A calculation apparatus includes a feature vector acquisition unit for acquiring a feature vector that corresponds to each alternative of a plurality of choice sets; an absolute evaluation calculation unit for calculating an absolute evaluation vector that represents an absolute evaluation of alternatives independent of a combination of the plurality of alternatives; a relativized-matrix calculation unit for calculating a relativized matrix that represents relative evaluations of the plurality of alternatives in a choice set; and a relative evaluation calculation unit for calculating a relative evaluation vector that represents a relative evaluation of each alternative of the plurality of alternatives from a product of multiplying the relativized matrix by the absolute evaluation vector. The calculation apparatus can predict intransitive choices of a person who exhibits intransitive preferences.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A calculation apparatus, comprising: a feature vector acquisition unit configured to acquire a feature vector corresponding to each of a plurality of alternatives in each of a plurality of choice sets; an absolute evaluation calculation unit configured to calculate an absolute evaluation vector that represents an absolute evaluation of alternatives independent of a combination of the plurality of alternatives, based on the feature vector corresponding to each alternative; a relativized-matrix calculation unit configured to calculate a relativized matrix that represents relative evaluations of the plurality of alternatives in the choice sets; and a relative evaluation calculation unit configured to calculate a relative evaluation vector that represents a relative evaluation of each alternative of the plurality of alternatives based on a product of multiplying the relativized matrix by the absolute evaluation vector. 2. The calculation apparatus according to claim 1, further comprising a similarity matrix calculation unit configured to calculate a similarity matrix that represents similarity of the feature vectors of the plurality of alternatives, wherein the relativized-matrix calculation unit calculates the relativized matrix based on the similarity matrix. 3. The calculation apparatus according to claim 2, wherein the relativized-matrix calculation unit calculates the relativized matrix to evaluate two alternatives with a higher similarity compared to two alternatives with a lower similarity. 4. The calculation apparatus according to claim 2, wherein the similarity matrix calculation unit calculates the similarity matrix of the plurality of alternatives from a product of multiplying a transpose of the feature vector of a first alternative by a constant matrix and the feature vector of a second alternative. 5. The calculation apparatus according to claim 2, wherein the relativized-matrix calculation unit calculates the relativized matrix from a product of the similarity matrix Si with a matrix inverse of the sum of the similarity matrix and a unit matrix. 6. The calculation apparatus according to claim 1, wherein the absolute evaluation calculation unit calculates the absolute evaluation vector from a product of multiplying the feature vector of each alternative by a weight vector that weights each feature value. 7. The calculation apparatus according to claim 6, wherein the absolute evaluation calculation unit calculates the absolute evaluation vector from a product of multiplying the feature vector of each alternative by the weight vector that weights each feature value and then adding a bias to each element. 8. The calculation apparatus according to claim 1, further comprising an estimation unit configured to estimate a choice probability that each alternative will be chosen from the relative evaluation of each alternative in the relative evaluation vector. 9. The calculation apparatus according to claim 1, wherein the relative evaluation calculation unit calculates a relative evaluation of a predetermined alternative in each of a plurality of choice sets, each including the predetermined alternative and differing in a combination of other alternatives, wherein the calculation apparatus further comprises a determination unit configures to choose the choice set based on the relative evaluation of the predetermined alternative and determine a combination of other alternatives to be presented together with the predetermined alternative. 10. An apparatus for learning parameters of a calculation apparatus, the learning apparatus comprising: a learning data acquisition unit configured to acquire learning data that includes a feature vector of each of a plurality of alternatives, and choice information that represents an alternative chosen by a user from the plurality of alternatives; and a learning processor configured to improve a relative evaluation of the alternative represented by the choice information by adjusting a conversion parameter that converts the feature vector into an absolute evaluation vector. 11. The learning apparatus according to claim 10, wherein: the learning data acquisition unit acquires the learning data for the plurality of alternatives from a plurality of choice sets; and the learning processor adjusts a conversion parameter used to convert the feature vector into the absolute evaluation vector to increase a total value obtained across the plurality of choice sets by adding values based on the relative evaluations of the alternatives represented by corresponding choice information. 12. The learning apparatus according to claim 10, wherein an absolute evaluation vector that represents an absolute evaluation of alternatives independent of a combination of the plurality of alternatives is calculated from a product of multiplying the feature vector by a weight vector that weights each feature value; and the learning processor adjusts the weight vector as the conversion parameter. 13. The learning apparatus according to claim 12, wherein: the absolute evaluation vector is calculated from a product of multiplying the feature vector of each alternative by the weight vector and then adding a bias to each element; and the learning processor adjusts the weight vector and the bias as the conversion parameters. 14. The learning apparatus according to claim 12, wherein the learning processor further adjusts a relativization parameter which defines a relativized matrix that represents relative evaluations of the plurality of alternatives. 15. The learning apparatus according to claim 14, wherein: the relativized matrix is calculated from a similarity matrix that represents similarity of the plurality of alternatives; the similarity matrix is calculated from the plurality of alternatives, as the relativization parameter, from a product of multiplying a transpose of the feature vector of a first alternative by a constant matrix and the feature vector of a second alternative; and the learning processor adjusts the constant matrix. 16. The learning apparatus according to claim 14, wherein the learning processor learns the relativization parameter with the conversion parameter fixed, and learns the conversion parameter with the relativization parameter fixed. 17. A computer-implemented method for calculating relative evaluations of alternatives, the method executed by the computer comprising the steps of: acquiring a feature vector that corresponds to each of a plurality of alternatives included in each of a plurality of choice sets; calculating an absolute evaluation vector that represents an absolute evaluation of alternatives independent of a combination of the plurality of alternatives based on the feature vector corresponding to each alternative; calculating a relativized matrix that represents conversion of relative evaluations of the plurality of alternatives in the choice sets; and calculating a relative evaluation vector that represents a relative evaluation of each alternative of the plurality of alternatives from a product of multiplying the relativized matrix by the absolute evaluation vector. 18. A computer-implemented method for learning parameters for a calculation method, the method executed by the computer comprising the steps of: acquiring learning data for each set of a plurality of alternatives, the learning data including a feature vector of each of the plurality of alternatives, and choice information that represents an alternative chosen by a user from the plurality of alternatives; and improving the relative evaluation of the alternative indicated by the choice information in the relative evaluation vector by adjusting a conversion parameter that converts the feature vector into the absolute evaluation vector. 19. A program storage device readable by a computer, tangibly embodying a program of instructions executed by the computer to implement a system for the calculation apparatus according to claim 1. 20. A program storage device readable by a computer, tangibly embodying a program of instructions executed by the computer to implement a system for the learning apparatus according to claim 10.