臺灣博碩士論文加值系統

在本篇論文中我們提出了一種新穎的線性降維判別分析法。藉由判斷鄰近空間中異質點的多寡及分布狀況，每一對同質點被給予不同的權重。此權重矩陣可決定一對同質點在新空間中是否可以被投影靠近。此方法成功的改善了過去判別分析法只根據同質點間距離規定在新空間的投影而產生的類別混雜問題。在圖形識別與二維資料分布上都得到較好的結果。

Many supervised linear dimensionality reduction methods face tradeoffs when deciding to preserve the within-class multimodality or to achieve a better between-class separation. These algorithms tend to preserve the neighborhood structure in the original space, and leave the determination to the optimization process. In this paper, we propose Hypersphere Distribution Discriminant Analysis (HDDA) to determine the projection of samples in the same class by defining a new within-class affinity matrix. This matrix is based on the distribution of nearby samples in different classes (heteropoints). When more heteropoints appear in the neighborhood space between a pair of the within-class samples, this pair should be projected separately to avoid mixing problems. Otherwise, the pair could be either projected together or not as long as better accuracy achieved. Considering both the distribution of heteropoints and the distance between the within-class pairs, HDDA shows effective results compared with the state of the art methods.

1 Introduction 1
2 Related Works 4
2.1 Frameworks of Linear Dimensionality Reduction 4
2.2 Linear Discriminant Analysis 4
2.3 Locality Preserving Projection 5
2.4 Local Fisher Discriminant Analysis 6
2.5 Local Sensitive Discriminant Analysis 8
2.6 Summary 9
3 Hypersphere Distribution Discriminant Analysis 10
3.1 Building the affinity matrix 10
3.2 Hypersphere Distribution Discriminant Analysis 13
3.2.1 Build the distribution matrix H with hyperspheres 13
3.2.2 Construct the new within-class affinity matrix A 13
3.2.3 Compute the transformation matrixW 14
3.3 Justification of the Weighting Fucntion 14
4 Justification and Extensions 17
4.1 Justification on Pointwise LDA 17
4.2 Kernel HDDA 18
5 Experimental Results 19
5.1 Synthetic Data 19
5.2 Classification for IDA Datasets 19
5.3 2D Data Visualization 21
6 Conclusion 28
7 Reference 29

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