The Computing Capacity of Three-Input Multiple-Valued One-Threshold Perceptrons

In this paper, an exact and general formula is derived for the number of linear partitions of a given point set V in three-dimensional space, depending on the configuration formed by the points of V. The set V can be a multi-set, that is it may contain points that coincide. Based on the formula, we obtain an efficient algorithm for counting the number of k-valued logic functions simulated by a three-input k-valued one-threshold perceptron.     

Perceptron Learning Revisited: The Sonar Targets Problem

Recently it was pointed out that a well-known benchmark data set, the sonar target data, indeed is linearly separable. This fact comes somewhat surprising, since earlier studies involving delta rule trained perceptrons did not achieve the separation of the training data. These results immediately raise the question of why a perceptron with a continuous activation function may fail to recognize linear separability and how to remedy this failure. The study of these issues directly leads to a performance comparison of a wide variety of different perceptron training procedures on real world data.     

关于部分多值逻辑函数集中准完备集的若干性质

Sheffer函数的最简判定是多值逻辑函数集完备性判定问题中的一个重要的理论和实际问题.文中根据多值逻辑函数理论中“保关系”的系统思想,使用群论和组合数学的工具,研究了部分多值逻辑函数集中准完备类相应关系的若干性质.给出并证明了非空关系Gm是完全关系以及子群H是Gm的对称群的充要条件,定出了部分k值逻辑中完满对称函数类Fs,m中函数集的个数.以上工作为解决部分多值逻辑中Sheffer函数的判定提供了研究基础.     

Extracting Phonetic Knowledge from Learning Systems: Perceptrons, Support Vector Machines and Linear Discriminants

Speech perception relies on the human ability to decode continuous, analogue sound pressure waves into discrete, symbolic labels (phonemes) with linguistic meaning. Aspects of this signal-to-symbol transformation have been intensively studied over many decades, using psychophysical procedures. The perception of (synthetic) syllable-initial stop consonants has been especially well studied, since these sounds display a marked categorization effect: they are typically dichotomised into voiced and unvoiced classes according to their voice onset time (VOT). In this case, the category boundary is found to have a systematic relation to the (simulated) place of articulation, but there is no currently-accepted explanation of this phenomenon. Categorization effects have now been demonstrated in a variety of animal species as well as humans, indicating that their origins lie in general auditory and/or learning mechanisms, rather than in some phonetic module specialized to human speech processing.In recent work, we have demonstrated that appropriately-trained computational learning systems (neural networks) also display the same systematic behaviour as human and animal listeners. Networks are trained on simulated patterns of auditory-nerve firings in response to synthetic continuua of stop-consonant/vowel syllables varying in place of articulation and VOT. Unlike real listeners, such a software model is amenable to analysis aimed at extracting the phonetic knowledge acquired in training, so providing a putative explanation of the categorization phenomenon. Here, we study three learning systems: single-layer perceptrons, support vector machines and Fisher linear discriminants. We highlight similarities and differences between these approaches. We find that the modern inductive inference technique for small sample sizes of support vector machines gives the most convincing results. Knowledge extracted from the trained machine indicated that the phonetic percept of voicing is easily and directly recoverable from auditory (but not acoustic) representations.     

一种新的归纳学习算法--基于特征可分性的归纳学习算法

本文提出了一种新的基于特征可分性的归纳学习算法(SBI)。与现有各种归纳学习算法相比,该方法直接从特征对不同类型的可分性出发,建立可分性判据,然后形成决策树,可对多种概念进行判别。SBI算法具有直观且计算简便等优点。本文以实例表明了SBI算法的有效性。     

Learning to Reason with a Restricted View

The Learning to Reason framework combines the study of Learning and Reasoning into a single task. Within it, learning is done specifically for the purpose of reasoning with the learned knowledge. Computational considerations show that this is a useful paradigm; in some cases learning and reasoning problems that are intractable when studied separately become tractable when performed as a task of Learning to Reason.In this paper we study Learning to Reason problems where the interaction with the world supplies the learner only partial information in the form of partial assignments. Several natural interpretations of partial assignments are considered and learning and reasoning algorithms using these are developed. The results presented exhibit a tradeoff between learnability, the strength of the oracles used in the interface, and the range of reasoning queries the learner is guaranteed to answer correctly.     

