Patent Document ID: 8572071
Application ID: 12797366

Base Claim:
1. A method for transforming data comprising: receiving, by a computing device, input data with categorical labels, the input data comprising vectors and each categorical label denoting a subset of the vectors; forming, by the computing device, higher-order links for each subset of the vectors; calculating, by the computing device, a higher-order transform for each attribute in each subset by calculating a higher-order prior for each attribute in each subset, wherein each higher-order prior represents a probability corresponding to the associated attribute that is based on one or more patterns of occurrence of the attribute, wherein calculating a higher-order prior comprises estimating the higher-order prior by: P ^ ⁡ ( x i = 1 | X ) =  φ ⁡ ( i , X )   Φ ⁡ ( X )  , and ⁢ ⁢ P ^ ⁡ ( x i = 0 | X ) = 1 - P ^ ⁡ ( x i = 1 | X ) where Φ(X) denotes a set of higher-order links of a specified order in a dataset X, φ(i,X) ⊂ Φ(X) denotes a subset of higher-order links that contain attribute i in dataset X, set φ(i,X) defines an event that a randomly chosen higher-order link contains attribute i, sets Φ(X) and φ(i,X) allow for characterization of each attribute i by a probability mass function {circumflex over (P)}(x i |X) defined over two events: presence of attribute i in a randomly chosen higher-order link, and an absence of that attribute from a randomly chosen higher-order link; and transmitting, by the computing device, transformed data to a learner to build a model.

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Claim 7:
7. The method of claim 1 , further comprising determining a second higher-order transform, wherein each attribute i partitions a n-dimensional boolean space X={0,1} n into two subspaces: X 1 (i)={x:x i =1, xεX} and X 0 (i)=XX 1 (i), wherein in each of the subspaces X 1 (i) and X 0 (i), attribute i is represented as a probabilistic first function of all attributes, this probabilistic first function being defined over a space of higher-order links, and a second function unifies representations across subspaces X 1 (i) and X 0 (i), and produces a final transformation.