Probabilistic Correlation Research Articles

Image Annotation and Retrieval for Weakly Labeled Images Using Conceptual Learning

One of the most promising new technologies for widespread application is image annotation and retrieval. Nevertheless, this task is very difficult to accomplish as target images differ significantly in appearance and belong to a wide variety of categories. In this paper, we propose a new image annotation and retrieval method for miscellaneous weakly labeled images, by combining higher-order local auto-correlation (HLAC) features and a framework of probabilistic canonical correlation analysis. The distance between images can be defined in the intrinsic space for annotation using conceptual learning of images and their labels. Because this intrinsic space is highly compressed compared to the image feature space, our method achieves both faster and more accurate image annotation and retrieval. The HLAC features are powerful global features with additive and position invariant properties. These properties work well with images, which have an arbitrary number of objects at arbitrary locations. The proposed method is shown to outperform existing methods using a standard benchmark dataset.

An improved index of interactivity for fuzzy numbers

In this paper we will introduce a new index of interactivity between marginal possibility distributions A and B of a joint possibility distribution C. The starting point of our approach is to equip each γ -level set of C with a uniform probability distribution, then the probabilistic correlation coefficient between its marginal probability distributions is interpreted as an index of interactivity between the γ -level sets of A and B. Then we define the index of interactivity between A and B as the weighted average of these indexes over the set of all membership grades. This new index of interactivity is meaningful for the whole family of joint possibility distributions.

P169 Three-dimensional probabilistic neuroanatomical correlation via the international 10–10 system oriented for brain mapping

P169 Three-dimensional probabilistic neuroanatomical correlation via the international 10–10 system oriented for brain mapping

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density function (PDF) of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a frame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.

Probabilistic event structures and domains

This paper studies how to adjoin probability to event structures, leading to the model of probabilistic event structures. In their simplest form, probabilistic choice is localised to cells, where conflict arises; in which case probabilistic independence coincides with causal independence. An event structure is associated with a domain—that of its configurations ordered by inclusion. In domain theory, probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion-free event structure correspond to the probabilistic event structures it supports. We explore how to extend probability to event structures which are not confusion-free via two notions of probabilistic runs of a general event structure. Finally, we show how probabilistic correlation and probabilistic event structures with confusion can arise from event structures which are originally confusion-free by using morphisms to rename and hide events.

Real-time analysis of intrusion detection alerts via correlation

With the growing deployment of networks and the Internet, the importance of network security has increased. Recently, however, systems that detect intrusions, which are important in security countermeasures, have been unable to provide proper analysis or an effective defense mechanism. Instead, they have overwhelmed human operators with a large volume of intrusion detection alerts. This paper presents a fast and efficient system for analyzing alerts. Our system basically depends on the probabilistic correlation. However, we enhance the probabilistic correlation by applying more systematically defined similarity functions and also present a new correlation component that is absent in other correlation models. The system can produce meaningful information by aggregating and correlating the large volume of alerts and can detect large-scale attacks such as distributed denial of service (DDoS) in early stage. We measured the processing rate of each elementary component and carried out a scenario-based test in order to analyze the efficiency of our system. Although the system is still imperfect, we were able to reduce the numerous redundant alerts 5.5% of the original volume without distorting the meaning through two-phase reduction. This ability reduces the management overhead drastically and makes the analysis and correlation easy. Moreover, we were able to construct attack scenarios for multistep attacks and detect large-scale attacks in real time.

Correlations and Entanglement in Probability Theory

We generalize the classical probability frame by adopting a wider family of random variables that includes non-deterministic ones. The frame that emerges is known to host a “classical” extension of quantum mechanics. We discuss the notion of probabilistic correlation and show that it includes two kinds of correlation: a classical one, which occurs for both deterministic and indeterministic observables, and a non-classical one, which occurs only for indeterministic observables. The latter will be called probabilistic entanglement and represents a property of intrinsically random systems, not necessarily quantum. It appears possible to separate the two kinds of correlation and characterize them by numerical functions which satisfy a simple product rule.

