Pattern Synthesis for Nonparametric Pattern Recognition

2011 ◽  
pp. 1511-1516
Author(s):  
P. Viswanath ◽  
Narasimha M. Murty ◽  
Bhatnagar Shalabh
Keyword(s):  
Pattern Recognition ◽  
Density Estimation ◽  
Nearest Neighbor ◽  
Curse Of Dimensionality ◽  
Parametric Methods ◽  
Pattern Synthesis ◽  
Parzen Window ◽  
Pattern Recognition Methods ◽  
The Given ◽  
Non Parametric

Parametric methods first choose the form of the model or hypotheses and estimates the necessary parameters from the given dataset. The form, which is chosen, based on experience or domain knowledge, often, need not be the same thing as that which actually exists (Duda, Hart & Stork, 2000). Further, apart from being highly error-prone, this type of methods shows very poor adaptability for dynamically changing datasets. On the other hand, non-parametric pattern recognition methods are attractive because they do not derive any model, but works with the given dataset directly. These methods are highly adaptive for dynamically changing datasets. Two widely used non-parametric pattern recognition methods are (a) the nearest neighbor based classification and (b) the Parzen-Window based density estimation (Duda, Hart & Stork, 2000). Two major problems in applying the non-parametric methods, especially, with large and high dimensional datasets are (a) the high computational requirements and (b) the curse of dimensionality (Duda, Hart & Stork, 2000). Algorithmic improvements, approximate methods can solve the first problem whereas feature selection (Isabelle Guyon & André Elisseeff, 2003), feature extraction (Terabe, Washio, Motoda, Katai & Sawaragi, 2002) and bootstrapping techniques (Efron, 1979; Hamamoto, Uchimura & Tomita, 1997) can tackle the second problem. We propose a novel and unified solution for these problems by deriving a compact and generalized abstraction of the data. By this term, we mean a compact representation of the given patterns from which one can retrieve not only the original patterns but also some artificial patterns. The compactness of the abstraction reduces the computational requirements, and its generalization reduces the curse of dimensionality effect. Pattern synthesis techniques accompanied with compact representations attempt to derive compact and generalized abstractions of the data. These techniques are applied with (a) the nearest neighbor classifier (NNC) which is a popular non-parametric classifier used in many fields including data mining since its conception in the early fifties (Dasarathy, 2002) and (b) the Parzen-Window based density estimation which is a well known non-parametric density estimation method (Duda, Hart & Stork, 2000).

Pattern Synthesis for Large-Scale Pattern Recognition

2011 ◽  
pp. 902-905
Author(s):  
P. Viswanath ◽  
M. Narasimha Murty ◽  
Shalabh Bhatnagar
Keyword(s):  
Pattern Recognition ◽  
Large Scale ◽  
Nearest Neighbor ◽  
Curse Of Dimensionality ◽  
Compact Representation ◽  
Pattern Synthesis ◽  
Approximate Methods ◽  
Compact Representations ◽  
The Given ◽  
Neighbor Classifier

Two major problems in applying any pattern recognition technique for large and high-dimensional data are (a) high computational requirements and (b) curse of dimensionality (Duda, Hart, & Stork, 2000). Algorithmic improvements and approximate methods can solve the first problem, whereas feature selection (Guyon & Elisseeff, 2003), feature extraction (Terabe, Washio, Motoda, Katai, & Sawaragi, 2002), and bootstrapping techniques (Efron, 1979; Hamamoto, Uchimura, & Tomita, 1997) can tackle the second problem. We propose a novel and unified solution for these problems by deriving a compact and generalized abstraction of the data. By this term, we mean a compact representation of the given patterns from which one can retrieve not only the original patterns but also some artificial patterns. The compactness of the abstraction reduces the computational requirements, and its generalization reduces the curse of dimensionality effect. Pattern synthesis techniques accompanied with compact representations attempt to derive compact and generalized abstractions of the data. These techniques are applied with nearest neighbor classifier (NNC), which is a popular nonparametric classifier used in many fields, including data mining, since its conception in the early 1950s (Dasarathy, 2002).

Scalable Non-Parametric Methods for Large Data Sets

2011 ◽  
pp. 1708-1713
Author(s):  
V. Suresh Babu ◽  
P. Viswanath ◽  
Narasimha M. Murty
Keyword(s):  
Nearest Neighbor ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Parametric Methods ◽  
Clustering Method ◽  
Data Set ◽  
Computational Burden ◽  
Set Size ◽  
Non Parametric

