JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (9): 105-113, 126.doi: 10.6040/j.issn.1671-9352.4.2022.5119

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Feasible region localization and fast causal instance selection for multi-instance learning

Mei YANG1,2,3,*(),Wenjing KE1,Dandong WANG1   

  1. 1. School of Computer Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China
    2. Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu 610500, Sichuan, China
    3. Lab of Machin Learning, Southwest Petroleum University, Chengdu 610500, Sichuan, China
  • Received:2022-08-02 Online:2023-09-20 Published:2023-09-08
  • Contact: Mei YANG E-mail:yangmei@swpu.edu.cn

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Abstract:

This paper proposes a feasible region localization and fast causal instance selection(FFCM)algorithm for multi-instance learning, incorporating three techniques. To minimize the feasible region of data, the fast feasible region localization technique is used to select representative instances from the positive bags as candidate instances based on distance measurement, and reduces the negative referee bags through probability analysis. The fast causal instance-based selection technique uses the causal relationship between candidate instances and negative referee bags to construct fusion bags. Subsequently, prior knowledge is employed to select causal instances from candidate instances based on the designed causal instance criteria. The bag mapping technique maps bags into single vectors with high distinguishability using causal instances and a difference-based mapping function. The proposed algorithm is compared with 6 state-of-the-art MIL algorithms on 27 commonly used datasets. The experimental results show that the proposed FFCM exhibits comparable classification performance.

Key words: causal instance, feasible region, mapping, multi-instance learning, probability analysis

CLC Number: 

  • TP181

Table 1

Notations"

符号 含义 符号 含义
$\mathscr{C}=\bf{R}^{d}$ 实例空间 $\mathit{{A}}$ 先验分类器
$\mathscr{Y}=\{+1，-1\}$ 标签空间 $\mathit{{A}}(\cdot)$ - 为正的概率
$\mathscr{B}=\left\{\left(\boldsymbol{B}_{i}，y_{i}\right)\right\}_{i=1}^{n}$ 数据集 $\boldsymbol{B}_{i}^{x}=\{\boldsymbol{x}\} \cup \boldsymbol{B}_{i}^{-}$ 融合包
$\boldsymbol{B}_{i}$ 包 C 候选实例集
$y_{i} \in \mathscr{Y}$ 包的标签 $\mathscr{B}^{r}$ 负裁判包集
$m_{i}$ 包中实例数 $\mathit{\boldsymbol{s}}_{i j}$ 因果性评判指标
$\mathit{\boldsymbol{x}}_{i j}$ 包中实例 R 因果实例集
$\mathscr{B}^{+}\left(\mathscr{B}^{-}\right)$ 正(负)包集合 $c$ 因果实例的个数
$N^{+}\left(N^{-}\right)$ 正(负) 包的个数 $\mathscr{V}$ 映射向量集

Fig.1

Schematic diagram of causal instance selection process"

Table 2

The characteristic of datasets"

数据集 子数据集个数 维度 包数 正包数 负包数 实例数 包内最大实例数 包内最小实例数 包内平均实例数
Musk1 1 166 92 47 45 476 40 2 5.17
Musk2 1 166 102 39 63 6 598 1 044 1 64.69
Elephant 1 230 200 100 100 1 391 13 2 6.96
Fox 1 230 200 100 100 1 320 13 2 6.60
Tiger 1 230 200 100 100 1 220 13 1 6.10
Mutagenesis1 1 7 188 125 63 10 486 88 28 55.78
Mutagenesis2 1 7 42 13 29 2 132 86 26 50.76
Messidor 1 687 1 200 654 546 12 352 12 8 10.29
Newsgroups 10 200 100 47~50 50~53 1 982~5 443 54~84 8~29 19.8~54.4
Web 9 5 863~6 519 113 21~88 25~92 3 423 200 4 30.29

Fig.2

Accuracy of FFCM under different c"

Fig.3

Time consumption of 10 times 10cv of FFCM under different c"

Table 3

Accuracy of FFCM under different pr %"

数据集 n×d pr=0.05 pr=0.10 pr=0.15 pr=0.20
Musk1 476×166 79.11±4.27 79.11±2.47 80.11±3.20 78.89±3.51
Musk2 6 598×166 78.20±4.09 77.00±2.68 75.60±3.38 78.10±2.80
Mutagenesis1 2 132×7 81.33±2.07 82.78±3.03 81.56±1.94 82.44±2.32
Elephant 1 391×230 84.15±2.01 84.05±1.56 84.80±1.55 84.45±1.17
Alt.atheism 5 443×200 87.62±0.80 88.10±1.54 87.20±1.22 88.10±1.45
Web4 3 423×6 059 85.00±1.59 85.73±1.03 84.91±1.77 84.82±1.59

