• Title/Summary/Keyword: Commute time embedding

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A Study on Classification of Waveforms Using Manifold Embedding Based on Commute Time (컴뮤트 타임 기반의 다양체 임베딩을 이용한 파형 신호 인식에 관한 연구)

  • Hahn, Hee-Il
    • Journal of the Institute of Electronics and Information Engineers
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    • v.51 no.2
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    • pp.148-155
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    • 2014
  • In this paper a commute time embedding is implemented by organizing patches according to the graph-based metric, and its properties are investigated via changing the number of nodes on the graph.. It is shown that manifold embedding methods generate the intrinsic geometric structures when waveforms such as speech or music instrumental sound signals are embedded on the low dimensional Euclidean space. Basically manifold embedding algorithms only project the training samples on the graph into an embedding subspace but can not generalize the learning results to test samples. They are very effective for data clustering but are not appropriate for classification or recognition. In this paper a commute time guided transform is adopted to enhance the generalization ability and its performance is analyzed by applying it to the classification of 6 kinds of music instrumental sounds.

Proposing the Methods for Accelerating Computational Time of Large-Scale Commute Time Embedding (대용량 컴뮤트 타임 임베딩을 위한 연산 속도 개선 방식 제안)

  • Hahn, Hee-Il
    • Journal of the Institute of Electronics and Information Engineers
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    • v.52 no.2
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    • pp.162-170
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    • 2015
  • Commute time embedding involves computing the spectral decomposition of the graph Laplacian. It requires the computational burden proportional to $o(n^3)$, not suitable for large scale dataset. Many methods have been proposed to accelerate the computational time, which usually employ the Nystr${\ddot{o}}$m methods to approximate the spectral decomposition of the reduced graph Laplacian. They suffer from the lost of information by dint of sampling process. This paper proposes to reduce the errors by approximating the spectral decomposition of the graph Laplacian using that of the affinity matrix. However, this can not be applied as the data size increases, because it also requires spectral decomposition. Another method called approximate commute time embedding is implemented, which does not require spectral decomposition. The performance of the proposed algorithms is analyzed by computing the commute time on the patch graph.

Analysis of Commute Time Embedding Based on Spectral Graph (스펙트럴 그래프 기반 Commute Time 임베딩 특성 분석)

  • Hahn, Hee-Il
    • Journal of Korea Multimedia Society
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    • v.17 no.1
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    • pp.34-42
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    • 2014
  • In this paper an embedding algorithm based on commute time is implemented by organizing patches according to the graph-based metric, and its performance is analyzed by comparing with the results of principal component analysis embedding. It is usual that the dimensionality reduction be done within some acceptable approximation error. However this paper shows the proposed manifold embedding method generates the intrinsic geometry corresponding to the signal despite severe approximation error, so that it can be applied to the areas such as pattern classification or machine learning.

Topological Analysis of Spaces of Waveform Signals (파형 신호 공간의 위상 구조 분석)

  • Hahn, Hee Il
    • Journal of Korea Multimedia Society
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    • v.19 no.2
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    • pp.146-154
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    • 2016
  • This paper presents methods to analyze the topological structures of the spaces composed of patches extracted from waveform signals, which can be applied to the classification of signals. Commute time embedding is performed to transform the patch sets into the corresponding geometries, which has the properties that the embedding geometries of periodic or quasi-periodic waveforms are represented as closed curves on the low dimensional Euclidean space, while those of aperiodic signals have the shape of open curves. Persistent homology is employed to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, which can be used to discriminate between the groups of waveforms topologically.

Analysis of Topological Invariants of Manifold Embedding for Waveform Signals (파형 신호에 대한 다양체 임베딩의 위상학적 불변항의 분석)

  • Hahn, Hee-Il
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.16 no.1
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    • pp.291-299
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    • 2016
  • This paper raises a question of whether a simple periodic phenomenon is associated with the topology and provides the convincing answers to it. A variety of music instrumental sound signals are used to prove our assertion, which are embedded in Euclidean space to analyze their topologies by computing the homology groups. A commute time embedding is employed to transform segments of waveforms into the corresponding geometries, which is implemented by organizing patches according to the graph-based metric. It is shown that commute time embedding generates the intrinsic topological complexities although their geometries are varied according to the spectrums of the signals. This paper employs a persistent homology to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, and discusses their applications.