松田 源立

日常的な議論において，どの言明が成立しているか，どの主張（言明から他の言明または主張への攻撃または支持）が重要か，攻撃されている言明を補強するには何が必要かを判断することは適切な結論を得るために重要であるだけなく，議論を深めていくためにも必要なことである．しかし，議論が複雑になったり，複数人が言明を提示しあっている状況では手作業でそのようなことを行うのは難しい．本論文では，議論要素（言明と主張の総称）からなる議論の議論グラフによる表現に対して，議論要素の値（0～1の実数値で表された成立の度合い）を求める評価手法と，その値に基づく分析指標を用いた分析手法からなる議論分析フレームワークDECRAGを提案する．DECRAGは，主張に対する攻撃/支持があるような議論グラフに対して，議論要素の値を実数値で求められるという点でこれまでなかったものである．本論文では，DECRAGで求めた議論要素の値が良い性質を満たし，どの言明が成立しているかを判定するために使用できることを理論的および実験的に示した．さらに，分析指標として提案した残留コスト・釣り合い・有効度が，どの主張が重要かなどを検討するために有用である可能性があることを実験的に示した． In an ordinary discussion, to determine which proposition holds and to find out what is missing to strengthen an attacked proposition is not only important for obtaining an appropriate conclusion but also necessary for deepening the discussion. However, when the discussion gets complex or when people are independently posting propositions and claims, it isn't easy to make such a decision manually. This paper proposes an argumentation analysis framework DECRAG consisting of an argumentation graph to represent a discussion by propositions and claims where a claim is an attack or support from a proposition to a proposition or claim, an evaluation method of it to give a value between 0 and 1 to the proposition or claim representing the degree of its holding, and an analysis method using metrics calculated from the values. DECRAG is new in that its evaluation method can give a value between 0 and 1 to the proposition or claim in an argumentation graph with an attack or support for another claim. We show that the values have good properties and properly represent how their propositions and claims hold theoretically and empirically. We also show that the metrics of remaining cost, balance, and effectiveness can be used to determine which propositions are important by experiments.

For university students, a syllabus gives fundamental information about a course, and is important for choosing a course. However, it is not an easy task for students to grasp the topics actually covered by a course syllabus because they have only little knowledge about topic words in the syllabus before they learn the course. We have been studying on a machine learning method of systematically analyzing syllabi by standard curricular guidelines such as "Computing Science Curricula CS2013," which is released by the ACM and IEEE Computer Society. We acquired a probabilistic topic model of computer science syllabi, and developed a tool for investigating the actual syllabi in the model. In this paper, we introduce a web-based tool and demonstrate its effectiveness by some examples. By applying our tool to a syllabus, students and teachers can know how strongly the syllabus and topics are related quantitatively, where each topic corresponds to the Knowledge Area of CS2013 such as "Algorithms and Complexity (AL)." In addition, the tool utilizes four meta-topics (HUMAN, THEORY, PROGRAMMING, and SYSTEM), which are extracted by investigating the actual syllabi. The tool also provides a list of syllabi similar to the given syllabus, which are selected from the actual syllabi of the top-ranked universities. These information are beneficial for students to understand the courses and for teachers to improve their syllabi.

With the growing number of location-based SNS (Social Networking Service) users, the utilization of SNS data is getting more and more important. In this paper, we focus on the prediction of users' locations from location-based SNS data. The location-based SNS data consists of sequence of checkins which are too sparse to predict the users' locations. In our previous research we generated users' probability distributions by smoothing the sparse check-in data using diffusion-type estimation. However, the generated probability distributions do not take the repeating nature of the check-in data into consideration and cannot be used to predict the users' future locations. In this paper, we propose a method to predict users' future locations by utilizing the repeating nature of the check-in data and similar users' check-in data. Experimental results show that our method outperformed the existing prediction methods.

We propose a new method for efficiently estimating the number of non-Gaussian sources in independent component analysis (ICA). While PCA can find only a few principal components incrementally in the order of significance, ICA has to estimate all the sources after giving the number of them in advance. Then, the appropriate number of sources is determined after the estimation if necessary. Here, we use the adaptive ICA function (AIF), which has been derived by using a simple probabilistic model. It is previously proved that the optimization of AIF with the Gram-Schmidt orthonormalization can find all the sources in descending order of the degree of non-Gaussianity. In this paper, we propose an efficient method for optimizing AIF in the deflation approach by combining fast ICA with the stochastic optimization. In addition, we propose a threshold for determining whether an estimated source is Gaussian or not, which is derived by utilizing the Fisher information of the probabilistic model of AIF. By terminating the optimization when the currently estimated source is Gaussian, the number of sources is estimated efficiently. The experimental results on blind image separation problems verify the usefulness of the proposed method.

