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博碩士論文 etd-0606118-151922 詳細資訊
Title page for etd-0606118-151922
論文名稱
Title
基於逐階核心張量萃取法的影像分類
Image classification via successive core tensor selection procedure
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
50
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2018-06-28
繳交日期
Date of Submission
2018-07-06
關鍵字
Keywords
資料特徵萃取、影像分類、張量分解
data feature extraction, image classification, tensor decomposition
統計
Statistics
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中文摘要
在人工智慧領域,具有高階張量結構的資料(higher-order tensor data)近來被廣泛關注,尤其是產線上的光學影像檢測和醫學上的核磁共振影像分析,因此張量分解(tensor factorization)和分類演算法成為重要的研究主題。

在傳統的類神經網路(neural network)或機器學習方法中,分類演算法是將訓練資料以向量的形式輸入進行模型訓練,所訓練出來的模型便可進行測試資料的辨識與分類。過去為了符合向量形式的輸入限制,高階張量資料常透過向量化展開成高維度(high-dimensional)的向量。但也導致相鄰於不同階(order)的空間關聯訊息遺失,因此限制了分類的表現。

本論文提出結合非負塔克拆解(non-negative Tucker decomposition)與高階張量主成分分析的分類模型,逐次提取特徵核心張量(feature core tensor)以提高分類準度。相較於傳統主成分分析,高階張量主成分分析透過輸入的張量在逐階考量不同的空間關係中的重要資訊下優化張量投影集,以避免任何一階之空間中的重要資訊在轉換後被遺失,使之萃取出更完整的特徵。對於信號處理與醫學影像等領域,資料在負值會失去其物理意義,因此許多非負分解和分析方法也成為重要研究議題。本文所引用的非負塔克拆解(non-negative Tucker decomposition)正是其一,也是非負矩陣分解經典的高階延伸之一。在分類模型中,非負塔克拆解除了能保持原始資料非負的物理意義,更能忽略同類別之間的微小差距,使得分類準度提升。

本篇研究對訓練模型的計算時間成本和分類準確度進行了探討。在影像辨識的實驗中發現,在結合非負塔克拆解後,高階張量主成分分析的訓練時間減少。就準度而言,訓練資料筆數越是減少,我們的模型在準度的領先幅度也越是顯著。
Abstract
In the field of artificial intelligence, high-order tensor data have been studied and analyzed, such as the automated optical inspection and MRI. Therefore, tensor decompositions and classification algorithms have become an important research topic.

In a traditional neural network or machine learning method, the classification algorithm inputs training data in the form of vectors, and the trained model can identify and classify the testing data. In order to conform the input constraints, high-order tensor data are often expanded into high-dimensional vectors. However, it also leads to the loss of spatially related information adjacent to different orders, thus damages the performance of the classification.

This thesis proposes a classification model combining non-negative Tucker decomposition and high-order tensors principal component analysis, and extracts feature core tensors successively to improve the accuracy of classification. Comparing with to neural network classifiers, we replace affine transformations with tensor transformations, which optimizes tensor projections to avoid missing information representing the spatial relationships in different orders, so that it extracts more complete features. For signal processing and medical image fields, data will lose its physical significance at negative values. So many non-negative decomposition and analysis methods have also become important research issues. The non-negative Tucker decomposition referred in this paper is one of them, and it is also one of the classic high-order extensions of non-negative matrix factorization. In the classification model, non-negative Tucker decomposition can not only maintain the non-negative physical meaning, but also can ignore the difference between same class, which makes the classification accuracy increase.

This study explores the computational time cost and classification accuracy of the model. In the experiment of image recognition, the training time of the high-order tensor principal component analysis was reduced to half after combining non-negative Tucker decomposition. In terms of accuracy, the smaller the number of training data, the more pronounced the lead of our model is.
目次 Table of Contents
論文審定書 i
摘要 ii
Abstract iii
1 Introduction 1
2 Preliminary: Tensor Algebra 2
2.1 Tensor matricization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Tensor vectorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Tensor multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 Kronecker, Khatri–Rao, and Hadamard Products . . . . . . . . . . . . . . 6
3 Tensor Decompositions 7
3.1 Why Multi-way Array Decompositions and Factorizations ? . . . . . . . 7
3.2 CP decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3 Tucker decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 The Principal Componen Analysis for Tensor 10
4.1 High-Order Principal Component Analysis . . . . . . . . . . . . . . . . . 11
4.2 Some discussions about HOPCA . . . . . . . . . . . . . . . . . . . . . . 20
5 Nonnegative methods 22
5.1 Nonnegative matrix factorization (NMF) . . . . . . . . . . . . . . . . . . 22
5.2 NMF (Facial feature extraction) . . . . . . . . . . . . . . . . . . . . . . 23
5.3 Third-order NTD (Facial feature extraction) . . . . . . . . . . . . . . . . 24
5.4 Fourth-order NTD (Gait feature extraction) . . . . . . . . . . . . . . . . 27
5.5 NTD feature tensor extraction . . . . . . . . . . . . . . . . . . . . . . . 30
5.6 Successive core tensor extraction (NTD-FTE + HOPCA): . . . . . . . . . 31
6 Experiments using real-world data 32
6.1 Gait recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.2 Object recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.3 Human face recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
參考文獻 References
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