一种结合限制的多任务学习策略及其应用

定义任务之间的偏序限制,基于偏序限制可以联系原先独立的任务.分析偏序限制的应用,给出一个协同演化的多任务学习框架,它反复地通过各个任务的独立演化以寻优,通过联合调整以结合偏序限制.给出本框架在构建猪肉预冷损耗曲线过程中的应用:考虑了低湿损耗曲线与中湿损耗曲线间的偏序关系,利用协同演化,在样本量很少时,也能获得合理的低湿和中湿损耗曲线.对于4个标准测试函数的测试显示了本策略对于一般问题的有效性.     

Complexity Results on Learning by Neural Nets

We consider the computational complexity of learning by neural nets. We are interested in how hard it is to design appropriate neural net architectures and to train neural nets for general and specialized learning tasks. Our main result shows that the training problem for 2-cascade neural nets (which have only two non-input nodes, one of which is hidden) is N-complete, which implies that finding an optimal net (in terms of the number of non-input units) that is consistent with a set of examples is also N-complete. This result also demonstrates a surprising gap between the computational complexities of one-node (perceptron) and two-node neural net training problems, since the perceptron training problem can be solved in polynomial time by linear programming techniques. We conjecture that training a k-cascade neural net, which is a classical threshold network training problem, is also N-complete, for each fixed k2. We also show that the problem of finding an optimal perceptron (in terms of the number of non-zero weights) consistent with a set of training examples is N-hard.Our neural net learning model encapsulates the idea of modular neural nets, which is a popular approach to overcoming the scaling problem in training neural nets. We investigate how much easier the training problem becomes if the class of concepts to be learned is known a priori and the net architecture is allowed to be sufficiently non-optimal. Finally, we classify several neural net optimization problems within the polynomial-time hierarchy.     

多示例学习的示例层次覆盖算法

在多示例学习（Multi-instance learning,MIL）中,核心示例对于包类别的预测具有重要作用。若两个示例周围分布不同数量的同类示例,则这两个示例的代表程度不同。为了从包中选出最具有代表性的示例组成核心示例集,提高分类精度,本文提出多示例学习的示例层次覆盖算法（Multi-instance learning with instance_level covering algorithm,MILICA）。该算法首先利用最大Hausdorff距离和覆盖算法构建初始核心示例集,然后通过覆盖算法和反验证获得最终的核心示例集和各覆盖包含的示例数,最后使用相似函数将包转为单示例。在两类数据集和多类图像数据集上的实验证明,MILICA算法具有较好的分类性能。     

一种新的连续动作集学习自动机

学习自动机（Learning automation,LA）是一种自适应决策器。其通过与一个随机环境不断交互学习从一个允许的动作集里选择最优的动作。在大多数传统的LA模型中,动作集总是被取作有限的。因此,对于连续参数学习问题,需要将动作空间离散化,并且学习的精度取决于离散化的粒度。本文提出一种新的连续动作集学习自动机（Continuous action set learning automaton,CALA）,其动作集为一个可变区间,同时按照均匀分布方式选择输出动作。学习算法利用来自环境的二值反馈信号对动作区间的端点进行自适应更新。通过一个多模态学习问题的仿真实验,演示了新算法相对于3种现有CALA算法的优越性。     

Classification methodologies of multilayer perceptrons with sigmoid activation functions

This paper studies the classification mechanisms of multilayer perceptrons (MLPs) with sigmoid activation functions (SAFs). The viewpoint is presented that in the input space the hyperplanes determined by the hidden basis functions with values 0's do not play the role of decision boundaries, and such hyperplanes do not certainly go through the marginal regions between different classes. For solving an n-class problem, a single-hidden-layer perceptron with at least log2(n-1)?2 hidden nodes is needed. The final number of hidden neurons is still related to the sample distribution shapes and regions, but not to the number of samples and input dimensions. As a result, an empirical formula for optimally selecting the initial number of hidden nodes is proposed. The ranks of response matrixes of hidden layers should be taken as a main basis for pruning or growing the existing hidden neurons. A structure-fixed perceptron ought to learn more than one round from different starting weight points for one classification task, and only the group of weights and biases that has the best generalization performance should be reserved. Finally, three examples are given to verify the above viewpoints.     