Recently, we have proposed a new objective function of ICA called the adaptive ICA function (AIF). AIF is a summation of weighted 4th-order statistics, where the weights are determined by adaptively estimated kurtoses. In this paper, the Gram-Schmidt orthonormalization is applied to the optimization of AIF. The proposed method is theoretically guaranteed to extract the independent components in the unique order of the degree of non-Gaussianity. Consequently, it enables us to fix the permutation ambiguity. Experimental results on blind image separation problems show the usefulness of the proposed method.

In this paper, we propose an objective function of ICA with adaptive estimation of the kurtoses of sources. It is derived by applying the Gaussian approximation to the distribution of sources in the second-order polynomial feature space. This objective function (called the adaptive ICA function (AIF)) is a simple form given as a summation of weighted 4th-order statistics, where the weights are determined by adaptively estimated kurtoses. It is proved by the convergence analysis that the ICA solution is a stable maximum of the objective function. We also propose a natural gradient algorithm optimizing the function. Experimental results show that the proposed method is effective in blind image separation problems.

In this paper, a new approach is proposed for extracting the spatio-temporal patterns from a location-based social networking system (SNS) such as Foursquare. The proposed approach consists of the following procedures. First, the spatio-temporal behaviors of users in SNS are approximated as a probabilistic distribution by using a diffusion-type formula. Since the SNS datasets generally consist of sparse check-in's of users at some time points and locations, it is difficult to investigate the spatio-temporal patterns on a wide range of time and space scales. The proposed method can estimate such wide range patterns by smoothing the sparse datasets by a diffusion-type formula. It is crucial in this method to estimate robustly the scale parameter by giving a prior generative model on check-in's of users. The robust estimation enables the method to extract appropriate patterns even in small local areas. Next, the covariance matrix among the time points is calculated from the estimated distribution. Then, the principal eigenfunctions are approximately extracted as the spatio-temporal patterns by principal component analysis (PCA). The distribution is a mixture of various patterns, some of which are regular ones with a periodic cycle and some of which are irregular ones corresponding to transient events. Though it is generally difficult to separate such complicated mixtures, the experiments on an actual Foursquare dataset showed that the proposed method can extract many plausible and interesting spatiotemporal patterns.

The curricula higher educational institutions offer is a key asset in enabling them to systematically educate their students. We have been developing a curriculum analysis method that can help to find out differences among curricula. On the basis of "Computing Science Curricula CS2013", a report released by the ACM and IEEE Computer Society, we applied our method to analyzing 10 computer science (CS) related curricula offered by CS departments of universities in the United States. Using the method enables us to compare courses across universities. Through an analysis of course syllabi distribution, we found that CS2013 uniformly covered a wide area of computer science. Some universities emphasized human factors, while others attached greater importance to theoretical ones. We also found that some CS departments offered not only a CS curriculum but also an electrical engineering one, and those departments showed a tendency to have more "Architecture and Organization (AR)" related curricula. Furthermore, we found that even though "Information Assurance and Security (IAS)" has not yet become a very popular field, some universities are already offering IAS related courses.

In this paper, a new objective function of ICA is proposed by a probabilistic approach to the quadratic terms. Many previous ICA methods are sensitive to the sign of kurtosis of source (sub-or super-Gaussian), where the change of the sign often causes a large discontinuity in the objective function. On the other hand, some other previous methods use continuous objective functions by using the squares of the 4th-order statistics. However, such squared statistics often lack the robustness because they magnify the outliers. In this paper, we solve this problem by introducing a new objective function which is given as a summation of weighted 4th-order statistics, where the kurtoses of sources are incorporated "smoothly" into the weights. Consequently, the function is always continuously differentiable with respect to both the kurtoses and the separating matrix to be estimated. In addition, we propose a new ICA method optimizing the objective function by the Givens rotations under the orthonormality constraint. Experimental results show that the proposed method is comparable to the other ICA methods and it outperforms them especially when sub-Gaussian sources are dominant.

