《计算机应用》唯一官方网站 ›› 2023, Vol. 43 ›› Issue (12): 3772-3778.DOI: 10.11772/j.issn.1001-9081.2022121838
收稿日期:
2022-12-12
修回日期:
2023-02-13
接受日期:
2023-02-16
发布日期:
2023-03-09
出版日期:
2023-12-10
通讯作者:
鲍胜利
作者简介:
王啸飞(1997—),男,湖南慈利人,硕士研究生,主要研究方向:机器学习、推荐算法基金资助:
Xiaofei WANG1,2, Shengli BAO1,2(), Jionghuan CHEN1,2
Received:
2022-12-12
Revised:
2023-02-13
Accepted:
2023-02-16
Online:
2023-03-09
Published:
2023-12-10
Contact:
Shengli BAO
About author:
WANG Xiaofei, born in 1997, M. S. candidate. His research interests include machine learning, recommendation algorithm.Supported by:
摘要:
针对传统聚类算法在对缺失样本进行数据填充过程中存在样本相似度难度量且填充数据质量差的问题,提出一种基于潜在因子模型(LFM)在子空间上的缺失值注意力聚类算法。首先,通过LFM将原始数据空间映射到低维子空间,降低样本的稀疏程度;其次,通过分解原空间得到的特征矩阵构建不同特征间的注意力权重图,优化子空间样本间的相似度计算方式,使样本相似度的计算更准确、泛化性更好;最后,为了降低样本相似度计算过程中过高的时间复杂度,设计一种多指针的注意力权重图进行优化。在4个按比例随机缺失的数据集上进行实验。在Hand-digits数据集上,相较于面向高维特征缺失数据的K近邻插补子空间聚类(KISC)算法,在数据缺失比例为10%的情况下,所提算法的聚类准确度(ACC)提高了2.33个百分点,归一化互信息(NMI)提高了2.77个百分点,在数据缺失比例为20%的情况下,所提算法的ACC提高了0.39个百分点,NMI提高了1.33个百分点,验证了所提算法的有效性。
中图分类号:
王啸飞, 鲍胜利, 陈炯环. 基于潜在因子模型在子空间上的缺失值注意力聚类算法[J]. 计算机应用, 2023, 43(12): 3772-3778.
Xiaofei WANG, Shengli BAO, Jionghuan CHEN. Missing value attention clustering algorithm based on latent factor model in subspace[J]. Journal of Computer Applications, 2023, 43(12): 3772-3778.
符号 | 定义 | 符号 | 定义 |
---|---|---|---|
缺失特征样本数据集 | 特征矩阵 | ||
第 | 特征 | ||
第 | 样本类别数 | ||
第 | 样本 | ||
第 | 隐向量维度 | ||
子空间矩阵 |
表1 符号和定义
Tab.1 Symbols and definitions
符号 | 定义 | 符号 | 定义 |
---|---|---|---|
缺失特征样本数据集 | 特征矩阵 | ||
第 | 特征 | ||
第 | 样本类别数 | ||
第 | 样本 | ||
第 | 隐向量维度 | ||
子空间矩阵 |
数据集 | 样本数 | 特征维度 | 类别数 |
---|---|---|---|
Hand-digits | 1 797 | 64 | 10 |
COIL20 | 1 440 | 1 024 | 20 |
Breast-cancer | 569 | 30 | 2 |
Wine | 178 | 13 | 3 |
表2 数据集信息
Tab. 2 Information of datasets
数据集 | 样本数 | 特征维度 | 类别数 |
---|---|---|---|
Hand-digits | 1 797 | 64 | 10 |
COIL20 | 1 440 | 1 024 | 20 |
Breast-cancer | 569 | 30 | 2 |
Wine | 178 | 13 | 3 |
数据集 | 缺失 比例/ % | 原始空间 | 子空间 | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0+K-means | Min+K-means | Max+K-mean | Mean+K-means | KISC算法 | 本文算法 | KISC算法 | 本文算法 | ||||||||||
ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ||
Hand-digits | 10 | 63.44 | 59.36 | 71.51 | 67.45 | 71.62 | 68.81 | 71.40 | 68.10 | 67.82 | 60.94 | 74.21 | 64.54 | 73.46 | 67.49 | 75.79 | 70.26 |
20 | 64.83 | 53.29 | 61.27 | 49.58 | 63.22 | 53.11 | 64.27 | 55.36 | 61.58 | 50.41 | 69.09 | 56.08 | 71.90 | 59.94 | 72.29 | 61.27 | |
30 | 32.50 | 19.82 | 39.23 | 25.29 | 42.07 | 26.74 | 35.73 | 23.66 | 55.60 | 40.55 | 58.65 | 43.05 | 44.07 | 28.05 | 49.25 | 30.27 | |
