@article{belkin-niyogi,2002lea, title={{Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering}}, author={Belkin, M. and Niyogi, P.}, journal={ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS}, volume={1}, pages={585--592}, year={2002}, publisher={MIT; 1998} annote={"This paper presents a technique for non-linear embedding high-dimensional datasets into low dimensional space. The method works by first contructing adjacency graph by putting an edge between xi and xj if they are "close" (KNN or ||xi-xj||^2 < e).The weights may be assigned in 2 ways. If we want the algorithm to be simple then we give weight 1 to edges between connected(by an edge) vertices else 0. If we want our model to be more informative then we use the gaussian heat kernel. Next we calculate the Laplacian matrix L= A-D, where A is the adjacency matrix and D is the degree matrix. The solution of a generalized eigenvector problem involvong L and D gives eigenmatrix from which we pick first d vectors inincreasing order of their eigen values, starting from the second vector. - Kushlendra Mishra, Feb 09."} } @article{shlens2003tutorial, title={{A tutorial on principal component analysis}}, author={Shlens, J.}, journal={Copy retrieved [10-27-2004] from: http://www. snl. salk. edu/shlens/notes. html}, year={2003}, publisher={Citeseer} annote= { This article is tutorial of Principle Component analysis. Excerpts: The goal of PCA is to compute the most meaningful basis to re-express a noisy data set. The hope is that this new basis will filter out the noise and reveal the hidden structure. PCA makes one stringent but powerful assumption:linearity. Lineariity vastly simplifies the problem by(1) restricting the set of potential bases, and(2) farmalizing teh implicit assumption of continuity in the data set. With this assumption PCA is now limited to re-expressing the data as a linear combination of its basis vectors. PX = Y The above equation represents a change of basis and thus can have many iterpretations. 1. P is a matrix that transforms X into Y. 2. Geometrically, P is a rotation and a stretch which again transforms X into Y. 3. The rows of P, {p1,...,pn}, are a set of new basis vectors for expressing the columns of X. The covariance measures the degreee of linear relationship between two variables. A large (small) value indicates high (low) redundancy. cova(A,B) >= 0 cova(A,B) = va(A) iff A = B The covariance matrix captures the correlations between all possible pairs of measurements (data points). The correlation values reflect the noise and redundancy in our measurements. -> In the diagonal terms, by assumtion, large(small) values correspond to interesting dynamics (or noise) -> In the off diagonal terms large (small) values correspond to high (low) redundancy. Our goals are (1) to minimize redundancy, measured by covariance, and (2) maximize the signal, measures by variance. Evidently, in an "optimized" matrix all off-diagonal terms in cova(Y) are zero. Thus cova(Y) must be diagonal. In PX = Y P acts as a generalized rotaion to a align a basis with the maximally variant axis. In multiple dimensions this could be performed by a simple algorithm: 1. Select a normalized direcction in m-dimensinal space along ehich the variance in X is maximized. Save this vector as p1 2. Find another direction along which the variance is maximized, however because of orthogonality condition, restrict the search to all directions perpendicular to al previous selected directions. Save this vector as pi. 3. Repeat this procedure until m vectors are selected. The resulting ordered set of p's are the princile components. Asumptions made for PCA: 1. Linearity: Linearity frames the problem as a change of basis. 2. Mean and variance are sufficiant staistics: It captures the notion that mean and variance entirely describe a probability distribution. The only class of distributions that are fully described by the first two moments are exponential(e.g. Gaussian, Exponential, etc.). 3. Large variances have important dynamics. 4. Principle components are orthogonal. Performing PCA is quite simple in practice: 1. Organize a data set as m*n matrix, where is the number of measurement types(dimensions) and n is the number of trials (data points). 2. Subtract of the mean for each measurement type. or row xi. 3. Calculate the SVD or the eigenvectors of the covariance. Both the strength and weakness of PCA is that it is a non-parametric analysis. One only needs to make the assumtions outlined above and tehn calculate the answer. No parameters to tweak and adjust the answer. } } @article{saxena-gupta-mukerjee:2004nld, title={{Non-linear Dimensionality Reduction by Locally Linear Isomaps}}, author={Saxena, A. and Gupta, A. and Mukerjee, A.