多示例学习的可行域定位及快速因果实例选择

doi:10.6040/j.issn.1671-9352.4.2022.5119

摘要/Abstract

摘要：

提出了一种多示例学习的可行域定位及快速因果实例选择(feasible region localization and fast causal instance selection for multi-instance learning, FFCM)算法, 包含3个技术。可行域定位技术基于距离度量, 从正包中选出具有代表性的实例作为候选实例; 然后利用概率分析筛选负裁判包, 以最大限度缩减选择因果实例的可行域范围。快速因果实例选择技术利用候选实例与负裁判包的因果关系构建融合包, 设计因果性评判指标, 使用先验知识从候选实例中选择出因果实例。包映射技术基于因果实例和差值映射函数, 将包映射为有较高可区分性的单向量。本算法在27个常用数据集上进行了实验, 并与6个前沿的MIL算法进行了对比, 实验结果展示了FFCM的良好分类性能。

关键词: 因果实例, 可行域, 映射, 多示例学习, 概率分析

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

中图分类号:

TP181

杨梅,柯文静,王丹东. 多示例学习的可行域定位及快速因果实例选择[J]. 《山东大学学报(理学版)》, 2023, 58(9): 105-113, 126.

Mei YANG,Wenjing KE,Dandong WANG. Feasible region localization and fast causal instance selection for multi-instance learning[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(9): 105-113, 126.

图/表 8

表1

图1

表2

图2

图3

表3

表4

FFCM与其他算法的准确率对比"

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

表4

图4

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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

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

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