Collective design and innovation are crucial in organizations. To investigate how the collective design and innovation processes would be affected by the diversity of knowledge and background of collective individual members, we conducted three collaborative design task experiments which involved nearly 300 participants who worked together anonymously in a social network structure using a custom-made computer-mediated collaboration platform. We compared the idea generation activity among three different background distribution conditions (clustered, random, and dispersed) with the help of the "doc2vec" text representation machine learning algorithm. We also developed a new method called "Idea Geography" to visualize the idea utility terrain on a 2D problem domain. The results showed that groups with random background allocation tended to produce the best design idea with highest utility values. It was also suggested that the diversity of participants' backgrounds distribution on the network might interact with each other to affect the diversity of ideas generated. The proposed idea geography successfully visualized that the collective design processes did find the high utility area through exploration and exploitation in collaborative work.