Non-parametric methods like the nearest neighbor classifier (NNC) and the Parzen-Window based density estimation (Duda, Hart & Stork, 2000) are more general than parametric methods because they do not make any assumptions regarding the probability distribution form. Further, they show good performance in practice with large data sets. These methods, either explicitly or implicitly estimates the probability density at a given point in a feature space by counting the number of points that fall in a small region around the given point. Popular classifiers which use this approach are the NNC and its variants like the k-nearest neighbor classifier (k-NNC) (Duda, Hart & Stock, 2000). Whereas the DBSCAN is a popular density based clustering method (Han & Kamber, 2001) which uses this approach. These methods show good performance, especially with larger data sets. Asymptotic error rate of NNC is less than twice the Bayes error (Cover & Hart, 1967) and DBSCAN can find arbitrary shaped clusters along with noisy outlier detection (Ester, Kriegel & Xu, 1996). The most prominent difficulty in applying the non-parametric methods for large data sets is its computational burden. The space and classification time complexities of NNC and k-NNC are O(n) where n is the training set size. The time complexity of DBSCAN is O(n2). So, these methods are not scalable for large data sets. Some of the remedies to reduce this burden are as follows. (1) Reduce the training set size by some editing techniques in order to eliminate some of the training patterns which are redundant in some sense (Dasarathy, 1991). For example, the condensed NNC (Hart, 1968) is of this type. (2) Use only a few selected prototypes from the data set. For example, Leaders-subleaders method and l-DBSCAN method are of this type (Vijaya, Murthy & Subramanian, 2004 and Viswanath & Rajwala, 2006). These two remedies can reduce the computational burden, but this can also result in a poor performance of the method. Using enriched prototypes can improve the performance as done in (Asharaf & Murthy, 2003) where the prototypes are derived using adaptive rough fuzzy set theory and as in (Suresh Babu & Viswanath, 2007) where the prototypes are used along with their relative weights. Using a few selected prototypes can reduce the computational burden. Prototypes can be derived by employing a clustering method like the leaders method (Spath, 1980), the k-means method (Jain, Dubes, & Chen, 1987), etc., which can find a partition of the data set where each block (cluster) of the partition is represented by a prototype called leader, centroid, etc. But these prototypes can not be used to estimate the probability density, since the density information present in the data set is lost while deriving the prototypes. The chapter proposes to use a modified leader clustering method called the counted-leader method which along with deriving the leaders preserves the crucial density information in the form of a count which can be used in estimating the densities. The chapter presents a fast and efficient nearest prototype based classifier called the counted k-nearest leader classifier (ck-NLC) which is on-par with the conventional k-NNC, but is considerably faster than the k-NNC. The chapter also presents a density based clustering method called l-DBSCAN which is shown to be a faster and scalable version of DBSCAN (Viswanath & Rajwala, 2006). Formally, under some assumptions, it is shown that the number of leaders is upper-bounded by a constant which is independent of the data set size and the distribution from which the data set is drawn.

Pattern Synthesis in SVM Based Classifier

2011 ◽  
pp. 1517-1523
Author(s):  
C. Radha
Keyword(s):  
Pattern Recognition ◽  
Pattern Classification ◽  
Discriminative Training ◽  
Training Set ◽  
Pattern Synthesis ◽  
Test Set ◽  
Generalization Performance ◽  
Learning Techniques ◽  
Training Examples ◽  
The Given

An important problem in pattern recognition is that of pattern classification. The objective of classification is to determine a discriminant function which is consistent with the given training examples and performs reasonably well on an unlabeled test set of examples. The degree of performance of the classifier on the test examples, known as its generalization performance, is an important issue in the design of the classifier. It has been established that a good generalization performance can be achieved by providing the learner with a sufficiently large number of discriminative training examples. However, in many domains, it is infeasible or expensive to obtain a sufficiently large training set. Various mechanisms have been proposed in literature to combat this problem. Active Learning techniques (Angluin, 1998; Seung, Opper, & Sompolinsky, 1992) reduce the number of training examples required by carefully choosing discriminative training examples. Bootstrapping (Efron, 1979; Hamamoto, Uchimura & Tomita, 1997) and other pattern synthesis techniques generate a synthetic training set from the given training set. We present some of these techniques and propose some general mechanisms for pattern synthesis.

INDUCTION OF CLASSIFIERS THROUGH NON-PARAMETRIC METHODS FOR APPROXIMATE CLASSIFICATION AND RETRIEVAL WITH ONTOLOGIES

2008 ◽  
Vol 02 (03) ◽  
pp. 403-423 ◽  
Author(s):  
NICOLA FANIZZI ◽  
CLAUDIA D'AMATO ◽  
FLORIANA ESPOSITO
Keyword(s):  
Semantic Web ◽  
Statistical Learning ◽  
Kernel Function ◽  
Nearest Neighbor ◽  
Knowledge Bases ◽  
Support Vector ◽  
Parametric Methods ◽  
K Nearest Neighbor ◽  
K Nearest Neighbor Algorithm ◽  
Non Parametric

This work concerns non-parametric approaches for statistical learning applied to the standard knowledge representation languages adopted in the Semantic Web context. We present methods based on epistemic inference that are able to elicit and exploit the semantic similarity of individuals in OWL knowledge bases. Specifically, a totally semantic and language-independent semi-distance function is introduced, whence also an epistemic kernel function for Semantic Web representations is derived. Both the measure and the kernel function are embedded in non-parametric statistical learning algorithms customized for coping with Semantic Web representations. Particularly, the measure is embedded in a k-Nearest Neighbor algorithm and the kernel function is embedded in a Support Vector Machine. The implemented algorithms are used to perform inductive concept retrieval and query answering. An experimentation on real ontologies proves that the methods can be effectively employed for performing the target tasks, and moreover that it is possible to induce new assertions that are not logically derivable.

scholarly journals Density estimation with non–parametric methods

1998 ◽  
Vol 127 (2) ◽  
pp. 335-352 ◽  
Author(s):  
D. Fadda ◽  
E. Slezak ◽  
A. Bijaoui
Keyword(s):  
Density Estimation ◽  
Parametric Methods ◽  
Non Parametric

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

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