}, journal={LECTURE NOTES IN COMPUTER SCIENCE}, pages={1038--1043}, year={2004}, publisher={Springer} annote={"This paper presents improved variant of the Basic Isometric feature mapping algorithm for manifold learning. Basic Isomap suffers from a serious shortcoming of short-circuiting which means that when the distance between two folds is very less or there is noise which causes two points in different folds to be classified as neighbors, then the distance computed in step 2 of the algorithm are not the geodesic-distances, hence the algorithm fails. The proposed algorithm first computes the candidate K nearest neighbors. Then these neighbors are usede to reconstruct the data point. The weight for each neighbor is estimated by reudcing the reconstruction error. The neighbors which are in locallly linear patch of the manifold get higher weights. Out of these K neighbors, Kll with higher weights are selected. Thus this algorithm uses two parameters, K and Kll. The performance of this algorithm is compared with with basic Isomap for three calsse of data. For all the test datasets, the new algorithm didn't suffer from short-circuiting and had lesser residual variance. - Kushlendra Mishra, Feb 09"} } @inproceedings{tenenbaum-silva-langford:2005, title={{A Global Geometric Framework for Nonlinear Dimensionality Reduction}}, author={Tenenbaum, J.B. and Silva, V. and Langford, J.C.}, journal={Science}, volume={290}, number={5500}, pages={2319--2323}, year={2000} annote={ "This aricle presents the basic Iosomettric Feature Mapping algorithm. The algoritm works in three steps: calculating distance between pairs of pointsand find out the neighbors of each point on the manifold, secondly, these neighborhood relation is represented as a weighted graph, the third step applies classical MDS to find a low dimensional isometric embedding of these points. One advantage of Isomap is that it gives an estimate of the dimensionality of the manifold. -Kushlendra Mishra, Feb 09"} } @article{martin,backer:2005, title={{Estimating Manifold Dimension by Inversion Error}}, author={Martin, S. and Backer, A.} booktitle = {SAC '05: Proceedings of the 2005 ACM symposium on Applied computing}, annote= { The article is about accurately estimating the dimension of a manifold embedded in a high dimension space. The method works by first calculating the inversion error of the low dimensional (d) mapping. If d is the correct dimension of the manifold then this error should ideally be 0. Same is true for a mapping of dimension greater than d.Practically however, it is neve zero so minimization is attempted. Support vector regression technique is used to find out an inve- rse mapping. This is a general technique of estimating the dimensionality of a manifold and works for any algorithm such as LLE and ISOMAP."} } @conference{carreiraperpinan2005pgc, title={{Proximity graphs for clustering and manifold learning}}, author={Carreira-Perpinan, M.A. and Zemel, R.S.}, booktitle={Advances in Neural Information Processing Systems 17: Proceedings Of The 2004 Conference}, year={2005}, organization={MIT Press} annote={ In graph based algorithms for manifold learning, the graph constructed from the nearest neighbor data doesn't reapresent the manifold well enough. This paper presents two graph construction algorithms from nearest neighbor data. First is PMST ensemble which uses a perutrbed dataset to first find the edge weights and then finds a MST. the graph is an ensemble of such spanning trees. The second method DMST applies kruskals algorithm on the same dataset, but the edges are not replaced, deriving an ensemble of MSTs. -Kushlendra Mishra } } @article{saul2003tgf, title={{Think globally, fit locally: unsupervised learning of low dimensional manifolds}}, author={Saul, L.K. and Roweis, S.T.}, journal={The Journal of Machine Learning Research}, volume={4}, pages={119--155}, year={2003}, publisher={MIT Press Cambridge, MA, USA} annote={"This paper gives a detailed description of the LLE algorithm. LLE tries to reconstruct the manifold by itegrating locally linear patches. First nearest neighbors of each sample point are found and the point is represented as a convex sum of its neighbors. Weight matrox is found that minimizes the reconstruction errors. This weight matrix contains local geometric information about each point, and is used to find a low dimensional embedding of the manifold. The implementation and extension of LLE given in this paper is a bit involved and difficult to grasp in the first reading. -Kushlendra Mishra, Feb 2009"} } @article{srinivas1994mou, title={{Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms}}, author={Srinivas, N. and Deb, K.}, journal={Evolutionary Computation}, volume={2}, number={3}, pages={221--248}, year={1994}, publisher={MIT Press} annote={ "This paper introduces the basic NSGA algoritm. The earlier methods for multiobjective optimisation required the user to pass a parameter in the form of a weight vector, which was a difficult problem. The NSGA only required a sharing parameter. The simulation tests compare the performance of VEGA and NSGA, in VEGA the set of non-dominated solutions tend to cluster around some regions, while NSGA always gives smoother pareto-front. Also keeping the sharing parameter values to the extremes gives poor performance. -Kushlendra Mishra, Feb 2009" } } @article{deb2002fae, title={{A fast and elitist multiobjective genetic algorithm: NSGA-II}}, author={Deb, K. and Pratap, A. and Agarwal, S. and Meyarivan, T.