Probabilistic Event Structures and Domains

This paper studies how to adjoin probability to event structures, leading to the model of probabilistic event structures. In their simplest form probabilistic choice is localised to cells, where conflict arises; in which case probabilistic independence coincides with causal independence. An application to the semantics of a probabilistic CCS is sketched. An event structure is associated with a domain--that of its configurations ordered by inclusion. In domain theory probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion-free event structure correspond to the probabilistic event structures it supports. We explore how to extend probability to event structures which are not confusion-free via two notions of probabilistic runs of a general event structure. Finally, we show how probabilistic correlation and probabilistic event structures with confusion can arise from event structures which are originally confusion-free by using morphisms to rename and hide events.

Dynamic programming in a heuristically confined state space: a stochastic resource-constrained project scheduling application

The resource-constrained project scheduling problem (RCPSP) is a significant challenge in highly regulated industries, such as pharmaceuticals and agrochemicals, where a large number of candidate new products must undergo a set of tests for certification. We propose a novel way of addressing the uncertainties in the RCPSP including the uncertainties in task durations and costs, as well as uncertainties in the results of tasks (success or failure) by using a discrete time Markov chain, which enables us to model probabilistic correlation of the uncertain parameters. The resulting stochastic optimization problem can be solved by using dynamic programming, but the computational load renders this impractical. Instead, we develop a new way to combine heuristic solutions through dynamic programming in the state space that the heuristics generate. The proposed approach is tested on a simplified version of RCPSP that has a fairly complicated stochastic nature, with 1,214,693,756 possible parameter realizations (scenarios), and involves five projects and 17 tasks. As a result, an on-line policy is obtained, which can use the information states in on-line decision making and improve the heuristics rather than a fixed solution obtained by the previous mathematical programming (MILP) problem formulations.

A contribution to the evaluation of the reliability of iterative-execution software

This paper deals with the reliability of software executed iteratively, as e.g. in process control applications. The probability of mission survival is evaluated taking account of two characteristics of iterative software: a) system failure is defined in terms of the behaviour of the software over successive iterations, because the controlled system can usually tolerate short bursts of errors; b) the probabilistic correlation between successive executions of the software, which is to be expected for various reasons. The paper presents models accounting for these characteristics and evaluates their effects. The interesting case of fault-toleran t software is considered as well. Using the example of a pair-and-spare type fault-tolerant scheme, the relationships between different aspects of failure behaviour that are covered by the models developed here and those used elsewhere for fault-tolerant software are shown.

Neural-network-based target tracking state-of-the-art survey

Target tracking research has been of interest to several different groups of researchers from different perspectives. An event of perhaps greatest importance in the history and development of target tracking research is the new trend in the architectural revolution in current algorithms and techniques that are used for target tracking, i.e., the advent of neural networks and their applications to nonlinear dynamical systems. It is established in the literature that the mathematical complexity of the state-of-the-art tracking algorithms has gone far beyond the computational power of conventional digital processors. Since the introduction of Kalman filtering, several powerful mathematical tools have been added to target tracking techniques, e.g., probabilistic data association, correlation and gating, evidential reasoning, etc. All these methods have one thing in common: they track targets rather differently from the way natural systems do. It is rather difficult to come up with a sound mathematical proof and verification of the concept for different parallel distributed architectures that seem appropriate for a general class of target tracking applications. However, the volume of contributions within the last decade in the application of various neural network architectures to different classes of target tracking scenarios can not simply be ignored. Therefore, the various neural-network-based tracking algorithms that have been introduced since 1986 are classified and addressed and their common views as well as their differences in results and in architectures are discussed. The role of mathematics in each of these algorithms and the extent that conventional methods are used in conjunction with the neural-network-based techniques are also addressed.

Correlation estimation and time-series modeling for nonstationary processes

Various types of statistical signal processing require the estimation of time-variant correlation functions and the fitting of time-variant models for nonstationary processes. In this paper, the situations for which nonstationary probabilistic correlation functions can be accurately estimated from a single sample path of a stochastic process are delineated. These include only (i) known form of nonstationarity, (ii) periodic or almost periodic nonstationarity, and (iii) slowly fluctuating nonstationarity. Known methods of estimation for each of these situations are reviewed within the unifying framework of orthogonal series expansions. The fact that estimators based on orthogonal series expansions for nonstationary correlation functions other than (i)–(iii) cannot be guaranteed to be accurate is established. Ramifications for time-variant autoregressive model fitting are discussed.