
	Where results make sense

Topic: Curse of dimensionality

Related Topics

Dragon Data

World Bank Group

List of emirs of Qatar

Stephanie Romanov

In the News (Fri 17 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	What is the curse of dimensionality?
		Curse of dimensionality (Bellman 1961) refers to the exponential growth of hypervolume as a function of dimensionality.
		One could argue that the average distance from a random point of the space to the nearest network unit measures the goodness of the representation: the shorter the distance, the better is the represention of the data in the sphere.
		The curse of dimensionality causes networks with lots of irrelevant inputs to be behave relatively badly: the dimension of the input space is high, and the network uses almost all its resources to represent irrelevant portions of the space.
	www.faqs.org /faqs/ai-faq/neural-nets/part2/section-13.html (558 words)

	The "Curse of Dimensionality"
		Monte Carlo simulation was developed by the Los Alamos team (the people who developed the nuclear bomb for the US during the 1940's).
		They had high-dimensional integrals to solve, and traditional methods of numerical integration failed them because of the curse of dimensionality.
		Effectively, Monte Carlo simulation was developed to break the curse of dimensionality.
	www.contingencyanalysis.com /archive/archive2/0000002d.htm (434 words)

	The blessing of dimensionality
		The phrase "curse of dimensionality" has many meanings (with 18800 references, it loses to "bayesian statistics" in a googlefight, but by less than a factor of 3).
		In statistics, "curse of dimensionality" is often used to refer to the difficulty of fitting a model when many possible predictors are available.
		In all the realistic "curse of dimensionality" problems I've seen, the dimensions--the predictors--have a structure.
	www.stat.columbia.edu /~cook/movabletype/archives/2004/10/the_blessing_of.html (618 words)

	[No title]
		The curse of dimensionality [koeppen2000] was coined by Bellman to describe the problem that occurs when searching in or estimating PDFs on high-dimensional (HD) spaces.
		With a fixed number of training samples, the dimension for which accurate estimation is possible is severely limited to a small number, usually about 5 depending on the specific problem.
		An interesting paper on the curse of dimensionality is by Mario Koeppen [koeppen2000]
	www.npt.nuwc.navy.mil /csf/curse.html (682 words)

	[No title]
		The row-scalability problem is sometimes referred to as “the curse of cardinality” and the column scalability problems is referred to as “the curse of dimensionality”.
		However, any such approach would only exacerbate the curse of cardinality (and to some extent the curse of dimensionality) if applied directly, that is, if it is applied by first joining the multiple tables into one massively large table and then vertically partitioning it.
		As to the curse of dimensionality, except for domain knowledge related and analytical (e.g., Principal Component Analysis) dimension reduction methods, there is no way to relieve the curse of dimensionality.
	www.cs.ndsu.nodak.edu /~perrizo/classes/765/buildingptree.doc (2058 words)

	Curse of Dimensionality
		he requirement in direct-sampling* Monte Carlo simulation that the number of samples per variable increase exponentially with the number of variables to maintain a given level of accuracy is called the "Curse of Dimensionality."
		Let the complete probability space for one variable be represented by the unit interval (0, 1), and imagine drawing ten samples along that interval.
		This is referred to in the Bayesian literature as the "curse of dimensionality" and places a practical limit of about a half dozen dimensions on direct-sampling Monte Carlo.
	www.statisticalengineering.com /curse_of_dimensionality.htm (389 words)

	dimensionality reduction - The reduction Spot
		The reduction Spot is always looking to add new links on our feature subject dimensionality reduction, so if you know of any great dimensionality reduction sites, please submit them to our site.
		Local Dimensionality Reduction If globally high dimensional data has locally only low dimensional distributions, it is advantageous to perform a local dimensionality reduction before further...
		The problem known as the "curse of dimensionality reduction" (Bellman, 1961) has been given a great deal of attention by researchers in the database and data...
	www.andersonsampservice.com /dimensionality-reduction (395 words)