}, journal={Evolutionary Computation, IEEE Transactions on}, volume={6}, number={2}, pages={182--197}, year={2002} annote={ "This article describes the improved version of the basic NSGA, the NSGA-II. This algorithm has overall time complexity of O(MN^2) whereas basic NSGA had a complexity of O(OMN^3). The paper introduces some innovations, such as Crowding Distance,Crowded-Comparison operator based on the former.The simulation results of this algorithm show a better performance incomparison to other contemporary elitist algoritms PAES and SPEA.Two mertics have been defined for comparison, the distance metric and the diversity metric. It also gives a way of integrating constraint handling in NSGA-II."} } @article{zeleny1998multiple, title={{Multiple criteria decision making: eight concepts of optimality}}, author={Zeleny, M.}, journal={Human Systems Management}, volume={17}, pages={97--107}, year={1998} annote={ excerpts: Because there are no tradeoffs along a single criterion, optimality is essentially a multi-criteria concept.The real optimality, being distinct from above simple computations, involves balancing multiple criteria and their tradeoffs. This corresponds to the vector optimization of Max $f_1(x)$, Max $f_2(x)$, ... and Max $f_k(x)$, i.e., simultaneously and subject to x<~ X. The concurrent maximization of individual objective functions should be non-scalarized, separate and distinct, i.e., not subject to aggregation, like forming a maximizing superfunction U{$f_1(x)$, ...}. Such an aggregation will effectively reduce multi-objective optimization to a single objective-optimization. Human decision making is obviously characterized by parallel search for both the criteria and alternatives in order tiachieve their optimal interaction and thus arrive at an optimal problem statement and it's optimal solution. Neither the criteria (f or F), nor nor the alternatives are given in genuine decision-making situations. There is a problem formulation representing an "optimal pattern" of interaction between alternatives and criteria. It is this optimal, ideal or cognitive equilibrium problem formulation or pattern that is to be approximated or matched as closely as possible by decision makers. Single-objective matching of the cognitive equilibrium is the simplest case. Pattern matching with multiple criteria is more involved and so far the most complex optimality concept. In all "matching" concepts there is a need to evaluate the closeness (resemblanceor match) of a proposed problem formulation (or pattern). @book{bransford2003people, title={{How people learn: Brain, mind, experience, and school}}, author={Bransford, J.}, year={2003}, publisher={National Academy Press} annote={ Excerpts from second chapter: Research shows that it's not simply general abilities that differentiate experts from novices. Instead experts have acquired extensive knowledge that affects what they notice and how they organise, represent, and interpret information in their envioronment. This in turn affects their abilities to remember, readon and solve problems. Key principles of experts' knowledge: 1. Experts notice features and meaningful patterns of information that ara not noticed by novices. 2. Experts have acquired a great deal of content knowledge that is organised in ways that reflect a deep understanding of their subject matter. 3. Experts' knowledge cannot be reduced to a set of isolated facts or propositions but, instead, reflects contexts of applicability: that is, the knowledge is "conditionalized" on a set of circumstances. 4. Experts are able to flexibly retrieve important aspects of their knowledge with little attention effort. 5. Though experts know their disciplines thoroughly, this does not guarantee that they are able to teach it to others effectively. 6. Experts have varying levels of flexibility in their approach to new situations. DegRoot concluded that the knowledge acquired over tens of thousands of chess playing hours of chess playing enabled chess masters to out-play their opponents. Specifically, masters were more likely to recognize meaningful chess configurations and realize the strategic implications of these situations; this recognition allowed them to consider sets of possible moves that were superior to others. The superior recall abilities of experts, illustrated in the example in the box, has been explained in terms of how they "chunk" various elements of a configuration that are related by an underlying funtion or strategy. Short term memory is enhanced when people are able to chunk information into familiar patterns. Chess masters percieve chunks of meaningful information, whichaffects their memory for what they see. Chess masters are able to chunk together several chess pieces in a configuration that is governed by some specific component of the game. The expert circuit technicians chunked several individual