40 | 19.59 | 7.68 | 20.09 | 6.83 | 19.59 | 5.66 | 18.20 | 6.38 | 32.38 | 19.47 | 35.63 | 22.29 | 21.31 | 6.29 | 21.65 | 07.37 | |
COIL20 | 10 | 62.04 | 76.01 | 61.71 | 74.59 | 60.74 | 74.92 | 61.16 | 74.74 | 63.11 | 77.27 | 70.84 | 78.72 | 70.81 | 78.61 | 71.11 | 79.10 |
20 | 61.74 | 75.12 | 62.65 | 74.83 | 61.40 | 74.41 | 60.10 | 73.76 | 60.33 | 73.77 | 68.67 | 78.02 | 69.62 | 79.59 | 70.03 | 79.72 | |
30 | 60.24 | 73.54 | 58.85 | 72.14 | 59.58 | 72.94 | 60.50 | 73.21 | 62.81 | 74.49 | 68.31 | 76.62 | 70.54 | 78.28 | 71.04 | 76.78 | |
40 | 52.22 | 68.16 | 54.31 | 69.10 | 53.35 | 69.05 | 55.77 | 69.57 | 57.40 | 71.64 | 63.99 | 74.38 | 62.71 | 71.83 | 64.86 | 71.31 | |
Breast-cancer | 10 | 83.02 | 41.42 | 82.99 | 41.34 | 82.99 | 41.28 | 82.97 | 41.30 | 83.17 | 41.02 | 83.69 | 42.70 | 85.15 | 45.78 | 85.44 | 46.48 |
20 | 81.16 | 37.38 | 81.09 | 37.24 | 81.07 | 37.01 | 81.14 | 37.34 | 80.76 | 36.69 | 81.16 | 37.50 | 82.41 | 42.15 | 84.46 | 44.19 | |
30 | 79.88 | 34.26 | 79.86 | 34.23 | 79.86 | 34.32 | 79.96 | 34.44 | 79.72 | 33.53 | 80.22 | 35.66 | 80.35 | 39.12 | 84.45 | 44.10 | |
40 | 78.70 | 29.74 | 78.65 | 30.02 | 78.63 | 29.82 | 78.65 | 29.92 | 78.73 | 30.45 | 79.28 | 31.21 | 80.30 | 34.17 | 82.39 | 35.95 | |
Wine | 10 | 41.42 | 36.84 | 41.34 | 36.97 | 41.34 | 37.35 | 41.30 | 35.71 | 41.02 | 35.79 | 42.70 | 37.45 | 45.78 | 38.40 | 46.48 | 38.78 |
20 | 37.38 | 29.54 | 37.24 | 29.70 | 37.34 | 28.61 | 37.34 | 29.33 | 36.69 | 30.60 | 37.50 | 31.42 | 42.15 | 32.56 | 44.19 | 34.65 | |
30 | 34.26 | 26.84 | 34.23 | 26.24 | 34.32 | 26.19 | 34.44 | 27.06 | 33.53 | 27.79 | 35.66 | 26.25 | 39.12 | 26.60 | 44.10 | 27.88 | |
40 | 29.74 | 23.68 | 30.02 | 22.69 | 29.82 | 22.57 | 29.92 | 23.01 | 30.45 | 20.46 | 31.21 | 22.11 | 34.17 | 22.45 | 35.95 | 22.29 |
表3 不同算法聚类结果的ACC和NMI比较 (%)
Tab.3 Comparison of ACC and NMI in clustering results between different algorithms
数据集 | 缺失 比例/ % | 原始空间 | 子空间 | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0+K-means | Min+K-means | Max+K-mean | Mean+K-means | KISC算法 | 本文算法 | KISC算法 | 本文算法 | ||||||||||
ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ACC | NMI | ||
Hand-digits | 10 | 63.44 | 59.36 | 71.51 | 67.45 | 71.62 | 68.81 | 71.40 | 68.10 | 67.82 | 60.94 | 74.21 | 64.54 | 73.46 | 67.49 | 75.79 | 70.26 |
20 | 64.83 | 53.29 | 61.27 | 49.58 | 63.22 | 53.11 | 64.27 | 55.36 | 61.58 | 50.41 | 69.09 | 56.08 | 71.90 | 59.94 | 72.29 | 61.27 | |
30 | 32.50 | 19.82 | 39.23 | 25.29 | 42.07 | 26.74 | 35.73 | 23.66 | 55.60 | 40.55 | 58.65 | 43.05 | 44.07 | 28.05 | 49.25 | 30.27 | |
40 | 19.59 | 7.68 | 20.09 | 6.83 | 19.59 | 5.66 | 18.20 | 6.38 | 32.38 | 19.47 | 35.63 | 22.29 | 21.31 | 6.29 | 21.65 | 07.37 | |
