In this paper, we study the impact of dialogue representations and classification methods in the task of theme identification of telephone conversation services having highly imperfect automatic transcriptions. Two dialogue representations are firstly compared: the classical Term Frequency-Inverse Document Frequency with Gini purity criteria (TF-IDF-Gini) method and the Latent Dirichlet Allocation (LDA) approach. We then propose to study an original classification method that takes advantage of the LDA topic space representation , highlighted as the best dialogue representation. To do so, two assumptions about topic representation led us to choose a Gaussian process (GP) based method. This approach is compared with a Support Vector Machine (SVM) classification method. Results show that the GP approach is a better solution to deal with the multiple theme complexity of a dialogue, no matter the conditions studied (manual or automatic transcriptions). We finally discuss the impact of the topic space reduction on the classification accuracy.