Data Mining - Concepts and Techniques.

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Much has been written about theory and practice in the law, and the tension between practitioners and theorists. Judges do not cite theoretical articles often; they rarely "apply" theories to particular cases. These arguments are not revisited. Instead the Essay explores the working and interaction of theory and practice, practitioners and theorists. The Essay starts with a story about solving a legal issue using our intellectual tools - theory, practice, and their progenies: experience and "gut." Next the Essay elaborates on the nature of theory, practice, experience and "gut." The third part of the Essay discusses theories that are helpful to practitioners and those that are less helpful. The Essay concludes that practitioners theorize, and theorists practice. They use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ. Theory, practice, experience and "gut" help us think, remember, decide and create. They complement each other like the two sides of the same coin: distinct but inseparable.

Of Theory and Practice

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

The Web of Human Sexual Contacts

Localizing a bug in a program can be a complex and time- consuming process. In this paper we propose a code coverage-based fault localization method to prioritize suspicious code in terms of its likelihood of containing program bugs. Code with a higher risk should be examined before that with a lower risk, as the former is more suspicious (i.e., more likely to contain program bugs) than the latter. We also answer a very important question: how can each additional test case that executes the program successfully help locate program bugs? We propose that with respect to a piece of code, the aid introduced by the first successful test that executes it in computing its likelihood of containing a bug is larger than or equal to that of the second successful test that executes it, which is larger than or equal to that of the third successful test that executes it, etc. A tool, chiDebug, was implemented to automate the computation of the risk of the code and the subsequent prioritization of suspicious code for locating program bugs. A case study using the Siemens suite was also conducted. Data collected from our study support the proposal described above. They also indicate that our method (in particular Heuristics III (c), (d), and (e)) can effectively reduce the search domain for locating program bugs.

Effective Fault Localization using Code Coverage

On the neural network approach in software reliability modeling

Software cybernetics explores the interplay between software theory/engineering and control theory/engineering. Following the idea of software cybernetics, the controlled Markov chains (CMC) approach to software testing treats software testing as a control problem. The software under test serves as a controlled object, and the (optimal) testing strategy determined by the theory of controlled Markov chains serves as a controller. This paper analyzes the behavior of the corresponding optimal test profile determined by the CMC approach to software testing and introduces adaptive software testing. It is shown that in some cases the optimal test profile is Markovian, whereas in some other cases the optimal test profile demonstrates a different scenario. The adaptive software testing adjusts software testing strategy on-line by using testing data collected during software testing in response to changes in our understanding of the software under test. Simulation results show that the adaptive strategy of software testing is feasible and significantly reduces the number of test cases required to detect and remove a certain number of software defects in comparison with the random strategy of software testing.

Optimal software testing and adaptive software testing in the context of software cybernetics

Software cybernetics explores the interplay between software and control and is motivated by the fundamental question whether or not and how software behavior can be controlled. In this paper, we formulate the underlying motivations and ideas of software cybernetics and review various existing research topics in this emerging area, including feedback mechanisms in software processes, bisimulation and controllability, adaptive software, software synthesis, software test process control, and adaptive testing. We identify software rejuvenation and performance control, software fault-tolerance, logical foundation for control systems, and communication complexity for control systems as potential research topics. Several on-going research projects are also summarized.

Kai-Yuan Cai

Papers

Effective Fault Localization using Code Coverage

On the neural network approach in software reliability modeling

Optimal software testing and adaptive software testing in the context of software cybernetics

An overview of software cybernetics

Software execution processes as an evolving complex network