circuit components (e.g. resistors and capacitors) that performes the function of a typical amplifier. By remembering the structure and funcion of a typical amplifier, experts were able to recall the arrangement of many of the individual circuit elements comprising "amplifier chunks." Experts in physics cite laws and ideas involved in the solution of a particular problem, whereas competent beginners refer to equations that they will use for a particular problem. Physics experts appear to evoke sets of related equations, with recall of one equation activating related equations that are retrieved rapidly. Novices, in contrast, retrieve equations more equally spaced in time, suggestiong a sequential search in memory.Experts appear to possess an efficient organization of knowledge with meaningful relations among real elements clustered into related units that are governed by underlying concepts and principles. Experts' knowledge is "conditionalized"--it includes specification of contexts in which it is applicabke. Knowledge that is not conditionalized is often inert because it is not activated, even though it relevant. } } @inproceedings{mukerjee2009design-symbols, title={{THE BIRTH OF SYMBOLS IN DESIGN}}, author={Amitabha Mukerjee and Madan Mohan Dabbeeru}, institution={ASME 2009 International Design Engineering Technical Conferences and Computers and Information Engineering Conference August-September 30-2, 2009} annote= {"This article proposes the groundwork by which CAD systems may acquire symbols by learnig usage patterns or image schemas grounded in experience. Excerpts: In human usage, each symbol has a vast range of associations , and any attempt at definition will miss many of these, resulting in brittleness. Human flexibility in symbol usage is possible because our symbols are learnt from a vast experience of the world. In many design tasks, the "good designs" lie along regions that can be mapped to lower dimensional manifolds, owing to latent interdependencoes between the variables. These low-dimensional structures (sometimes called chunks) may constitute teh intermediate step between the raw experience and the eventual symbol that arises after these pattern become stabilized through communication. Unfortunately the term "symbol", as it is used in the logic and computaional community is considerably different from its usage in cognitive linguistics and in every-day life. In the latter usage symbols are imbued with meaning grounded in experience, whereas in the formal usage, it is merely a token constructed from finite alphabet, and is related ony to other terms . If we may present an analogy, the symbol "red" as it is used in a computer, is akin to the understanding of the symbol by a blind man; he knows that it is a "color" (whatever that means) and that "green" and "blue" are other colors, and maybe even that "crimson" is a shade of "red" but his understanding of red is dramatically different from that of a sighted person, because the semantic pole is not connected to direct experience. On the other hand "symbol" has come to be understood in cog sci (and also in traditional linguistics) as the tight binding of the psychological impression of the sound( the phonological pole) with mental image of the meaning( the semantic pole). The human design process is a constant, motivated exploration of the design space e.g. through sketching. All the while designer is focussing on the "good" design, and eventually some patterns emerge as teh common characteristics of these designs. These patterns result in constraints whereby many of the initial design variables can be combined, a process cognitively known as chunking. It is well known that a designer who is an expert in a particular design domain is "confident of choosing a good design based on experience", and this is partly because of these patterns she has internalized. Often, these relations remain implicit, so that the human designer justifies the decision vaguely as "looks right". However, if these patterns do cross the consciousness boundary and get explicitly noticed, the designer may recognize it as an "aha!" moment. By grounded, we refer to the progressive manner in which a human designer learns her concepts - the more abstract ones are based on earlier, concrete concepts, but are still presented thruogh instances. @conference{deb2008deciphering, title={{Deciphering innovative principles for optimal electric brushless dc permanent magnet motor design}}, author={Deb, K. and Sindhya, K.}, booktitle={IEEE Congress on Evolutionary Computation, 2008. CEC 2008.(IEEE World Congress on Computational Intelligence)}, pages={2283--2290}, year={2008} annote= { A search and optimization procedure on natural evolutions and natural genetics can be an effective mean to arrive at an innovative design for a single objective scenario. } } @conference{hegde2007random, title={{Random projections for manifold learning}}, author={Hegde, C. and Wakin, M.B. and Baraniuk, R.G.