74 lines
3.3 KiB
TeX
74 lines
3.3 KiB
TeX
\documentclass[12pt]{article}
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\begin{document}
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\pagestyle{plain}
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\begin{center}
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\textbf{Proposal Summary}
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\end{center}
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\textbf{Goal:} Compute the intrinsic dimension of several speech
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representations. Fast computation for kernel matrix. Fast
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optimization of the kernel matrix. Nearest neighbor speech
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recognition.
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\textbf{Contributions:}
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\begin{enumerate}
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\item Fast computation for kernel matrix.
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\item Fast optimization of the kernel matrix.
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\item On-line kernel adaptive filters.
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\end{enumerate}
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\textbf{Specific tasks (Done):}
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\begin{enumerate}
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\item \textit{The Nearest Neighbor Problem} Approached the problem
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with trees that give the exact nearest neighbor. We could have also
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considered the approximate nearest neighbor problem that can be
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solved with other methods. But still trees is the best approach
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and also it is not yet known whether approximate nearest neighbor
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gives better performance.
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\item \textit{Multidimensional Trees} Studied developed and
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optimized kd-trees and ball trees. We didn't consider other types
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since comparative study has shown that they are still the state of
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the art.
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\item \textit{All nearest Neighbors} Implemented the best
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algorithm (dual tree) algorithm.
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\item \textit{Large scale trees, for out of core memory} Followed
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different caching practices for trees that don't fit in the main
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memory. Optimized code. Showed that the dual tree algorithm has
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very good locality structure.
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\item \textit{Fast k-nearest neighbor kernel computation} It is
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based on direct application of the all-nearest neighbor algorithm
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\item \textit{tuning the kernel bandwidth} Developed and algorithm
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for tuning non-parametrically the gaussian kernel in spectral
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clustering algorithms such as kernel-pca and diffusion mapping
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\item \textit{Phoneme classification with nearest neighbor
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classifier} Experimented with MFCC and NRAF features on the whole
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TIMIT database and managed to get up to 60\% correct phoneme
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classification only by looking at the nearest neighbor. The method
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can scale up linearly.
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\end{enumerate}
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\textbf{Specific tasks (To do):}
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\begin{enumerate}
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\item \textit{Customizing Kernels with semidefinite programming}
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There is an existing method for optimizing the kernel matrix based
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on semidefinite programming. There are certain optimizations that
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can be done along with the dual tree algorithm for linear scaling,
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such as application of stochastic optimization
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\item \textit{Fast kernel summation with trees, Kernel Matrix
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inversion} Direct computation of the kernel(Gaussian) kernel leads
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to a non-sparse matrix. There is a way though to compute the
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inverse/eigenvalues without explicitly computing the kernel
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matrix. Several optimizations can be done for high dimensions
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\item \textit{Speech recognition with nearest neighbor search}
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Implement a merge reduce scheme to create different descriptions
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of speech. Use nearest neighbor algorithms to replace gaussian
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mixtures in hidden markov models.
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\item \textit{Parallelize the code to handle larger datasets} The
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goal is to measure the intrinsic dimension of the broadcast news
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dataset. Test it with fast gaussian summation and with optimized
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kernels.
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\end{enumerate}
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\end{document}
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