1. An information retrieval apparatus by which a user retrieves information, comprising: a program information storage unit storing program information of a program including a plurality of retrieval keys; a usage history information storage unit storing usage history information indicating a history of operation content of the program that a user has made; and a computer processing unit connected to a memory comprising: an information acquisition unit acquiring the usage history information from the usage information storage unit, acquiring the program information of the program that the user operated from the program information storage unit, and acquiring a degree of importance information indicating a degree of importance of a user operation; a weight calculation unit calculating a weight of a retrieval key included in the program information of the program that the user operated by using the usage history information, the program information, and the degree of importance information acquired by the information acquisition unit; a user's preference tendency extraction unit extracting a sum of a weight of the plurality of retrieval keys calculated by the weight calculation unit as information indicating a tendency of a preference of the user; a statistic acquisition unit acquiring one of an average number of effective elements, a maximum number of effective elements, and a median value of the number of the effective elements as a first statistic, and acquiring an average value of weight of the effective elements as a second statistic, wherein effective elements are elements whose values are not zero; and a normalization unit comparing a number of elements of the vector of the program information with the first statistic, and when the number of the elements of the vector is smaller than the fist statistic and normalizing the vector of the program information by using a length of a normalizing vector which is expressed by the equation ∑ i n ⁢ ⁢ ( W i ) 2 + ∑ j N - n ⁢ ⁢ ( AW j ) 2 , wherein n is the number of effective elements, W i is the weight of element i, N is the first statistic and AW j is the second statistic.