}, booktitle={Neural Information Processing Systems (NIPS)}, year={2007} annote = { This paper proposes that a small number N of random projections of sample points in R^N belonging to an unknown K-dimensional Euclideann manifold, can be used to estimate the intrinsic dimension of the sample set. It also proves that using only this random projections, the structure of the underlying manifold can be estimated. In both the cases the number of random projections required is linear in K and logarithmic in N. A greedy algorithm is developed to estimate the smallest size of smallest size of the projection space required to perform manifold learning. Data that possesses merely K "intrinsic" degrees of freedom can be assumed to lie on a K-imensional manifold in the high-dimensinal ambient space. Once the manifold is identified, any point on it can be represented using essentially K pieces of information. Grassberger-Procaccia(GP) algorithm is used for estimating the intrinsic dimensionsionality. It takes as input the set of pairwise distances between sample points. It then computes the scale-dependent correlation dimension of the data } @article{strube-cognitive, title={{Cognitive Science}}, author={Strube, G.}, journal={International Encyclopedia of the Social and Behavioral Sciences (IESBS). Oxford: Elsevier} annote={ This article is an introduction to the field of cognitive sciences. Excerpts -It was Leibniz who advocated the use of formal reasoning in the hope that fruitless discussions of all kinds, and even wars, might be deemed unnecessary by formalizing the arguments and computing the conclusions- hopelessly optimistic from our point of view(afterall there would be endless debate on how to formalize the premises), but a milestone, nevertheless, towards an account of thinking as symbol processing. A physical symbol system is a type of formal system. Like all formal systems, it has an 'alphabet'(atleast of two) arbitrarily defined symbols, as well as operators to create and transform symbol structures(symbolic expressions and syntactic rules. This system is physical in the sense that it has been implemented in a suitable way. Examples of suitable encoding are levels of voltages or spikes(action potentials) of neurons. Other representations are also possible, but the aforementioned already show how the theory can be applied to organisms as well as to technical systems. In sum, such a system needs physical implementation in order to function in the real world and move from the idealized to the concrete. The type of implementation is arbitrary, however, because the system functions according to its symbolic expressions and syntactic rules, quite idependent of its implementation. Symbols are arbitrary signs, but they designate objects or processes, including internalprocesses in the system itself. Their symantics is defined either by reference to an object(depending on the respective symbolic expression, the system exerts an influence on the object or is influenced by it), or by the symbolic expression being executed as a program. } @article{cayton2005algorithms, title={{Algorithms for manifold learning}}, author={Cayton, L.}, journal={University of California, San Diego, Tech. Rep. CS2008-0923}, year={2005} annote ={ Manifold learning is an approach to nonlinear dimensionality reduction. Algortims for this task are based on the idea that the dimensionalityof many datasets is only artificially high; though each data point consists of perhaps thousands of features, it may be described as a function of only a few underlying parameters. That is, the data are actually samples from a low-dimensional manifold that is embedded in a high-dimensional space. Manifold algorithms attempt to uncover these parameters in order to find a low-dimensional representaion of the data. A dimensionality reduction procedure may help reveal what the underlying forces governing a data set are. For example, suppose we are to classify an emailas spam or not spam. A typical approach to this problem would be to represent an email as a vector of counts of words appearing in the email. The dimensionality of this data can easily be in the hundreds, yet an effective dimensionalityreduction technique may reveal that there are only a few exceptionlly telling features, such as the word "Viagra". Given a data set, PCA finds the directions(vectors) along which the data has the maximum variance in addition to the relative importance of these directions. For example,suppose that we feed a set of three-dimensional points that all lie on a two-dim plane to PCA. PCA will return two vectors that span the plane along with a third vector that is orthogonal to the plane(so that all of R^3 is spanned by these vectors). The two vectors that span the plane will be given positive weights, but the third vector will have a weight of zero, since the data does not varry along that direction. PCA is most useful when the data lies on or close to a linear subspace of the data set. A Homeomorphism is a continous function whose inverse is also a continuous function. A d-dimensional manifold M is a set