Igor Chikalov

Three approaches to data analysis

In this book, the following three approaches to data analysis are presented: - Test Theory, founded by Sergei V. Yablonskii (1924-1998); the first publications appeared in 1955 and 1958, - Rough Sets, founded by Zdzisaw I. Pawlak (1926-2006); the first publications appeared in 1981 and 1982,- Logical Analysis of Data, founded by Peter L. Hammer (1936-2006); the first publications appeared in 1986 and 1988. These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected. - Logical Analysis of Data, founded by Peter L. Hammer (1936-2006); the first publications appeared in 1986 and 1988. These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected. These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected.

On optimization of decision trees

In the paper algorithms are considered which allow to consecutively optimize decision trees for decision tables with many-valued decisions relatively different complexity measures such as number of nodes, weighted depth, average weighted depth, etc. For decision tables over an arbitrary infinite restricted information system [5] these algorithms have (at least for the three mentioned measures) polynomial time complexity depending on the length of table description. For decision tables over one of such information systems experimental results of decision tree optimization are described.

On Algorithm for Constructing of Decision Trees with Minimal Number of Nodes

An algorithm is considered which for a given decision table constructs a decision tree with minimal number of nodes. The class of all information systems (finite and infinite) is described for which this algorithm has polynomial time complexity depending on the number of columns (attributes) in decision tables.

Average Time Complexity of Decision Trees

No wonder you activities are, reading will be always needed. It is not only to fulfil the duties that you need to finish in deadline time. Reading will encourage your mind and thoughts. Of course, reading will greatly develop your experiences about everything. Reading average time complexity of decision trees is also a way as one of the collective books that gives many advantages. The advantages are not only for you, but for the other peoples with those meaningful benefits.

Learning probabilistic models of hydrogen bond stability from molecular dynamics simulation trajectories.

BackgroundHydrogen bonds (H-bonds) play a key role in both the formation and stabilization of protein structures. They form and break while a protein deforms, for instance during the transition from a non-functional to a functional state. The intrinsic strength of an individual H-bond has been studied from an energetic viewpoint, but energy alone may not be a very good predictor.MethodsThis paper describes inductive learning methods to train protein-independent probabilistic models of H-bond stability from molecular dynamics (MD) simulation trajectories of various proteins. The training data contains 32 input attributes (predictors) that describe an H-bond and its local environment in a conformation c and the output attribute is the probability that the H-bond will be present in an arbitrary conformation of this protein achievable from c within a time duration Δ. We model dependence of the output variable on the predictors by a regression tree.ResultsSeveral models are built using 6 MD simulation trajectories containing over 4000 distinct H-bonds (millions of occurrences). Experimental results demonstrate that such models can predict H-bond stability quite well. They perform roughly 20% better than models based on H-bond energy alone. In addition, they can accurately identify a large fraction of the least stable H-bonds in a conformation. In most tests, about 80% of the 10% H-bonds predicted as the least stable are actually among the 10% truly least stable. The important attributes identified during the tree construction are consistent with previous findings.ConclusionsWe use inductive learning methods to build protein-independent probabilistic models to study H-bond stability, and demonstrate that the models perform better than H-bond energy alone.

Providing common I/O clock for wireless distributed platforms

We propose a novel synchronization scheme for distributed audio-video input and output on heterogeneous general purpose computers (GPC) such as laptops, tablets, PDA, smart telephones, audio recorders, and camcorders. These devices typically possess sensors such as microphones and possibly cameras, and actuators such as loudspeakers and displays. In order to combine them wirelessly into a distributed array signal processing system, it is necessary to provide relative time synchronization to sensors and actuators. In this work we propose a setup and an algorithm to synchronize input and output for a network of distributed multichannel audio sensors and actuators connected to GPC. An IEEE 802.11 wireless network is used to deliver the global clock to distributed GPC, while the interrupt mechanism is employed to distribute the clock between I/O devices. Experimental results demonstrate a precision in A/D D/A synchronization precision better than 50 /spl mu/s (a couple of samples at 48 kHz).

On Decision Trees with Minimal Average Depth

Decision trees are studied in rough set theory [6],[7] and test theory [1], [2], [3] and are used in different areas of applications. The complexity of optimal decision tree (a decision tree with minimal average depth) construction is very high. In the paper some conditions reducing the search are formulated. If these conditions are satisfied, an optimal decision tree for the problem is a result of simple transformation of optimal decision trees for some problems, obtained by decomposition of the initial problem. The decompostion properties are used to show that bounds given in [4] are unimprovable bounds on minimal average depth of decision tree.

Rule induction for identifying multi layer tool commonalities

A methodology based on association rule concepts is given for detecting fab tool commonality of affected lots. The performance of the methodology is then compared to several traditional methods such as ANOVA and contingency tables using eight actual production cases. In each case, the offending tool is affecting lots at multiple process layers.

Providing Common Time and Space in Distributed AV-Sensor Networks by Self-Calibration

Array audio-visual signal processing algorithms require time-synchronized capture of AV-data on distributed platforms. In addition, the geometry of the array of cameras, microphones, speakers and displays is often required. In this chapter we present a novel setup involving network of wireless computing platforms with sensors and actuators onboard, and algorithms that can provide both synchronized I/O and self-localization of the I/O devices in 3D space. The proposed algorithms synchronize input and output for a network of distributed multi-channel audio sensors and actuators connected to general purpose computing platforms (GPCs) such as laptops, PDAs and tablets. IEEE 802.11 wireless network is used to deliver the global clock to distributed GPCs, while the interrupt timestamping mechanism is employed to distribute the clock between I/O devices. Experimental results demonstrate a precision in A/D D/A synchronization precision better than 50 μs (a couple of samples at 48 kHz). We also present a novel algorithm to automatically determine the relative 3D positions of the sensors and actuators connected to GPCs. A closed form approximate solution is derived using the technique of metric multidimensional scaling, which is further refined by minimizing a non-linear error function. Our formulation and solution account for the errors in localization, due to lack of temporal synchronization among different platforms. The performance limit for the sensor positions is analyzed with respect to the number of sensors and actuators as well as their geometry. Simulation results are reported together with a discussion of the practical issues in a real-time system.

Learning Probabilistic Models of Hydrogen Bond Stability from Molecular Dynamics Simulation Trajectories

Hydrogen bonds (H-bonds) play a key role in both the formation and stabilization of protein structures. H-bonds involving atoms from residues that are close to each other in the main-chain sequence stabilize secondary structure elements. H-bonds between atoms from distant residues stabilize a protein’s tertiary structure. However, H-bonds greatly vary in stability. They form and break while a protein deforms. For instance, the transition of a protein from a non-functional to a functional state may require some H-bonds to break and others to form. The intrinsic strength of an individual H-bond has been studied from an energetic viewpoint, but energy alone may not be a very good predictor. Other local interactions may reinforce (or weaken) an H-bond. This paper describes inductive learning methods to train a protein-independent probabilistic model of H-bond stability from molecular dynamics (MD) simulation trajectories. The training data describes H-bond occurrences at successive times along these trajectories by the values of attributes called predictors. A trained model is constructed in the form of a regression tree in which each non-leaf node is a Boolean test (split) on a predictor. Each occurrence of an H-bond maps to a path in this tree from the root to a leaf node. Its predicted stability is associated with the leaf node. Experimental results demonstrate that such models can predict H-bond stability quite well. In particular, their performance is roughly 20% better than that of models based on H-bond energy alone. In addition, they can accurately identify a large fraction of the least stable H-bonds in a given conformation. The paper discusses several extensions that may yield further improvements.