N-tuple Method Research Articles

The N-Tuple Subspace Classifier: Extensions and Survey

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 everything going on in the N-tuple subspace classifier. Extensions of the N-tuple method are discussed using a generalized product expression and we relate the generalization to graphical models. We discuss the sum rule, the product rule, and the plurality voting rule for combining the scores of the subspace classifiers. We selected a representative sample of papers that the 1959 N-tuple subspace classifier inspired. Some of the papers introduced specialized improvements. Many of the papers showed the value of the N-tuple subspace classifier in all kinds of applications and compared the results of one or more varieties of the N-tuple subspace classifier with other state-of-the-art classifiers. Their experiments showed that the N-tuple subspace classifier was competitive with the state-of-the-art classifiers and often had a higher accuracy. Finally, we highlight some papers that describe experiments of the N-tuple subspace classifier executing in a quantum computer.

Hand Written Recognition Using Modified N_Tuple Method

In a world running on data, accurate handwriting recognition could become a powerful tool. With it, hastily scribbled notes and formal, handwritten letters become readable by a computer. In a writer recognition system, the system searches one to many in a wide database of manual samples from established authors, and returns a potential list of candidates. A n-tuple method of pattern recognition is developed and evaluated for use with unique references to unconstraint manually written characters for classification of non-deterministic content. A new method is seen to update the system and to increase the implementation and certainty of the findings. The results show that a superior can be achieved and show the legitimacy of the procedures proposed.

Dependence

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 valued variables our discussion centers on information theoretic measures related to mutual information and we describe some that are also metrics. We visually illustrate the difference between these two kinds of measures with a texture example that computes the joint probability image: an image in which the gray level of each pixel is the joint probability of the gray levels of the pixels in its neighborhood. Neighborhoods can be regular such as 5 × 5 or they can be irregular. Finally, we discuss manifold methods for classification: the N-tuple method, the subspace classifiers, the subspace ensemble classifiers, including the graphical model for representing the class conditional probability distribution. We describe a procedure to convert an N-tuple classifier to a graphical model classifier. We also conjecture that there is new form of a universal approximation theorem by which not too complex classification functions from measurement space to the set of classes can be approximately represented in the form of a subspace classifier using multiple subspaces such as the N-tuple method.

Improving the clustering performance of the scanning n-tuple method by using self-supervised algorithms to introduce subclasses

The scanning n-tuple technique (as introduced by Lucas and Amiri, 1996) is studied in pattern recognition tasks, with emphasis placed on methods that improve its recognition performance. We remove potential edge effect problems and optimize the parameters of the scanning n-tuple method with respect to memory requirements, processing speed and recognition accuracy for a case study task. Next, we report an investigation of self-supervised algorithms designed to improve the performance of the scanning n-tuple method by focusing on the characteristics of the pattern space. The most promising algorithm is studied in detail to determine its performance improvement and the consequential increase in the memory requirements. Experimental results using both small-scale and real-world tasks indicate that this algorithm results in an improvement of the scanning n-tuple classification performance.

The Theoretical and Experimental Status of the n-tuple Classifier

A number of theoretical approaches related to the n-tuple classification system are reviewed including Kanerva's SDM, the n-tuple regression network, the Hamming distance framework and likelihood estimation. The limitations of these methods are pointed out and resemblances that exist between them are underlined. Large-scale experiments carried out on StatLog project datasets confirm the n-tuple method as a viable competitor to more popular methods due to its speed, simplicity and accuracy on the majority of a wide variety of classification problems. A further investigation into the failure of the method on certain datasets shows its inner workings and reveals two main problems: difficulties with highly skewed class priors and more importantly, a mismatch between the scales involved in generalization, the amount of training data available, and the volume of the region in which data is likely to exist. This highlights areas where improvements in the method are needed and further theoretical progress would be helpful.

N-tuple texture recognition and the zero crossing sketch

The authors present a novel approach to real-time texture classification, derived from the n-tuple method of Bledsoe and Browning. Methods for texture classification based on approximations to the nth order co-occurrence spectrum are discussed. Limitations of these methods are highlighted, and a new method based around Marr's zero crossing sketch is presented. Preliminary results are presented comparing the new method and other n-tuple based schemes.

Recognition of chain-coded handwritten character images with scanning n-tuple method

A method of applying n-tuple recognition techniques to handwritten OCR, which involves scanning an n-tuple classifier over a chain-code of the image, is described. The traditional advantages of n-tuple recognition, i.e. training and recognition speed, are retained, while offering superior recognition accuracy, as demonstrated by results on three widely used data sets.

Reduction of the storage requirements of Bledsoe and Browning's n-tuple method of pattern recognition

Random superimposed coding has reduced the massive storage requirements of the Bledsoe and Browning Method of Pattern Recognition, applied to unconstrained hand-printed numerals with n = 14, by a factor of roughly four. A fourfold reduction in storage area can also be achieved by the use of associative memory, but at higher cost per bit. A third approach aims to achieve economy by exploiting any non-randomness of stored n-tuple states, but this is discussed only in outline.

Experiments with the n-tuple Method of Pattern Recognition

The n-tuple method of pattern recognition has been simulated on a somewhat larger and more comprehensive scale than previously reported. The nonweighted version has been found to work better than the maximum likelihood weighted version, and to achieve about 93 percent successful recognition of unconstrained hand-printed numerals, but at the cost of about 42 million bits of storage.