In this paper, a new approach is proposed for extracting localized spatio-temporal patterns from Foursquare, which is a location-based social networking system (SNS). Previously, we have proposed a method estimating the probabilistic distribution of users in Foursquare by a diffusion-type formula and have extracted various spatio-temporal patterns from the distribution by principal component analysis. However, as the distribution was the average over all the users, only the "global" patterns were extracted. So, we can not extract localized patterns showing the detailed behaviors of limited users in local areas. In this paper, a new method is proposed in order to extract the localized patterns by clustering users. First, the distance among users is measured by the Hellinger distance among the distributions of each user. Next, Ward's method (which is a widely used method in hierarchical cluster analysis) is applied to the users with their distance. Finally, the spatio-temporal patterns are extracted from the distributions for each cluster of users. The results on the real Foursquare dataset show that the proposed method can extract various and interesting localized patterns from each cluster of users.

In this paper, we extract various patterns of the spatio-temporal distribution from Foursquare. Foursquare is a location-based social networking system which has been widely used recently. For extracting patterns, we employ ICA (Independent Component Analysis), which is a useful method in signal processing and feature extraction. Because the Foursquare dataset consists of check-in's of users at some time points and locations, ICA is not directly applicable to it. In order to smooth the dataset, we estimate a continuous spatio-temporal distribution by employing a diffusion-type formula. The experiments on an actual Foursquare dataset showed that the proposed method could extract some plausible and interesting spatio-temporal patterns. © 2014 Springer International Publishing Switzerland.

We have been developing a personalized teaching material generator for beginner level learners of English. Our system keeps personalized vocabularies of learners and recommends suitable teaching materials to them by using their vocabularies. Once the learners choose materials, the system provides each learner with the personalized glossary of words which is expected to be unknown to him/her in order to assist his/her learning suitably. Our basic idea is the concept of 'word set.' We consider the learners' vocabularies and the reading materials as word sets and operate their sets by the set operations. For estimating the difficulty of materials for each learner, it is important to use a proper set of words. Our previous system used the general service list (GSL) and the academic word list (AWL) as word sets. In this paper, we adopted the JACET word list, which is a word list created by the Japan Association of College English Teachers based on the English education system in Japan. We refined our previous system by using JACET as the word set. In addition, the estimation method of the difficulty of materials is improved. Then, the estimation of the difficulty level of reading materials and that of the English skill levels of the learners and materials became more accurate. Moreover, according to many requests from the learners to refine our design of the web site for better usability, our site was improved by adopting a more friendly user interface. In addition, we conducted a questionnaire survey to confirm the improvement of our system.

The ACM Education Board and the IEEE Computer Society's Education released Computing Science Curricula CS2013 in December 2013. In this paper, we applied our curriculum analysis method to analyze the Computing Science Curricula CS2013. By comparing the maps and the topic words of previous curricula CS2008 and CS2013, we found some significantly changed Knowledge Units (KUs) and Knowledge Areas (KAs). We also found other significant changes of CS2013 by using the actual courses of the three universities. Moreover, we discovered that the Body of Knowledge (BOK) of CS2013 had higher explainability that those of other previous computing curricula.

大学の授業の体系性を維持する要となるのがカリキュラムであり，カリキュラムを改良するためには，過去のカリキュラムや他大学のカリキュラムとの比較も必要となってくる．しかし，カリキュラムの比較は，教員がシラバスなどの内容を読んで比較しなければならず簡単ではなかった．本研究では，確率的な文書モデルであるLDAと次元圧縮手法であるIsomapを用いて，授業の内容を説明するシラバスからマップを生成し，カリキュラムを比較する手法を提案する．この手法を用いて2つの学科の情報系のカリキュラムを分析することで，本手法の有効性を評価する．A curriculum is crucial to maintaining the integrity of various courses of universities, and an effort to improve a curriculum may include an analysis of the curriculum by comparing the curriculum with previous curricula or curricula of other universities. However, comparing them by hand is too labor-intensive. In this paper, we propose a method to project syllabi on a map by latent Dirichlet allocation (LDA) and Isomap for the comparison of curricula embodied by the syllabi. We applied this method to information science-related curricula of two departments and evaluated the effectiveness of the method.