	Johns Hopkins Gazette: March 18, 1996
		On Faculty: Breaking the "Curse of Dimensionality" Phil Sneiderman ----------------------------------- Homewood News and Information Lenore Cowen is trying to find a way around a roadblock that often stops statisticians dead in their tracks.
		But some researchers believe this handicap may help Cowen succeed where others have failed in their efforts to crack a complex problem called the "Curse of Dimensionality." The curse rears its head when a statistician is working with data in a sufficiently high-dimensional space that it becomes impossible to make reliable predictions from the data.
		These obstacles were presented in a form that was new to Cowen but seemed to have promising analogies in discrete mathematics, the area in which she works.
	www.jhu.edu /~gazette/janmar96/mar1896/18cowen.html (924 words)

	Headlines@Hopkins: Johns Hopkins University News Releases
		The curse rears its head when a statistician is working with data in a sufficiently high dimensional space that it becomes impossible to make reliable predictions from the data.
		But Cowen, using her expertise in combinatorics--the mathematics of finite objects and combinations of objects--believes she can sometimes sneak around the curse and pull useful information from problems that usually stump the statisticians.
		The weighted graph of pairwise distances between samples is distorted to a simpler structure in a lower- dimensional space where, nonetheless, the original distances are approximately preserved.
	www.jhu.edu /news_info/news/home96/mar96/curse.html (787 words)

	Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform - Murtagh, Starck, Berry ...
		Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform (2000)
		50.6%: Overcoming the Curse of Dimensionality in Clustering by..
		Murtagh, F., Starck, J.L. and Berry M., \Overcoming the curse of dimensionality in clustering by means of the wavelet transform", The Computer Journal, 1999, submitted.
	citeseer.ist.psu.edu /312178.html (644 words)

	Abstract for Cowles Foundation Discussion Paper 925 (Site not responding. Last check: 2007-10-25)
		By doing so, they attempt to circumvent the curse of dimensionality that afflicts the estimation of fully nonparametric regression models.
		In this paper, we present a finite sample bound and asymptotic rate of convergence results for the mean average squared error of series estimators that show the AIR models do circumvent the curse of dimensionality.
		The rate of convergency of these estimators is shown to depend on the order of the AIR model and the smoothness of the regression function, but not on the dimension of the regressor vector.
	cowles.econ.yale.edu /P/ab/a09/a0925.htm (174 words)

	Locally Lifting the Curse of Dimensionality for Nearest Neighbor Search
		It further illuminates the nature of the curse, and may therefore someday contribute to improved general purpose algorithms for high dimensions and for general metric spaces.
		Experiments are presented in section 4, which confirm in practice the dimensional invariance established by analysis.
		Next observe that as a consequence of the central limit theorem the distributions of Proposition 3.1 are asymptotically normal -- and we remark that as a practical matter this is a good approximation; even for moderate dimension.
	www.pnylab.com /pny/papers/vp3/vp3/index.html (4695 words)

	The Dwarf Data Cube Eliminates the High Dimensionality Curse - Sismanis, Roussopoulos (ResearchIndex)
		Abstract: The data cube operator encapsulates all possible groupings of a data set and has proved to be an invaluable tool in analyzing vast amounts of data.
		Recently the idea of the dwarf data cube model was introduced, and showed that highdimensional "dwarf data cubes" are orders of magnitudes smaller in size than the original data cubes even when they calculate and store every possible...
		The dwarf data cube eliminates the high dimensionality curse.
	citeseer.ist.psu.edu /sismanis03dwarf.html (539 words)

	Curse of Dimensionality?
		The expression ``curse of dimensionality'' is due to Bellman and in statistics it relates to the fact that the convergence of any estimator to the true value of a smooth function defined on a space of high dimension is very slow.
		In terms of microarrays, this means that, a priori, we need an ``enormous'' amount of observations (hybridizations to different cell lines) to obtain a ``good'' estimate of a function of the genes (that identifies, for example, which genes have altered expression patterns in a specific tumor type).
		Some of these may be applicable to microarrays, even though certainly not in a blind fashion.
	www.stat.ucla.edu /~sabatti/statarray/textr/node5.html (1005 words)

