Smoothing. Smoothing always involves some form of local averaging of data such that the nonsystematic components of individual observations cancel each other out.
Smoothing: which works to remove noise from the data
Aggregation: where summary or aggregation operations are applied to the data. For example, the daily sales data may be aggregated so as to compute weekly and annuual total scores.
Path smoothing
Path smoothing is fairly easy with the resulting paths, as long as the movement costs are constant. The algorithm is simple: if there's line of sight from the navigation point i to point i+2, remove point i+1.
[edit] Smoothing
The task is to compute, given the parameters of the model and a particular output sequence up to time t, the probability distribution over hidden states for a point in time in the past, i.e. to compute for some k < t.
KNN for Smoothing and Prediction
By Kardi Teknomo, PhD.
Using the same principle, we can extend the K-Nearest Neighbor (KNN) algorithm for smoothing (interpolation) and prediction (extrapolation) of quantitative data (e.g. time series).
4.5.1 Laplace Smoothing
4.5.2 Good-Turing Discounting
4.5.3 Some Advanced Issues in Good-Turing Estimation ...
Several successful algorithms have been developed for filtering, prediction, smoothing and finding explanations for streams of data,[99] such as hidden Markov models,[100] Kalman filters[101] and dynamic Bayesian networks.
This pattern classifier was run on the unsmoothed fMRI data - smoothing is normally applied because fMRI is thought to be a relatively noisy recording technique.
Momentum can increase the performance of gradient descent by smoothing the trajectory of xt. Gradient descent with momentum is describe by the following rule:
xt+1 = xt - atf(xt) + m(xt - xt-1) ...
The starting point of the bins (not very important), and
The bin width, that acts as a "smoothing parameter" (very important).
Its just that these parameters cannot be interpreted in terms of global properties of the distribution.
"Constrained Clustering as an Optimization Method" (Rose, Gurewitz, & Fox, IEEE Trans Patt Anal and Mach Intel 15(8), 1993, pp785--794)
"GTM: The Generative Topographic Mapping"
"Self-Organization as an Iterative Kernel Smoothing Process" ...
On the 16 Mhz 386 processor created in 1986, the engineers used a smoothing engraver at 1.5 micron (0.0015 of a millimetre). In comparison, a hair is about 1 micron thick.
 See also: Distribution, Regression, Classification, Data mining, Variance
  
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