一种新的基于粒群优化的BP网络学习算法

标准BP学习算法是多层感知器的一种训练学习算法，是基于无约束极值问题的梯度法而设计的。针对标准算法存在的收敛速度慢、目标函数易陷入局部极小等缺点，该文提出了一种基于粒群优化的全新学习算法——粒群学习算法。该算法采用并行全局寻优策略，使网络以更快的速度收敛至全局最优解，且更易于编程实现。仿真实例证明，该算法是一种简洁高效的BP神经网络学习算法，有着极为广泛的应用前景。     

减少噪声对数据污染的一种鲁棒算法

利用聚类对噪声干扰的抵抗能力和对好的样本进行强化学习的思想,引入了聚类分析和鲁棒因子,提出一种新颖的鲁棒学习算法（包括了选择不同鲁棒因子而构成的鲁棒算法１ 和鲁棒算法２）,并对三维曲面和混合噪音进行了仿真实验研究。仿真结果表明,该算法在鲁棒性、收敛性方面明显优于普通的ＢＰ算法。     

多代理模糊收益及策略学习

本文研究了基于模糊知识的多代理决策问题。通过建立代理决策目标的模糊知识,我们给出了基于模糊收益的多代理决策模型,并研究了基于梯度的代理策略学习算法。     

浅谈数字语言学习系统应该实现的功能

文章从一线教学需求的角度全面论述了数字语言学习系统应该具备的主要功能,并在自主学习、网络化考试、智能化评价和互动交流四个方面提出了新的看法。     

基于双稀疏正则的图像集距离学习

随着视频采集和网络传输技术的快速发展,以及个人移动终端设备的广泛使用,大量图像数据以集合形式存在.由于集合内在结构的复杂性,使得图像集分类的一个关键问题是如何度量集合间距离.为了解决这一问题,本文提出了一种基于双稀疏正则的图像集距离学习框架（DSRID）.在该框架中,两集合间距离被建模成其对应的内部典型子结构间的距离,从而保证了度量的鲁棒性和判别性.根据不同的集合表示方法,本文给出了其在传统的欧式空间,以及两个常见的流形空间,即对称正定矩阵流形（symmetric positive definite matrices manifold,SPD manifold）和格林斯曼流形（Grassmann manifold）上的实现.在一系列的基于集合的人脸识别、动作识别和物体分类任务中验证了该框架的有效性.     

On Learning Sets and Functions

This paper presents some results on the probabilistic analysis of learning, illustrating the applicability of these results to settings such as connectionist networks. In particular, it concerns the learning of sets and functions from examples and background information. After a formal statement of the problem, some theorems are provided identifying the conditions necessary and sufficient for efficient learning, with respect to measures of information complexity and computational complexity. Intuitive interpretations of the definitions and theorems are provided.     

浅谈数字语言学习系统应该实现的功能

文章从一线教学需求的角度全面论述了数字语言学习系统应该具备的主要功能,并在自主学习、网络化考试、智能化评价和互动交流四个方面提出了新的看法。     

一种基于Rough集获取规则知识的增量式学习方法

将Rough集理论应用于规则归纳系统,提出了一种基于粗糙集获取规则知识库的增量式学习方法,能够有效处理决策表中不一致情形,采用启发式算法获取决策表的最简规则,当新对象加入时在原有规则集基础上进行规则知识库的增量式更新,避免了为更新规则而重新运行规获取算法。并用UCI中多个数据集从规则集的规则数目、数据浓缩率、预测能力等指标对该算法进行了测试。实验表明了该算法的有效性。