	Curse of Dimensionality
		When dealing with very high-dimensional data, one is faced with the `curse of dimensionality' [
		Essentially the amount of data to sustain a given spatial density increases exponentially with the dimensionality of the input space, or alternatively, the sparsity increases exponentially given a constant amount of data, with points tending to become equidistant from one another.
		Figure 2.2 gives a simple illustration of the curse of dimensionality.
	www.lans.ece.utexas.edu /~strehl/diss/node28.html (150 words)

	Bioinformatics Institute
		A major challenge is the curse of dimensionality which occurs when one attempts to integrate these equations.
		While stochastic simulation techniques effectively address the curse, many repeated simulations are required to provide precise information about stationary points, bifurcation phenomena and other properties of the stochastic processes.
		An alternative way to address the curse of dimensionality is provided by sparse grid approximations and we will derive such an approximation which is used to solve the chemical master equations.
	www.cebl.auckland.ac.nz /index.php?target=seminars&item=2 (201 words)

	Monte Carlo Simulation
		Second, standard error does not depend upon the dimensionality of the integral [6].
		Most techniques of numerical integration—such as the trapezoidal rule or Simpson's method—suffer from the curse of dimensionality.
		It is as applicable to a 1000-dimensional integral as it is to a one-dimensional integral.
	www.riskglossary.com /articles/monte_carlo_method.htm (1715 words)

	ECS EPrints Service - Overcoming the curse of dimensionality of fuzzy logic
		Overcoming the curse of dimensionality of fuzzy logic
		Harris, C. Overcoming the curse of dimensionality of fuzzy logic.
		EPrints is free software developed by the University of Southampton to facilitate Open Access to research.
	eprints.ecs.soton.ac.uk /31 (91 words)

	High Dimensionality — Bioinformatics Research and Development Lab
		Many biological datasets are characterized by the dimensionality problem.
		Many statistical applications are confronted with high dimensional data.
		Thus, in theory, it should not be a "curse" to have more data, but in practice it is often the case.
	www.bioinformatica.crs4.org /Members/ecapob/high-dimensionality (217 words)

	ResearchChannel - The Curse of Dimensionality for Local Learning
		We present a series of arguments supporting the claim that a large class of modern learning algorithms based on local kernels are highly sensitive to the curse of dimensionality.
		The results show that these algorithms are local in the sense that crucial properties of the learned function at X depend on the neighbors of X in the training set.
		There is a large class of data distributions for which non-local solutions could be expressed compactly and potentially be learned with few examples, but which will require a large number of local bases and therefore a large number of training examples when using a local learning algorithm.
	www.researchchannel.org /prog/displayseries.aspx?fID=1721&pID=342 (215 words)

	[No title]
		One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories) (see graph number 1, below).
		The term curse of dimensionality (Bellman, 1961, Bishop, 1995) generally refers to the difficulties involved in fitting models, estimating parameters, or optimizing a function in many dimensions, usually in the context of neural networks.
		As the dimensionality of the input data space (i.e., the number of predictors) increases, it becomes exponentially more difficult to find global optima for the parameter space, i.e., to fit models.
	www.statsoft.com /textbook/glosc.html (7574 words)

	A Probabilistic Spell for the Curse of Dimensionality (Site not responding. Last check: 2007-10-25)
		The so-called "curse of dimensionality" (well known in vector spaces) is also observed in metric spaces, and the term refers to the odd situation where using an index for proximity searching may be worse (in total elapsed time) than an exhaustive search.
		There are at least two reasons behind the curse of dimensionality: a large search radius and/or a high intrinsic dimension of the metric space.
		We present an approximate analysis of the technique which helps understand the process, as well as empirical evidence showing dramatic improvements in the search time at the cost of a very small error probability.
	garota.fismat.umich.mx /~elchavez/publica/alenex01.html (207 words)