Joint approximate diagonalization (JAD) is a widely-used method for blind source separation, which can separate non-Gaussian sources without any other prior knowledge. In this paper, a new extension of JAD (named ensemble JAD) is proposed in order to ameliorate the robustness for a small size of samples by an information theoretic approach. In JAD, the cumulant matrices are estimated and represented by the average (namely, the first-order moment) over given samples. On the other hand, ensemble JAD preserves the ensemble of all the cumulant matrices for each sample without averaging them. Then, the second-order moments among the ensemble are utilized for estimating the sources. Numerical experiments verify the validity of this method when the sub- Gaussian (negative kurtosis) sources are included. © Springer-Verlag 2013.

In order to implement multidimensional scaling (MDS) efficiently, we propose a new method named "global mapping analysis" (GMA), which applies stochastic approximation to minimizing MDS criteria. GMA can solve MDS more efficiently in both the linear case (classical MDS) and non-linear one (e.g., ALSCAL) if only the MDS criteria are polynomial. GMA separates the polynomial criteria into the local factors and the global ones. Because the global factors need to be calculated only once in each iteration, GMA is of linear order in the number of objects. Numerical experiments on artificial data verify the efficiency of GMA. It is also shown that GMA can find out various interesting structures from massive document collections.

Joint approximate diagonalization (JAD) is a method solving blind source separation, which can extract non-Gaussian sources without any other prior knowledge. However, it is not robust when the sample size is small because JAD is based on an algebraic objective function. In this paper, a new robust objective function of JAD is derived by an information theoretic approach. It has been shown in previous works that the "true" probabilistic distribution of non-diagonal elements of approximately-diagonalized cumulant matrices in JAD is Gaussian with a fixed variance. Here, the distribution of the diagonal elements is also approximated as Gaussian where the variance is an adjustable parameter. Then, a new objective function is defined as the likelihood of the distribution. Numerical experiments verify that the new objective function is effective when the sample size is small. © 2012 Springer-Verlag.

Joint approximate diagonalization (JAD) is one of well-known methods for solving blind source separation. JAD diagonalizes many cumulant matrices of given observed signals as accurately as possible, where the optimization for each pair of signals is repeated until the convergence. In each pair optimization, JAD should decide whether the pair is actually optimized by a convergence decision condition, where a fixed threshold has been employed in many cases. Though a sufficiently small threshold is desirable for the accuracy of results, the speed of convergence is quite slow if the threshold is too small. In this paper, we propose a new decision condition with an adaptive threshold for JAD under a probabilistic framework. First, it is assumed that the errors in JAD (non-diagonal elements in cumulant matrices) are given by the exponential distribution. Next, it is shown that the maximum likelihood estimation of the probabilistic model is equivalent to JAD. Then, an adaptive threshold is theoretically derived by utilizing the model selection theory. Numerical experiments verify the efficiency of the proposed method for blind source separation of artificial sources and natural images. It is also shown that the proposed method is especially effective when the number of samples is limited. (C) 2011 Elsevier B.V. All rights reserved.

Joint approximate diagonalization (JAD) is a solution for blind source separation, which can extract non-Gaussian sources without any other prior knowledge. However, because JAD is based on an algebraic approach, it is not robust when the sample size is small. Here, JAD is improved by an information theoretic approach. First, the "true" probabilistic distribution of diagonalized cumulants in JAD is estimated under some simple conditions. Next, a new objective function is defined as the Kullback-Leibler divergence between the true distribution and the estimated one of current cumulants. Though it is similar to the usual JAD objective function, it has a positive lower bound. Then, an improvement of JAD with the lower bound is proposed. Numerical experiments verify the validity of this approach for a small number of samples.

A good curriculum is crucial for a successful university education. When developing a curriculum, topics, such as economics, natural science, informatics, etc. are set first, and course syllabi are written accordingly. However, the topics actually covered by the course syllabi are not guaranteed to be identical to the initially set topics. To find out if the actual topics covered by the developed course syllabi, we developed a method of systematically analyzing course syllabi that uses latent Dirichlet allocation (LDA) and Isomap. In this paper, we propose the web-based curriculum analysis tool with this method, and demonstrate an example of the way the tool is used for analyzing computer science curricula. ©2010 IEEE.

A good curriculum is crucial for a successful university education. When developing a curriculum, topics, such as natural science, informatics, and so on are set first, course syllabi are written accordingly. However, the topics actually covered by the courses are not guaranteed to be identical to the initially set topics. To find out if the actual topics are covered by the developed course syllabi, we developed a method of systematically analyzing syllabi that uses latent Dirichlet allocation (LDA) and Isomap. We applied this method to the syllabi of MIT and those of the Open University, and verified that the method is effective.

