How to Rank Answers in Text Mining

In this thesis, we mainly focus on case studies about answers. We present the methodology CEW-DTW and assess its performance about ranking quality. Based on the CEW-DTW, we improve this methodology by combining Kullback-Leibler divergence with CEW-DTW, since Kullback-Leibler divergence can check the difference of probability distributions in two sequences. However, CEW-DTW and KL-CEW-DTW do not care about the effect of noise and keywords from the viewpoint of probability distribution. Therefore, we develop a new methodology, the General Entropy, to see how probabilities of noise and keywords affect answer qualities. We firstly analyze some properties of the General Entropy, such as the value range of the General Entropy. Especially, we try to find an objective goal, which can be regarded as a standard to assess answers. Therefore, we introduce the maximum general entropy. We try to use the general entropy methodology to find an imaginary answer with the maximum entropy from the mathematical viewpoint (though this answer may not exist). This answer can also be regarded as an “ideal” answer. By comparing maximum entropy probabilities and global probabilities of noise and keywords respectively, the maximum entropy probability of noise is smaller than the global probability of noise, maximum entropy probabilities of chosen keywords are larger than global probabilities of keywords in some conditions. This allows us to determinably select the max number of keywords. We also use Amazon dataset and a small group of survey to assess the general entropy. Though these developed methodologies can analyze answer qualities, they do not incorporate the inner connections among keywords and noise. Based on the Markov transition matrix, we develop the Jump Probability Entropy. We still adapt Amazon dataset to compare maximum jump entropy probabilities and global jump probabilities of noise and keywords respectively. Finally, we give steps about how to get answers from Amazon dataset, including obtaining original answers from Amazon dataset, removing stopping words and collinearity. We compare our developed methodologies to see if these methodologies are consistent. Also, we introduce Wald–Wolfowitz runs test and compare it with developed methodologies to verify their relationships. Depending on results of comparison, we get conclusions about consistence of these methodologies and illustrate future plans

On Musical Self-Similarity : Intersemiosis as Synecdoche and Analogy

Self-similarity, a concept borrowed from mathematics, is gradually becoming a keyword in musicology. Although a polysemic term, self-similarity often refers to the multi-scalar feature repetition in a set of relationships, and it is commonly valued as an indication for musical ‘coherence’ and ‘consistency’. In this study, Gabriel Pareyon presents a theory of musical meaning formation in the context of intersemiosis, that is, the translation of meaning from one cognitive domain to another cognitive domain (e.g. from mathematics to music, or to speech or graphic forms). From this perspective, the degree of coherence of a musical system relies on a synecdochic intersemiosis: a system of related signs within other comparable and correlated systems. The author analyzes the modalities of such correlations, exploring their general and particular traits, and their operational bounds. Accordingly, the notion of analogy is used as a rich concept through its two definitions quoted by the Classical literature—proportion and paradigm, enormously valuable in establishing measurement, likeness and affinity criteria. At the same time, original arguments by Benoît B. Mandelbrot (1924–2010) are revised, alongside a systematic critique of the literature on the subject. In fact, connecting Charles S. Peirce’s ‘synechism’ with Mandelbrot’s ‘fractality’ is one of the main developments of the present study