	Evaluating spatial- and temporal-oriented multi-dimensional visualization techniques. Yu, Chong Ho & Shawn Stockford
		From the standpoint of human perception and understanding, the potentially extreme multi-dimensionality of multivariate data presents serious difficulties due to many cognitive limitations, and is what many call the "curse of dimensionality" (Bellman, 1961; Fox, 1997).
		The objective of this article is to discuss the efficacy of various high-dimensional visualization methods and to provide guidelines to instructors.
		The so-called "curse of dimensionality" is tied to the problem of our limited perceptive capability.
	pareonline.net /getvn.asp?v=8&n=17 (5081 words)

	RL FAQ
		The curse of dimensionality refers to the tendency of a state space to grow exponentially in its dimension, that is, in the number of state variables.
		Many RL methods are able to partially escape the curse by sampling and by function approximation.
		Basically, no. Tile coding is a quite general idea and many of the ways it can be used avoid the curse of dimensionality.
	www.cs.ualberta.ca /~sutton/RL-FAQ.html (4030 words)

	Citations: Data Mining and Knowledge Discovery - Friedman (ResearchIndex)
		Friedman, J. On bias, variance, 0/1-loss, and the curse of dimensionality.
		On bias, variance, 0/1 loss, and the curse of dimensionality.
		Friedman, J. H.: On bias, variance, 0/1-loss, and the curse of dimensionality.
	citeseer.ist.psu.edu /context/31357/0 (1596 words)

	ECS EPrints Service - High Dimensional Neurofuzzy Systems: Overcoming the Curse of Dimensionality
		The problems occur due to the lack of both available training data and the required computational resources necessary for building and calculating the response of the model.
		This paper outlines several techniques for partially overcoming the curse of dimensionality associated with high-dimensional data modelling problems and compares and contrasts them with several algorithms developed in the statistical community.
		The work is intended to outline both conventional concepts which can be usefully applied in neurofuzzy models and new developments in this field.
	eprints.ecs.soton.ac.uk /245 (212 words)

	Data Requirements
		However, in Machine Learning it is well known that the more variables one needs to model, the harder the modeling task becomes, because the size of the search space increases exponentially with the number of parameters of the model.
		This is often referred to as the Curse of Dimensionality.
		Similarly, for Boolean networks, constraining the rules for each gene to be biologically plausible can significantly reduce the number of Boolean rules that match the data we have on the regulation of each gene.
	www.cs.unm.edu /~patrik/networks/datareq.html (1421 words)

	DiSC - Optimal Grid-Clustering: Towards Breaking the Curse of Dimensionality in High-Dimensional Clustering
		Most clustering algorithms, however, do not work effectively and efficiently in high-dimensional space, which is due to the so-called ``curse of dimensionality''.
		In this paper, we review and compare the existing algorithms for clustering high-dimensional data and show the impact of the curse of dimensionality on their effectiveness and efficiency.
		The comparison reveals that condensation-based approaches (such as BIRCH or STING) are the most promising candidates for achieving the necessary efficiency, but it also shows that basically all condension-based approaches have severe weaknesses with respect to their effectiveness in high-dimensional space.
	www.sigmod.org /disc/p_optimalgridclusalda.htm (572 words)

	Coppejans, Mark: Braking the Curse of Dimensionality (Site not responding. Last check: 2007-10-25)
		We derive a method that only requires 2(r+1)+1 restrictions, where r is the number of interior knots.
		Rates of convergence in L_2 are the same as the optimal rate for the one-dimensional case.
		A simulation experiment shows that the estimator works well when optimization is performed by using the back-fitting algorithm.
	www.nuff.ox.ac.uk /users/doornik/eswc2000/a/0830.html (227 words)

Try your search on: Qwika (all wikis)