COIL20 | 10 | 62.04 | 76.01 | 61.71 | 74.59 | 60.74 | 74.92 | 61.16 | 74.74 | 63.11 | 77.27 | 70.84 | 78.72 | 70.81 | 78.61 | 71.11 | 79.10 |
20 | 61.74 | 75.12 | 62.65 | 74.83 | 61.40 | 74.41 | 60.10 | 73.76 | 60.33 | 73.77 | 68.67 | 78.02 | 69.62 | 79.59 | 70.03 | 79.72 | |
30 | 60.24 | 73.54 | 58.85 | 72.14 | 59.58 | 72.94 | 60.50 | 73.21 | 62.81 | 74.49 | 68.31 | 76.62 | 70.54 | 78.28 | 71.04 | 76.78 | |
40 | 52.22 | 68.16 | 54.31 | 69.10 | 53.35 | 69.05 | 55.77 | 69.57 | 57.40 | 71.64 | 63.99 | 74.38 | 62.71 | 71.83 | 64.86 | 71.31 | |
Breast-cancer | 10 | 83.02 | 41.42 | 82.99 | 41.34 | 82.99 | 41.28 | 82.97 | 41.30 | 83.17 | 41.02 | 83.69 | 42.70 | 85.15 | 45.78 | 85.44 | 46.48 |
20 | 81.16 | 37.38 | 81.09 | 37.24 | 81.07 | 37.01 | 81.14 | 37.34 | 80.76 | 36.69 | 81.16 | 37.50 | 82.41 | 42.15 | 84.46 | 44.19 | |
30 | 79.88 | 34.26 | 79.86 | 34.23 | 79.86 | 34.32 | 79.96 | 34.44 | 79.72 | 33.53 | 80.22 | 35.66 | 80.35 | 39.12 | 84.45 | 44.10 | |
40 | 78.70 | 29.74 | 78.65 | 30.02 | 78.63 | 29.82 | 78.65 | 29.92 | 78.73 | 30.45 | 79.28 | 31.21 | 80.30 | 34.17 | 82.39 | 35.95 | |
Wine | 10 | 41.42 | 36.84 | 41.34 | 36.97 | 41.34 | 37.35 | 41.30 | 35.71 | 41.02 | 35.79 | 42.70 | 37.45 | 45.78 | 38.40 | 46.48 | 38.78 |
20 | 37.38 | 29.54 | 37.24 | 29.70 | 37.34 | 28.61 | 37.34 | 29.33 | 36.69 | 30.60 | 37.50 | 31.42 | 42.15 | 32.56 | 44.19 | 34.65 | |
30 | 34.26 | 26.84 | 34.23 | 26.24 | 34.32 | 26.19 | 34.44 | 27.06 | 33.53 | 27.79 | 35.66 | 26.25 | 39.12 | 26.60 | 44.10 | 27.88 | |
40 | 29.74 | 23.68 | 30.02 | 22.69 | 29.82 | 22.57 | 29.92 | 23.01 | 30.45 | 20.46 | 31.21 | 22.11 | 34.17 | 22.45 | 35.95 | 22.29 |
数据集 | 缺失率/% | 时间/s | |
---|---|---|---|
结构未优化 | 结构优化 | ||
Wine | 10 | 0.363 | 0.230 |
20 | 0.491 | 0.296 | |
30 | 0.499 | 0.302 | |
40 | 0.495 | 0.310 | |
Breast-cancer | 10 | 11.150 | 3.140 |
20 | 12.370 | 3.190 | |
30 | 12.440 | 3.230 | |
40 | 12.340 | 3.200 | |
Hand-digits | 10~20 | 3 272.4 | 617.1 |
30~40 | 3 716.6 | 670.6 | |
COIL20 | 10~20 | 8 961.3 | 1 816.4 |
30~40 | 9 200.8 | 1 900.2 |
表4 特征相似度权重图优化前后时间对比
Tab. 4 Time comparison of feature similarity weight graph before and after optimization
数据集 | 缺失率/% | 时间/s | |
---|---|---|---|
结构未优化 | 结构优化 | ||
Wine | 10 | 0.363 | 0.230 |
20 | 0.491 | 0.296 | |
30 | 0.499 | 0.302 | |
40 | 0.495 | 0.310 | |
Breast-cancer | 10 | 11.150 | 3.140 |
20 | 12.370 | 3.190 | |
30 | 12.440 | 3.230 | |
40 | 12.340 | 3.200 | |
Hand-digits | 10~20 | 3 272.4 | 617.1 |
30~40 | 3 716.6 | 670.6 | |
COIL20 | 10~20 | 8 961.3 | 1 816.4 |
30~40 | 9 200.8 | 1 900.2 |
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