that is locally homeomorphic with R^d. That is for each x in M, there is an open neighborhood around x, N_x, and a homeomorphism f:N_x -> R^d. these neighborhoods are referred to as coordinate patches. and the map is referred to as coordinate chart. The image of coordinate charts is referred to as the parameter space. Isomap. It may be viewed as an extension to Multidimensional Scaling (MDS), a classical method for embedding dissimilarity information into Euclidean space. Consists of two main steps: 1. Estimate the geodesic distances (distances along a manifold) between the points in the input using shortest path distances on the data set's k nearest neighbor map. 2. Use MDS to find points in the low-dimensional Euclidean space whose interpoint distances match the distances found in step 1. Isometric chart; a chart that preserves the distances beetween points. Euclidean distance between nearby points is assumed to be a good enough approximation to the geodesic distance between them. To perform the estimation of geodesic distance between far away points, the algorithm first constructs a k-nearest neighbor graph that is weightes by the euclidean distances. Then the algorithm runs a shortest-path algorithm (Dijkstra's or Floyd's) and uses it's output as the estimate of the remaining geodesic distances. Once these geodesic distances are found Isomap finds points whose Euclideean distances equal these geodesic distances. Since the manifold is isometrically embedded such points exist, and in fact they are unique upto translation and rotation. Multidimensional scaling is a classical technique that may be used to find such points. One particularly helpful feature of Isomap that is not found in other algorithms is that it automatically provides an estimates of the dimensionality of the underlying manifold. The number of non-zero eigenvalues found in cMDS gives the underlying dimensionality. Isomap also has optimality guarantee undder some assumptions. Isomap is guaranteed to recover the parameterization of a manifold under the following asssumptions: 1. The manifold is isometrically embedded into R^D. 2. The underlying parameter space is convex- i.e. the distance between any two points in the parameter space is given by a geodesic that lies entirely within the parameter space. 3. The manifold is well sampled everywhere. 4. The manifold is compact. Many extensions to Isomap have been proposed. C-Isomap has been proposed to handle conformal mappings(conformal mappings preserve angles). Landmark Isomap has been proposed to handle very large data sets. Landmark points are used to speed up the calculations of interpoint distances and cMDS. Both of these steps require O(n^3) steps. The idea is to select a small set of l landmark points where l > d, but l << n. Next the approximate geodesic distance of each point to these l landmark points is calculated. In place of nxn distances only nxl are computed. Then cMDS is run on the lxl distance matrix of the landmark points. Finally the other points are located using a simple formula based on their distances to the landmarks. The complexity of L-Isomap is O(d ln log(n) + l^3). LLE is based on a substatntially different intuition. The idea comes from visualizing the manifold as a collection of overlapping coordinate patches. If the neighborhood sizes are small and the manifold is is sufficiently smooth, then these patches will be approximately linear. Moreover, the chart from the manifold to R^d will be roughly linear on these patches. The idea is to identify these linear patches, characterize their geometry, and find a mapping to R^d that preserves this local geometry and is nearly linear. It is assumed that these local patches will overlap with one another so that local reconstructions will combine ito a global one. The number of neighbors is a parameter of the algorithm. To characterize the geometry of the linear patches LLE attempts to represent each x_i as a weighted, convex combination of its nearest neighbors. The weights are chosen to minimize the squared error for each i. The weight matrix W is used as a surrogate for the local geometry of the patches. W_i reveals the layout of the points around x_i. Since it is invariant to rotations translations and scalings, W_i also characterises the local geometry around x_i for any linear mapping of the neighborhood patch surrounded by x_i Second step of the algorithm finds a configuration in d-dimensions (the dimensionality of the parameter space) whose local geometry is characterized well by W. Unlike Isomap, d must be known apriory or estimated. } @article{van2007dimensionality, title={{Dimensionality reduction: A comparative review}}, author={Van Der Maaten, LJP and Postma, EO and Van Den Herik, HJ}, journal={Preprint}, year={2007}, publisher={Citeseer} } @article{de2002locally, title={{Locally linear embedding for classification}}, author={de Ridder, D. and Duin, R.P.W.