Transcription of Text by Incremental Support Vector machine Anurag Sahajpal and Terje Kristensen

Outline Introduction Theory of Incremental SVM Application Discussion, further work and references

Introduction Phoneme : the basic abstract symbol representing speech sound Transcription : process of converting text (word) into corresponding phonetic sequence Letter-to-phoneme correspondence is generally not one-to-one Examples : ”lønnsoppgaver” trascribes to ”natt” transcribes to nAt while rar to rA:r

The Problem Phoneme transcription an instance of more general problem of Pattern recognition Phonetic rules compiled by experts are time consuming and fixed for a particular langauge What is required is an automatic approach, independent of any particular language

The Problem Machine learning approach using SVM reported in earlier paper The phonemic data in a language shows regional variation Distributed learning by SVM may be tried to adapt to geografically distributed phonemic data

Support Vector Machine Distribution free Non-parametric Non-linear High-dimensional Small training data sets Convex QP problem Good generalization performance Support Vectors Margin Width x2x2 x1x1

Support Vector Machine In a nutshell: map the data to a predetermined very high- dimensional space via a kernel function Find the hyperplane that maximizes the margin between the two classes If data are not separable find the hyperplane that maximizes the margin and minimizes the (a weighted average of the) misclassifications

Which Separating Hyperplane to Use? Var 1 Var 2

Maximizing the Margin Var 1 Var 2 Margin Width IDEA 1: Select the separating hyperplane that maximizes the margin!

MultiClass SVMs One-versus-all Train n binary classifiers, one for each class against all other classes. Predicted class is the class of the most confident classifier One-versus-one Train n(n-1)/2 classifiers, each discriminating between a pair of classes Several strategies for selecting the final classification based on the output of the binary SVMs

Outline Theory of Incremental SVM

SVM in Incremental and Distributed Settings Performance constriants with SVM training for large-scale problems Cumulative learning algorithms that incorporate new data over time (incremental) and space (distributed) Modifications to batch SVM learning to adapt to cumulative settings Calls for provable convergence properties

A naive approach to cumulative learning SVM learns D 1 and generate a set of support vectors SV 1 add SV 1 to D 2 to get a data set D ` 2 SVM learns D ` 2 and generate a set of support vectors SV 2

Incremental SVM Learning Convex hull of a set of points, S, is the smallest convex set containing S U-Closure property satisfied for convex hulls Vconv(Vconv(A 1 ) U A 2 ) = Vconv(A 1 U A 2 ) where Vconv(A) denote the vertices of a convex hull of a set A

Incremental SVM Learning learning algorithm, L, computes Vconv(D 1 (+) ) and Vconv(D 1 (-) ) Add Vconv(D 1 (+) ) to D 2 (+) to obtain D` 2 (+) Add Vconv(D 1 (-) ) to D 2 (-) to obtain D` 2 (-) L computes Vconv(D` 2 (+) ) and Vconv(D` 2 (-) ) Generate a training: D 12 = Vconv(D` 2 (+) ) U Vconv(D` 2 (-) ) compute SVM (D 12 )

Outline Application

SAMPA for Norwegian SAMPA (Speech Assessment Methods Phonetic Alphabet) - A computer readable phonetic alphabet Consonants and Vowels are classified into different subgroups : Consonants – plosives(6), fricatives(7), sonorant consonants(5) Vowels – long(9), short(9), Diphthongs(7) In our work, an estimate of 43 phonemes plus 10 additional phonetic symbols

Example of Training data file Some examples of transcription of words using the Sampa notation: WordsTranscription

Transcription Method Each letter pattern is a window onto a segment of the word where the phoneme to be predicted is in the middle of the window The size of the window is selected to 7 letters in all the experiments * e l e v e n context active

Pre-processing and coding A pattern file of data consist of words and their trancription Each pattern file is preprocessed before it is fed into SVM An internal coding table is defined in the program to represent each letter and its corresponding phoneme Example data file for LIBSVM

0 4:52 5:51 6:38 7:51 0 3:52 4:51 5:38 6:51 7:37 0 2:52 3:51 4:38 5:51 6:37 0 1:52 2:51 3:38 4:51 5:37 0 1:51 2:38 3:51 4:37 1 4:55 5:54 6:53 7:55 0 3:55 4:54 5:53 6:55 0 2:55 3:54 4:53 5:55 0 1:55 2:54 3:53 4:55 0 4:55 5:54 6:53 7:51

Experiment Various steps in the experiment One-versus-all training patterns Generation of 54 class files Separate training for 54 corresponding models

Experiment Various steps in the experiment The test file containing patterns is tested by each model and voting was carried out The output file and the true output was compared to find the accuracy

Outline Discussion, further work and references

Discussion and Future Work Complexity of convex hull computations have an exponential dependence on the dimensionality of the feature space. Implementation and modification to the standard batch-mode SVM to incorporate convex hull algorithm Extension to non-linear SVM classifier

References Caragea D. and Silvescu A and Honavar V “Agents that learn from distributed data sources” In fourth International Conference on Autonomous Agents C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Knowledge Discovery and Data Mining, 2(2), 1998.