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And the data nonlinearity could be preserved by nonlinear dimensionality reduction methods such as LLE, LE and ISOMAP.
Data Set The data set that we used is Washing DC image is which was collected by the HYDICE sensor over a Mall in Wash-ington DC.
The spatial re-solution of the Washington DC data set is 2 m/pixel.
Washing DC Data Set.
Data Eng., vol. 21, no. 9, pp. 1299–1313, Sep. 2009

The crystallographic texture was derived from EBSD data.
These data were collected from the center of the sheets thickness on longitudinal section.
Fig. 1 Optical micrograph in longitudinal sections before and after rolling: a) initial b) RT, 15% reduction, c) CT, 15% reduction, d) RT, 50% reduction and e) CT, 50% reduction.
Fig. 2 ϕ2 = 45°, 65° and 90° sections of ODFs before and after rolling: a) initial, b) RT, 15% reduction, c) RT, 50% reduction, d) CT, 15% reduction and e) CT, 50% reduction.( Levels: 1, 2…18.)
However, in present work, the β fiber consisted of a highest S, a medium B and a lowest C at 50% reduction and showed homogeneously at 15% reduction.

However, few reports can be found focusing on the study of high-solid anaerobic digestion of sewage sludge, and no data were available on the start-up performance of high-solid anaerobic digestion at mesophilic temperatures.
The performance data of the first 20 days indicated that starting OLR should be controlled to avoid VFA accumulation above 3 g/l.
With OLR increased from 2.0 to 3.0 kg VS m-3d-3, the methane yield decreased from 0.266 (average of the data in Fig.1 a from day 50 to 59) to 0.231 l CH4 g-1 VSadded-1 d-1 and the VS reduction decreased from 42.2% (average of the data in Fig.1 a from day 70 to 85) to 33%.
a b c Fig.1 Performance data of semi-continuous reactors with designed fed-sludge TS of 10%(a), 15%(b) and 20%(c).
As focusing on start-up period, there is shown the performance data at the same OLR but different TS in Fig.4.

This approach will produce large amounts of measurement data, some data in the cross section, some data is not in the cross section, and even some of the data deviated from the cross section too far to become invalid data.
Field data collection methods and data formats and graphical analysis The field data was collected using the 8-shaped data sampling method, shown in Fig. 1.
The difference between the design cross-section data and actual cross-section data.
Furthermore, in considering the valid data operator is visible in the process of data reduction, which is the problem of visualization.
While the data, away from the section, not in the buffer_data1, is the invalid data.

The results of these tests indicate that the strength and hardness of HAZ of this material exhibit a W-shaped reduction.
Based on the analytical deduction and experimental data fitting, the theoretical strength model for HAZ of aluminum alloy is proposed.
The change law of tensile strength in HAZ can be gained by data processing and analyzing as long as the tensile strength of specimens from different distance to weld seam center is measured.
For convenient application, the theoretical model for strength distribution of the HAZ is to fit the experimental data into the curve as illustrated in Fig.10.
For the butt welding specimens at 30-day ageing hardening with TIG welding are damaged, the curve fitting adopts 7-day specimens data which may lead the width of reduction zone be slightly larger.

This method makes full use of the advantage of" let the data speak".
As a method of dealing with imprecise, uncertain and incomplete data, rough set is only based on pure data to delete redundant information, and to compare the roughness of knowledge and importance.
In rough sets, the information table is used to describe the universe in the data set, the decision table is a kind of a decision attribute characteristics of information table.
Attribute reduction.
[4] Z Pawlak.Rough Sets,Theoretical Aspects of Reasoning about Data [M].Kluwer Academic Publishing,1991:9-51

There exists a universal method of finding regularities in data sequences.
Relevant Optimization Since the detection method requires finding k nearest neighbors on each class, we need o(n) distance computations, per each point to be diagnosed, where is the number of data points in the normal data set.
Moreover, to find out the k nearest neighbors for the normal data set, we require o(n2) comparisons.
In Table 1, building time denotes the time for calculating the strangeness and p-values of training data, detection time represents the time for diagnose all the test data.
Manuel, “Using Evolutionary Algorithms as Instance Selection for Data Reduction in KDD: An Experimental Study,” IEEE transactions on evolutionary computation, pp.561-575, 2006.

Experimental date and analysis The data may be determined by break samples.
According to test datas, relation picture of stretch rate and reduction of cross section area with temperature was drawn.
The reduction of cross section area may be to 96.4%.
The reduction of cross section area may be raised in 700˚C to 950˚C, reduction of cross section area is rised with deform temperature rise.
The reduction of cross section area is 47.7% in 1300˚C.

Comparative study of various data conversion methods for torsion tests applied to a HSLA steel J.
Conversion of torsion data The conversion of torsion data to true stress, true strain and strain rate was conducted by means of the methods described previously.
The open circles are the experimental data and the lines correspond to predictions of Eq. 11.
The open circles are the experimental data and the lines represent the fit obtained by Eq. 11.
A good correlation is obtained indicating the quality of the data reduction process.

The results show that our model can both enhance learning performance and classification accuracy. 1 Feature Reduction based on Manifold Learning Since the original dimensionality of the feature space gathered from the primary image data is usually very large, which will seriously affect the performance and results of classification, dimensionality reduction for the original feature space is thus not a negligible phase.
Linear dimensionality reduction will usually satisfy the tasks of linear distributed reduction, but in nonlinear cases it will lose certain efficiency and accuracy.
The methods of nonlinear dimensionality reduction are hence widely introduced for such nonlinear reduction situations.
Its basic idea is that the overall information served by overlapping the local neighbors maintains the original topology structure of the primary image data, using local linear approximation to the overall linear to the global and meanwhile keeping the local geometry structures unchanged.
[9] Belkin M and Niyogi P, “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation[J],” Neural Computation, 2003,15(6), pp. 1373–1396.