Robert Martin Haralick

CUNY Graduate Center | CUNY · Program in Computer Science

In this paper, we discourse an analysis of classical first-order predicate logic as a constraint satisfaction problem, CSP. First, we will offer our general framework for CSPs, and then apply it to first-order logic. We claim it would function as a new semantics, constraint semantics, for logic. Then, we prove the soundness and completeness theorem...

We present a new measure of dependence suitable for time series forecasting: Partial Monotone Correlation (PMC) that generalizes Monotone Correlation. Unlike the Monotone Correlation, the new measure of dependence uses piecewise strictly monotone transformations that increase the value of the correlation coefficient. We explore its properties, its...

This article is written in recognition of W. Bledsoe, who with Browning, introduced the N-tuple subspace classifier in 1959. This 1959 article was the first article to introduce subspace classifiers and the sum rule to combine the outputs of the classifiers. A mathematical notation is given to easily express in a precise and unambiguous way everyth...

We discuss a more powerful probabilistic graphical model for discovering semantic patterns from sequential text data, such as sentences. It is developed based on the idea that each word (or each symbol) in a sentence itself might carry lexical, semantic, or syntactic information, which can be used to replace conditional dependences in existing meth...

This paper discusses different kinds of dependency. For numerically valued variables our discussion centers on the maximal correlation coefficient and its cousin the monotone correlation coefficient. We show how to calculate the maximal correlation coefficient in the case the random variables take on a finite set of values. For non-numerically valu...

Given a data set taken over a population, the question of how can we construct possible explanatory models for the interactions and dependencies in the population is a discovery question. Projection and Relation Join is a way of addressing this question in a non-deterministic context with mathematical relations. In this paper, we apply projection a...

Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis on polycyclic and metabelian groups that are of interest to non-commutative cryptography. As a prototypical exa...

In this study, we revisit quadratic discriminant analysis (QDA). For this purpose, we present a majorize-minimize (MM) optimization algorithm to estimate parameters for generative classifiers, of which conditional distributions are from the exponential family. Furthermore, we propose a block-coordinate descent algorithm to sequentially update param...

Information retrieval methods represent query results in a ranked, one dimensional list without revealing connections among documents and document groups. We propose a new model of document representation and extend the notion of similarity to consider document length and word synonyms to organize documents into topically relevant groups. Matches t...

Data Mining explanatory models must deal with relevance: how values of different data items are relevant to the values of other data items. But to be able to construct explanatory models, and in particular causal explanatory models, we must do so by first understanding irrelevance and exactly how irrelevance plays a role in explanatory models. The...

This paper discusses an algorithm for identifying semantic arguments of a verb, word senses of a polysemous word, noun phrases in a sentence. The heart of the algorithm is a probabilistic graphical model. In contrast with other existed graphical models, such as Naive Bayes models, CRFs, HMMs, and MEMMs, this model determines a sequence of optimal c...

Machine vision systems used in industrial applications must execute their algorithms in real time to perform such tasks as inspecting a wire bond or guiding a robot to install a part on a car body moving along a conveyer. The real time speed is achieved by employing simple-minded algorithms and by designing parallel architectures and parallel algor...

A recent technology-comment article in Nature magazine exemplifies a growing problem in the sciences, in the reliance upon unfactual material sourced only to popular literature or to the "skeptic" press and generally written by prejudiced journalists, for evaluations of controversial scientific findings. There is no greater example of this than how...

Existing linear solutions for the pose estimation (or exterior orientation) problem suffer from a lack of robustness and accuracy partially due to the fact that the majority of the methods utilize only one type of geometric entity and their frameworks do not allow simultaneous use of different types of features. Furthermore, the orthonormality cons...

We present a probabilistic graphical model that finds a sequence of optimal categories for a sequence of input symbols. Based on this mode, three algorithms are developed for identifying semantic patterns in texts. They are the algorithm for extracting semantic arguments of a verb, the algorithm for classifying the sense of an ambiguous word, and t...

We propose a probabilistic graphical model that works for recognizing three types of text patterns in a sentence: noun phrases; the meaning of an ambiguous word; and semantic arguments of a verb. The model has an unique mathematical expression and graphical representation compared with existing graphic models such as CRFs, HMMs, and MEMMs. In our m...

In this paper, we present an Automatic Target Detection system that operates on a simulated E3D(Exploitation of 3D Data) image dataset. Simulated E3D images are range images where each value represents the height above the ground. In our work, we treat the 3D data as if the height values were pixel intensity values(2D) and a set of mathe-matical mo...

A major challenge in single-trial electroencephalography (EEG) analysis and Brain Computer Interfacing (BCI) is the so called, inter-subject/inter-session variability: (i.e large variability in measurements obtained during different recording sessions). This variability restricts the number of samples available for single-trial analysis to a limite...

