across all measures of solution acceptability. That is, the Pareto Front is sought, even under the situation that it may not be theoretically known
Evolutionary Algorithms: A subset of evolutionary computation, which generally only involve techniques inspired by biological evolution such as reproduction, mutation, recombination, natural selection and survival of the fittest. Candidate solutions to an optimization problem play the role of individuals in a population, and the fitness function determines the environment within which the solutions “live”. Evolution of the population then takes place after the repeated application of the above operators.http://en.wikipedia.org/wiki/Evolutionary_Computation
Gene: 1. A unit of DNA that carries information for the biosynthesis of a specific product in the cell. 2. Ultimate unit by which inheritable characteristics are transmitted to succeeding generations in all living organisms. Genes are contained by, and arranged along the length of, the chromosome. The gene is composed of deoxyribonucleic acid (DNA). Each chromosome of a species has a definite number and arrangement of genes, which govern both the structure and metabolic functions of the cells and thus of the entire organism. Genes provide information for the synthesis of enzymes and other proteins and specify when these substances are to be made. Alteration of either gene number or arrangement can result in mutation (a change in the inheritable traits).http://www.amfar.org/cgi-bin/iowa/bridge.html?page=G
Virtual Reality: (often called VR for short) Is an attempt to provide more natural, human interfaces to software. It can be as simple as a pseudo 3D interface or as elaborate as an isolated room in which the computer can control the user’s senses of vision, hearing, and even smell and touch. http://www.saugus.net/Computer/Terms/
Cancer: A term for diseases in which abnormal cells divide without control and can invade other tissues. Cancer cells can spread to other parts of the body through the blood and lymph systems. Cancer is not just one disease but many diseases. There are more than 100 different types of cancer. http://www.cancer.gov/cancertopics/what-is-cancer
Hybrid Space: A constructed space that attempts to preserve more than one property (possibly in conflict) of the original space. For example, preserving distances between objects and the class structure of the original space