Joint approximate diagonalization (JAD) is one of the well-known methods for solving independent component analysis and blind source separation. It estimates a separating matrix which diagonalizes many cumulant matrices of given observed signals as accurately as possible. It is derived by not a probabilistic model but a linear algebraic approach. Therefore, its validity is rigorously guaranteed only if the diagonalization succeeds completely. However, the condition is not satisfied in practical cases, where JAD lacks the theoretical foundation. In this paper, we propose a probabilistic framework for JAD. The framework uses a probabilistic model of the estimation errors of cumulants instead of source signals. By applying the central limit theorem to the errors, a likelihood function of cumulants is derived. It is shown that a lower bound of the likelihood function is maximized by JAD. Numerical experiments verify the validity of the proposed framework.

It has been well known that ICA can extract edge filters from natural scenes. However, it has been also known that the existing cumulant-based ICA. can not extract edge filters. It suggests that the simple ICA model is insufficient for explaining the properties of natural scenes. In this paper, we propose a highly overcomplete model for natural scenes. Besides, we show that the 4-th order covariance has a positive constant lower bound under this model. Then, a new cumulant-based ICA algorithm is proposed by utilizing this lower bound. Numerical experiments show that this cumulant-based algorithm can extract edge filters.

Linear multilayer independent component analysis (LMICA) is an approximate algorithm for ICA. In LMICA, approximate independent components are efficiently estimated by optimizing only highly dependent pairs of signals when all the sources are super-Gaussian. In this paper, the nonlinear functions in LMICA are generalized, and a new method using adaptive PCA is proposed for the selection of pairs of highly dependent signals. In this method, at first, all the signals are sorted along the first principal axis of their higher-order correlation matrix. Then, the sorted signals are divided into two groups so that relatively highly correlated signals are collected in each group. Lastly, each of them is sorted recursively. This process is repeated until each group consists of only one or two signals. Because a well-known adaptive PCA algorithm named PAST is utilized for calculating the first principal axis, this method is quite simple and efficient. Some numerical experiments verify the effectiveness of LMICA with this improvement.

Joint approximate diagonalization is one of well-known methods for solving independent component analysis and blind source separation. It calculates an orthonormal separating matrix which diagonalizes many cumulant matrices of given observed signals as accurately as possible. It has been known that such diagonalization can be carried out efficiently by the Jacobi method, where the optimization for each pair of signals is repeated until the convergence of the whole separating matrix. Generally, the Jacobi method decides whether the optimization is actually applied to a. given pair by a convergence decision condition. Then, the whole convergence is achieved when no pair is actually optimized any more. Though this decision condition is crucial for accelerating the speed of the whole optimization, many previous works have employed simple conditions based on an arbitrarily selected threshold. In this paper, we propose a novel decision condition which is based on Akaike information criterion (AIC). It is derived by assuming each cumulant matrix to be a sample generated independently. In each pair optimization, the condition compares the reduction rate of the objective function with a constant depending on the number of cumulant matrices. It involves no thresholds (and no parameters) to be set manually. Numerical experiments verify that the proposed decision condition can accelerate the optimization speed for artificial data.

Joint approximate diagonalization is one of well-known methods for solving independent component; analysis and blind source separation. It calculates an orthonormal separating matrix which diagonalizes many cumulant matrices of given observed signals as accurately as possible. It has been known that such diagonalization can be carried out efficiently by the Jacobi method, where the optimization for each pair of signals is repeated until the convergence of the whole separating matrix. The Jacobi method decides whether the optimization is actually applied to a given pair by a convergence decision condition. Generally, a fixed threshold is used as the condition. Though a. sufficiently small threshold is desirable for the accuracy of results, the speed of convergence is quite slow if the threshold is too small. In this paper, we propose a new decision condition with an adaptive threshold for joint approximate diagonalization. The condition is theoretically derived by a model selection approach to a simple generative model of cumulants in the similar way as in Akaike information criterion. In consequence; the adaptive threshold is given as the current average of all the cumulants. Only if the expected reduction of the cumulants on each pair is larger than the adaptive threshold, the pair is actually optimized. Numerical results verify that the method can choose a suitable threshold for artificial data and image separation.