An efficient and exact dynamic programming algorithm is introduced to quantise a continuous random variable into a discrete random variable that maximises the likelihood of the quantised probability distribution for the original continuous random variable. Quantisation is often useful before statistical analysis and modelling of large discrete netw...

Traditional analysis methods for single-trial classificat ion of electro-encephalography (EEG) focus on two types of paradigms: phase-locked methods, in which the amplitude of the signal is used as the feature for classification, that is, event related poten tials; and second-order methods, in which the feature of interest is the power of the signa...

In past years, there has been substantial work on the problem of entity coreference resolution whereas much less attention has been paid to event coreference resolution. Starting with some motivating examples, we formally state the problem of event coreference resolution in the ACE program, present an agglomerative clustering algorithm for the task...

We discuss a probabilistic graphical model for recognizing patterns in texts. It is derived from the probability function for a sequence of categories given a sequence of symbols under two reasonable conditional independence assumptions and represented by a product of combinations of conditional and marginal probability functions. The novelty of ou...

A key task in counterterrorism is finding useful records and combinations of records in very large heterogeneous databases. The bits and pieces of information come from many sources and the pieces do not all tightly connect together. Some (possibly disconnected) pieces tightly connect to some other (possibly disconnected) pieces. The databases are...

We present a probabilistic graphical model for identifying noun phrase patterns in texts. This model is derived from mathematical processes under two reasonable conditional independence assumptions with different perspectives compared with other graphical models, such as CRFs or MEMMs. Empirical results shown our model is effective. Experiments on...

Dimension reduction methods are often applied in machine learning and data mining problems. Linear subspace methods are the commonly used ones, such as principal component analysis (PCA), Fisher's linear discriminant analysis (FDA), common spatial pattern (CSP), et al. In this paper, we describe a novel feature extraction method for binary classifi...

Dynamic programming is introduced to quantize a continuous random variable into a discrete random variable. Quantization is often useful before statistical analysis or reconstruction of large network models among multiple random variables. The quantization, through dynamic programming, finds the optimal discrete representation of the original proba...

Classical clustering algorithms are based on the concept that a cluster center is a single point. Clusters which are not compact around a single point are not candidates for classical clustering approaches. In this paper we present a new clustering paradigm in which the cluster center is a linear manifold. Clusters are groups of points compact arou...

Dimension reduction methods are often applied in machine learning and data mining problems. Linear subspace methods are the commonly used ones, such as principal component analysis (PCA), Fisher’s linear discriminant analysis (FDA), et al. In this paper, we describe a novel feature extraction method for binary classification problems. Instead of fi...

One of the ultimate goals of cluster analysis is not only to reveal structure but also to understand it. Most clustering methods focus only on the grouping aspect and do not provide a descriptive model with which the population underlying the data can be described or with which statistical inference such as predictions can be made. Linear manifold...

A new, fast template-matching method using the Singular Value Decomposition (SVD) is presented. This approach involves a two-stage algorithm, which can be used to increase the speed of the matching process. In the first stage, the reference image is orthogonally separated by the SVD and then low-cost pseudo-correlation values are calculated. This r...

The detection of correlations is a data mining task of increasing im-portance due to new areas of application such as DNA microarray analy-sis, collaborative filtering, and text mining. In these cases object similar-ity is no longer measured by physical distance, but rather by the behavior patterns objects manifest or the magnitude of correlations...

In recent applications of clustering such as gene expression microarray analysis, collaborative filtering, and Web mining, object similarity is no longer measured by physical distance, but rather by the behavior patterns objects manifest or the magnitude of correlations they induce. Current state of the art algorithms aiming at this type of cluster...

The Whitehead Minimization problem is a problem of finding elements of the minimal length in the automorphic orbit of a given element of a free group. The classical algorithm of Whitehead that solves the problem depends exponentially on the group rank. Moreover, it can be easily shown that exponential blowout occurs when a word of minimal length ha...

In this paper we discuss several heuristic strategies which allow one to solve the Whitehead's minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most non-...

We review some basic methodologies from pattern recognition that can be applied to helping solve combinatorial problems in free group theory. We illustrate how this works with recognizing Whitehead minimal words in free groups of rank 2. The methodologies reviewed include how to form feature vectors, principal components, distance classifers, linea...

This paper describes an algorithm for the determination of zone content type of a given zone within a document image. We take a statistical based approach and represent each zone with 25 dimensional feature vectors. An optimized decision tree classifier is used to classify each zone into one of nine zone content classes. A performance evaluation pr...

Computer vision algorithms are composed of different sub-algorithms often applied in sequence. Determination of the performance of a total computer vision algorithm is possible if the performance of each of the sub-algorithm constituents is given. The problem, however, is that for most published algorithms, there is no performance characterization...