}, journal={Pattern Recognition Group, Dept. of Imaging Science \& Technology, Delft University of Technology, Delft, The Netherlands, Tech. Rep. PH-2002-01}, year={2002} annote = { Excerpts To find a good LLE mapping, threee parameters have to be set: the dimensionality m to map to, the number of neighbors k to take into account and the regularisation parameter r. Mapping quality is quite sensitive to these parameters. If m is set too high, the mapping will enhance noise; if it's too low points will be overlapped. If k is too small it the mapping will not reflect any global properties; if it's too high, the mapping will lose its nonlinear character and behave like traditional PCA, as the entire data set is seen as local neighborhood. Finally if r is set incorrectly, the eigenvalues may not converge. } @article{de2003supervised, title={{Supervised locally linear embedding}}, author={de Ridder, D. and Kouropteva, O. and Okun, O. and Pietikainen, M. and Duin, R.P.W.}, journal={Lecture Notes in Computer Science}, pages={333--341}, year={2003}, publisher={Springer} annote ={ Excerpts Often the ideal decision boundary between different classes in such sets is highly nonlinear. A classifier should therefore have many degrees of freedom, and consequently a large number of parameters. As a result training a classifier on such sets is quite complicated: a large number of parameters has to be estimated using a limited number of samples. The curse of dimensionality. One can overcome this problem by first mapping the data to a high dimensional space in which the classes become linearly separable. An alternative is to lower the data dimensionality, rather than increase it; the reduction in parameters one needs to estimate can result in better performance. Supervised LLE was introduced to deal with data sets containing multiple (often disjoint) manifolds. For fully disjoint manifolds, the local neighborhood of a sample x_i from class c (1 <= c <= C) should be composed of samples belonging to the same class only. This can be achieved by artificially increasing the precalculated distance between samples belonging to different classes, but leaving them unchanged if they belong to the same class. For 1-SLLE, distances between samples in different classes will be as large as the maximum distance in the entire data set. this means neighburs of a sample in class c will be always picked up from the same class. It is a non parameterised supervised LLE. In contrast alpha-SLLE introduces an aditional parameter alpha which controls the amount of supervision. For 0 < alpha < 1, a mapping is found which preserves some of the manifold structure but introduces separation between classes. This allows supervised data analysis, but may also need to better generalisations than 1-SLLE on previously unseen samples. } } @article{deloache2004becoming, title={{Becoming symbol-minded}}, author={DeLoache, J.S.}, journal={Trends in cognitive sciences}, volume={8}, number={2}, pages={66--70}, year={2004}, publisher={Elsevier} annote = { Infants initially accept a wide range of of entities as potential symbols and young children are often confused about the nature of symbol-referent relations. A symbol is something that someone intends to represent something other than itself. The component someone points to humans as the symbol species. How to define a symbol? Disagreements persist about symbol use, including what the symbol properly refers to in the first place. The confusion stems in part from the fact that different theorists have distinguished in very different and inconsistent ways among the terms such as 'sign', 'signal', 'index', 'icon' , and so on. Philosopher Peirce and psychologists Bruner, Olver and Greenfield reserve the term for entities that have purely arbitrary, formal and conventional relations to whatever they stand for. The emergence in evolution of the symbolic capacity irrevovcably transformed our species, vastly expanding our intellectual horizons and making possible the cultural transmission of knowledge to succeding generations. Defining characteristics of symbols 1. Symbols represent things. Symbols 'represent'; they refer to, they denote, they are about something. They are not merely associated with their referents. 2. Symbols are general. Virtually anything can be used to refer to anything. e.g. 'baby signs' - idiosyncratic gestures used ( and often invented) by the child to refer to to communicate with others, like indicating a dog by sticking out the tongue and panting. 