Table 4

Accuracy of FFCM and comparison algorithms %"

数据集 miVLAD miFV MILDM StableMIL PL ELDB FFCM
Musk1 83.11±2.21 91.11±1.41 79.11±2.15 90.67±2.29 80.89±1.78 89.60±1.90 80.33±2.63
Musk2 78.20±2.64 84.80±1.72 79.11±2.33 84.80±3.06 76.40±4.27 85.04±2.25 76.30±3.38
Elephant 84.00±0.84 84.80±0.81 77.10±1.74 66.10±2.60 71.80±4.15 76.00±3.10 85.00±1.24
Fox 61.70±1.66 60.50±1.73 54.80±4.23 58.00±2.21 52.00±2.39 55.90±2.40 61.10±1.87
Tiger 84.70±0.75 78.40±1.02 69.80±1.17 67.50±2.66 69.70±2.56 71.10±2.20 80.50±0.67
Mutagenesis1 81.50±1.96 80.78±1.09 80.00±2.11 83.56±2.47 79.35±1.65 84.67±0.84 80.78±2.51
Mutagenesis2 78.50±2.29 80.50±1.00 81.00±2.55 86.00±3.00 74.00±10.56 59.93±6.40 71.00±5.61
Messidor 67.43±0.39 70.57±0.47 63.92±0.64 62.73±0.91 54.52±0.38 57.40±2.41 63.84±1.25
News.aa 84.70±1.42 82.60±1.74 54.60±4.03 51.80±7.14 80.60±1.50 84.67±1.35 87.60±1.02
News.cg 79.00±1.48 80.40±1.02 52.20±6.37 48.60±2.73 78.40±1.50 77.72±2.98 81.00±1.90
News.co 68.30±1.55 72.00±1.41 48.00±4.15 48.40±5.08 63.60±2.06 65.94±2.81 71.20±1.33
News.csm 78.70±1.73 77.80±1.60 49.20±2.79 53.40±2.87 77.60±0.80 76.13±4.58 79.00±2.14
News.mf 71.90±1.64 73.80±1.94 43.40±2.87 50.40±2.87 63.20±4.53 64.60±3.29 68.00±1.90
News.rsb 82.90±0.94 84.00±1.10 46.20±3.12 51.00±6.10 81.20±0.98 77.80±2.40 81.20±1.17
News.rsh 88.60±0.92 88.60±1.85 51.20±1.83 51.00±3.41 81.20±0.98 81.35±1.42 89.10±1.14
News.se 91.90±0.30 93.00±1.10 55.80±5.60 51.40±3.20 92.00±1.26 88.20±2.10 93.50±0.81
News.sm 81.90±1.70 83.00±1.67 53.80±3.43 49.20±2.71 81.60±1.50 80.40±1.56 82.40±1.43
News.ss 84.70±1.10 86.60±2.33 48.20±2.99 55.40±3.07 76.80±2.32 77.60±2.30 86.70±1.49
Web1 82.00±0.89 84.55±0.57 82.91±0.89 82.00±1.34 81.82±3.25 81.27±1.38 81.45±0.73
Web2 81.00±2.35 82.36±0.45 83.45±0.68 81.64±0.89 78.91±1.67 72.18±1.65 80.73±0.68
Web3 82.00±1.56 82.73±1.72 82.73±1.29 81.82±1.15 80.73±0.68 80.72±2.91 81.27±0.60
Web4 84.45±1.43 80.73±1.34 79.09±1.00 74.00±2.48 77.45±0.36 77.27±3.02 84.82±1.99
Web5 83.00±1.35 77.45±0.68 80.00±1.72 87.05±0.79 77.27±0.81 74.18±1.29 83.27±1.59
Web6 84.36±2.14 80.36±1.69 82.73±1.15 77.64±0.93 77.82±0.73 81.82±2.64 86.36±0.91
Web7 74.00±2.67 67.82±2.34 61.09±3.65 62.00±2.10 52.73±1.29 51.73±4.52 71.82±2.87
Web8 73.27±2.04 69.82±1.76 56.91±1.59 59.27±0.68 54.18±6.18 51.27±4.39 76.00±3.38
Web9 76.55±2.87 75.82±2.20 56.73±2.55 54.00±4.69 53.27±6.02 48.07±2.60 75.55±2.17
Mean Rank 2.63 2.48 4.85 4.93 5.37 5.00 2.74

Fig.4

CD diagram comparing FFCM with 6 contrasting algorithms using the Bonferroni-Dunn test"

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