This paper presents a statistical estimation from which a new objective function for exterior orientation from line correspondences is derived. The objective function is based on the assumption that the underlying noise model for the line correspondences is the Fisher distribution. The assumption is appropriate for 3D orientation, is different from...

Typical gene expression clustering algorithms are restricted to a specific underlying pattern model while overlooking the possibility that other information carrying patterns may co-exist in the data. This may potentially lead to a large bias in the results. In this paper we discuss a new method that is able to cluster simultaneously various types...

This is the second part of a tutorial discussing the experimental protocol issues in testing the Torah code hypothesis. The principal concept is the test statistic which is used to do the actual hypothesis testing of the Null hypothesis against a simple alternative or against a complex of alternatives. We illustrate the methodology using the data s...

Because of variable dependence, high dimensional data typically have much lower intrinsic dimensionality than the number of its variables. Hence high dimensional data can be expected to lie in (nonlinear) lower dimensional manifold. In this paper, we describe a nonlinear manifold clustering algorithm. By connecting data vectors with their neighbors...

This is the first part of a tutorial discussing the major strategies and methodologies by which a test of the Null hypothesis of no Torah effect can be done. The basic concepts of equidistant letter sequence, skip specification, resonance specification, and compactness features are discussed here

We describe a nonparametric pixel appearance probability model to represent local image information. It allows an optimal image analysis framework that in-tegrates low-and high-level stages to substantially improve overall accuracy of object reconstruction. In this framework, feature detection would be an overall consequence rather than an intermed...

Computer vision software is complex, involving many tens of thousands of lines of code. Coding mistakes are not uncommon. When the vision algorithms are run on controlled data which meet all the algorithm assumptions, the results are often statistically predictable. This renders it possible to statistically validate the computer vision software and...

In this paper we describe a new cluster model which is based on the concept of linear manifolds. The method identifies subsets of the data which are embedded in arbitrary oriented lower dimensional linear manifolds. Minimal subsets of points are repeatedly sampled to construct trial linear manifolds of various dimensions. Histograms of the distance...

In this paper, we discuss a unified theory for and performance evaluation of the ridge direction estimation through the minimization of the integral of the second directional derivative of the gray-level intensity function. The primary emphasis of this paper is on the ridge orientation estimation. The subsequent ridge detection can be performed usi...

An interesting problem associated with the World Wide Web (Web) is the definition and delineation of so called Web communities. The Web can be characterized as a directed graph whose nodes represent Web pages and whose edges represent hyperlinks. An authority is a page that is linked to by high quality hubs, while a hub is a page that links to high...

We describe a linear time probabilistic algorithm to recognize Whitehead minimal elements (elements of minimal length in their automorphic orbits) in free groups of rank 2. For a non-minimal element the algorithm gives an automorphism that is most likely to reduce the length of the element. This method is based on linear regression and pattern...

In this survey we review the image processing literature on the various approaches and models investigators have used for texture. These include statistical approaches of autocorrelation functions, optical transforms, digital transforms, textural edgeness, structural element, gray tone co-occurrence, run lengths, and autoregressive models. We discu...

We define a cluster to be characterized by regions of high density separated by regions that are sparse. By observing the downward closure property of density, the search for interesting structure in a high dimensional space can be reduced to a search for structure in lower dimensional subspaces. We present a hierarchical projection pursuit cluster...

The main goal of this paper is to show that pattern recognition techniques can be successfully used in abstract algebra. We introduce a pattern recognition system to recognize words of minimal length in their automorphic orbits in free groups of rank 2. This system is based on linear regression and does not use any particular results from group the...

This paper presents a table structure understanding algorithm designed using optimization methods. The algorithm is probability based, where the probabilities are estimated from geometric measurements made on the various entities in a large training set. The methodology includes a global parameter optimization scheme, a novel automatic table ground...

We review some basic methodologies from pattern recognition that can be applied to helping solve combinatorial problems in free group theory. We illustrate how this works with recognizing Whitehead minimal words in free groups of rank 2. The methodologies reviewed include how to form feature vectors, principal components, distance classifiers, line...

The main goal of this paper is to show that pattern recognition techniques can be successfully used in abstract algebra. We introduce a pattern recognition system to recognize words of minimal length in their automorphic orbits in free groups of rank 2. This system is based on linear regression and does not use any particular results from group the...

We present an approach to estimating high dimensional discrete probability distributions with decomposable graphical models. Starting with the independence assumption we add edges and thus gradually increase the complexity of our model. Bounded by the minimum description length principle we are able to produce highly accurate models without overfit...

We discuss efficient forward selection in the class of decomposable graphical models. This subclass of graphical models has a number of desirable properties. The contributions of This work are twofold. First we improve an existing algorithm by addressing cases previously not considered. Second we extend the algorithm to reflect model graphs with mu...

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