A good curriculum is crucial for a successful university education. When developing a curriculum, topics, such as natural science, informatics, etc. are set first, and then course syllabi are written accordingly. However, there is no guarantee that the topics actually covered by the course syllabi are identical to the initially set topics. To find out if the actual topics covered by the developed course syllabi, we developed a method of systematically analyzing course syllabi that uses latent Dirichlet allocation (LDA) and Isomap. We applied this method to the syllabi of MIT and the Open University curricula, and verified the method is promising.

Overcomplete ICA is a method for solving blind source separation problems if the number of observed signals is less than that of source ones. In this paper, we propose an overcomplete ICA algorithm based on a simple contrast function which is defined as the sum of the covariances of the squares of signals over all the pairs. By applying non-orthogonal pair optimizations to the function, a simple ICA algorithm is derived. Theoretical analysis and numerical experiments suggest the validity of the proposed algorithm.

It is well known that edge filters in the visual system can be generated by the InfoMax principle. But, such models are nonlinear and employ fully-connected network structures. In this paper, a new artificial network model is proposed, which is based on the "InfoMin" principle and linear multilayer ICA (LMICA). This network utilizes cumulant-based objective functions which are derived from the Infomax and InfoMin principles with large noise. Because the objective functions do not rely on any nonlinear models, a linear model can be employed. It simplifies the model considerably. Besides, this network can deal with quite large number of neurons by employing a connection-limited structure as in LMICA. In addition, it is more efficient than even LMICA because it does not need any prewhitening. Numerical experiments show that this network generates hierarchical edge filters from large-size natural scenes and verify the validity of the InfoMin principle.

Linear multilayer ICA (LMICA) is an approximate algorithm for independent component analysis (ICA). In LMICA, approximate independent components are efficiently estimated by optimizing only highly-dependent pairs of signals. Recently, a new method named "recursive multidimensional scaling (recursive MDS)" has been proposed for the selection of pairs of highly-dependent signals. In recursive MDS, signals are sorted by one-dimensional MDS at first. Then, the sorted signals are divided into two sections and each of them is sorted by MDS recursively. Because recursive MDS is based on adaptive PCA, it does not need the stepsize control and its global optimality is guaranteed. In this paper, the LMTCA algorithm with recursive MDS is applied to large natural scenes. Then, the extracted independent components of large scenes are compared with those of small scenes in the four statistics: the positions, the orientations, the lengths, and the length to width ratios of the generated edge detectors. While there are no distinct differences in the positions and the orientations, the lengths and the length to width ratios of the components from large scenes are greater than those from small ones. In other words, longer and sharper edges are extracted from large natural scenes.

It is known that the number of the edge detectors significantly e xceeds that of input signals in the visual system of the brains. This phenomenon has been often regarded as overcomplete indepenent component analysis (ICA) and some generative models have been proposed. Though the models are effective, they need to assume some ad-hoc prior probabilistic models. Recently, the InfoMin principle was proposed as a comprehensive framework with minimal prior assumptions for explaining the information processing in the brains and its usefulness has been verified in the classic non-overcomplete cases. In this paper, we propose a new ICA contrast function for overcomplete cases, which is deductively derived from the InfoMin and InfoMax principles without any priior models. Besides, we construct an efficient fixed-point algorithm for optimizing it by an approximate Newton's method. Numerical experiments verify the effectiveness of the proposed method.

In this letter, a new ICA algorithm, linear multilayer ICA (LMICA), is proposed. There are two phases in each layer of LMICA. One is the mapping phase, where a two-dimensional mapping is formed by moving more highly correlated (nonindependent) signals closer with the stochastic multidimensional scaling network. Another is the local-ICA phase, where each neighbor (namely, highly correlated) pair of signals in the mapping is separated by MaxKurt algorithm. Because in LMICA only a small number of highly correlated pairs have to be separated, it can extract edge detectors efficiently from natural scenes. We conducted numerical experiments and verified that LMICA generates hierarchical edge detectors from large-size natural scenes.

It has been well known that edge filters in the visual system can be generated by the InfoMax principle. In this paper, the "InfoMin" principle is proposed, which asserts that the information through some neighboring signals on a two-dimensional mapping must be minimized. It is shown that the standard Comon's ICA can be derived from the combination of the InfoMax principle for the whole signals and the InfoMin one for each signal under a linear model with sufficiently large noise. It is also shown that the InfoMin principle for the signals within neighboring areas can generate a topographic mapping in the same way as in topographic ICA. © Springer-Verlag Berlin Heidelberg 2006.