3. Symbols are intentional. A person's intention that one entity represent another is both necessary and sufficient to establish a symbolic relation. Nothing is inherently a symbol; only as a result of someone using it with goal of denoting or referring does it take a symbolic role. Infants and toddlers are sensitive to the intentions of other people in interpreting their symbolic activity. When a present adult utters a novel word but children see no novel object for it to refer to, they look around for one or they look enquiringly at the speaker. Children are asked to draw two persons. Their drawings are not very distinguishable. However when latter asked to name the drawings they had produced the children insisted that a given drawing was of whatever they had originally intended it to be. Learning symbols-referent relations Although infants can percieve a difference between real and depicted objects, they do not understand the significance of that difference, so they investigate. A vital function of symbols is to enable humans to acquire information without direct experience. Our vast stores of cultural knowledge exist only because we can learn indirectly through symbolic representations. Dual nature of symbols A unique aspect of symbolic objects is their inherently dual nature. A symbolic artefact such as a picture or a model is both a concrete object and a representation of something other than itself. To use such objects effectively one must achieve dual representation, that is one mentally represent the concrete object itself and its abstract relation to what it stands for. } } @article{gobet2001chunking, title={{Chunking mechanisms in human learning}}, author={Gobet, F. and Lane, P.C.R. and Croker, S. and Cheng, P.C.H. and Jones, G. and Oliver, I. and Pine, J.M.}, journal={Trends in Cognitive Sciences}, volume={5}, number={6}, pages={236--243}, year={2001}, publisher={Elsevier} annote = { This article addresses the question of how chunk might be represented within a cognitive system. A chunk is a collection of elements having strong associations with one another, but weak associations with elements in other chunks. Some of the clearest evidence of perceptual chunking is found in how primitive stimuli are grouped together into larger conceptual groupes, such as the manner in which letters are grouped into words, sentnces or even paragraphs. This grouping leads to memory and behavioural effects, in which the latencies for output of items comprising a chunk are shorter than when those items comprise a number of smaller chunks. The manner in which chunks are constructed affects the type of generalizations and so predicts typical errors or successes. Elementary perciever and memorizer (EPAM) Learning is simulated by the growth of a discrimination network, where the internal nodes test for the presence of perceptual features, and the leaf nodes store 'images', the internal representation of the external objects. EPAM has a limited short term memory. Iformation flows through EPAM as follows. First a stimulus is percieved and converted into a set of features. Second, these features are sorted by the tests of the discrimination network, to retrrieve a pinter to a node within LTM; this pointer is then stored within STM. Third depending on an internal comparison process, learning may or may not occur within the network. Finally, an action might be taken by the system or next stimulus is retrieved from the environment. The extent of system's knowledge about a given stimulus is indicated by the leaf nide reached after sorting that stimulus through the discrimination network. Learning occurs by comparing the information held in the leaf node with that in the stimulus. If there is a perfect match, no learning occurs. If the image is the subset of the stimulus additional information is added t to the leaf node. Finally if there is a mismatch, the network is augmented: the leaf node becomes an internal node with a test for the mismatch , and the stimmulus and the old image are used ad the basis of new leaf nodes. Chunk Heirarchy and Retrieval structures -- CHREST It features a number of additions to EPAM's basic learning mechanisms, providing a greater degree of self-organization and adaptation to complex data. One small addition is that every node within CHREST's discrimination network can contain an image. The major change is in the form of creating lateral links between nodes, and for elaborating information within chunks to form more complex schemata; these changes improve tehrichness of the semantic memory without affecting the important properties of the previous simulations. } } @article{chandrasekaran1999ontologies, title={{What are ontologies, and why do we need them?}}, author={Chandrasekaran, B. and Josephson, J.R. and Benjamins, V.R.}, journal={IEEE Intelligent systems}, volume={14}, number={1}, pages={20--26}, year={1999}, publisher={Citeseer} annote = { Excerpts: In ontology is the study of the kinds of things that exist. It is often said that ontologies "carve the world at its joints." In AI the term ontology has come to mean one of two related things. First of all ontologyo is a representation voculabory, often specialized to some domain or subject matter. More precisely, it is not the vocabulary as such that qualifies as ontology, but conceptualizations that the terms init the vocabulary are intended to capture. Thus, translating the terms in an otnology from one language to another doesn't change the ontology conceptually. In its second sense the term ontology is sometimes used to refer to a body of knowledge describing some domain, typically a common sense knowledge domain, using a representation vocabulry }