In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Language learning is thought to be a highly complex process. One of the hurdles in learning a language is to learn the rules of syntax of the language. Rules of syntax are often ordered in that before one rule can applied one must apply another. It has been thought that to learn the order of n rules one must go through all n! permutations. Thus to learn the order of 27 rules would require 27! steps or 1.08889x10 steps. This number is much greater than the number of seconds since the beginning of the universe! In an insightful analysis the linguist Block ([Block 86], pp. 62-63, p.238) showed that with the assumption of transitivity this vast number of learning steps reduces to a mere 377 steps. We present a mathematical analysis of the complexity of Block’s algorithm. The algorithm has a complexity of order n given n rules. In addition, we improve Block’s results exponentially, by introducing an algorithm that has complexity of order less than n log n.

A: On the complexity of learning a language: An improvement of Block’s algorithm
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Q: We extend the standard rough set-based approach to deal with huge amounts of numeric attributes versus small amount of available objects. Here, a novel approach of clustering along with dimensionality reduction; Hybrid Fuzzy C Means-Quick Reduct (FCMQR) algorithm is proposed for single gene selection. Gene selection is a process to select genes which are more informative. It is one of the important steps in knowledge discovery. The problem is that all genes are not important in gene expression data. Some of the genes may be redundant, and others may be irrelevant and noisy. In this study, the entire dataset is divided in proper grouping of similar genes by applying Fuzzy C Means (FCM) algorithm. A high class discriminated genes has been selected based on their degree of dependenc e by applying Quick Reduct algorithm based on Rough Set Theory to all the resultant clusters. Average Correlation Value (ACV) is calculated f or the high class discriminated genes. The clusters which have the ACV value a s 1 is determined as significant clusters, whose classification accuracy will be equal or high when comparing to the accuracy of the entire dataset. The proposed algorithm is evaluated using WEKA classifiers and compared. Finally, experimental results related to the leukemia cancer data confirm that our approach is quite promising, though it surely requires further research.

A: A Novel Approach for Single Gene Selection Using Clustering and Dimensionality Reduction
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Q: Within the framework of ADABOOST.MH, we propose to train vector-valued decision trees to optimize the multi-class edge without reducing the multi-class problem toK binary one-againstall classifications. The key element of the method is a vector-valued decision stump, factorized into an input-independent vector of length K and label-independent scalar classifier. At inner tree nodes, the label-dependent vector is discarded and the binary classifier can be used for partitioning the input space into two regions. The algorithm retains the conceptual elegance, power, and computational efficiency of binary ADABOOST. In experiments it is on par with support vector machines and with the best existing multi-class boosting algorithm AOSOLOGITBOOST, and it is significantly better than other known implementations of ADABOOST.MH.

A:
The return of ADABOOST.MH: multi-class Hamming trees
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