Data field for mining big data

Figures & data

Table 1. Terms and interpretations.

Terms	Interpretation
Data space	Ω ⊆ R^P that is P-dimensional.
Data-set	D = {X1, X2, …, Xn} that is an independent random sample in Ω.
Data object	Xi = [Xi1 Xi2 … XiP]^T with i = 1, 2, …, n in D.
Arbitrary data object (point)	x = [x1 x2 … xP]^T in Ω.
Object distance	||x − Xi|| to measure the distance between the given Xi and an arbitrary x.
Physical field	∀x ∈ Ω, if a certain physical parameter or mathematical function correspondingly has a determined value, there exists a field of the parameter or function in Ω.
Physical potential	The work to move a unit particle from a point to a referenced point in the given field. It is also the energy difference between the point and its referenced point in the given field.
Physical potential function	is the potential function of the field generated by Xi. It is treated as a single-valued function of spatial position, regardless of whether there is a unit particle in the field or not.
Data field	Given a task, data object Xi diffuses its data contribution from its position to Ω under physical fields. The diffusing data contribution makes a virtual field encircling Xi, which is called data field. All data fields are superposed in Ω.
Potential of data field	Given a task, the contribution to move a unit object from a position to a referenced position in the given field. It is also the contribution difference between the object position and its referenced position in the given field.
Potential function of data field	Under physical field, the function may mathematically describe the potential of data field if it satisfies three conditions: (a) a continuous, smooth and finite function; (b) isotropic; (c) is a decreasing single-valued function of the distance. When the distance from the field source increases, the function value decreases. Simplified as .

Figure 1. Different kernel estimation results: (a) rule-of-thumb method, (b) Sheather-Jones’ plug-in method, (c) maximal smoothing principle, (d) likelihood cross validation method.

Figure 2. Underlying function and its kernel estimation: (a) underlying function, (b) rule-of-thumb method, (c) Sheather-Jones’ plug-in method, (d) maximal smoothing principle, (e) likelihood cross validation method.

Figure 3. Estimation results of different potential function with rule-of-thumb method: (a) potential function 1, (b) potential function 2.

Figure 4. Algorithm flow of feature selection using data field.

Figure 5. Algorithm flow of HGCUDF.

Figure 6. Data field of KA’s happy face: (a) a facial image, (b) 2-dimensional visualization of a facial data field, (c) 3-dimensional visualization of a facial data field.

Figure 7. Technical flow of face recognition with data field.