Chad Hogg
Review of "Propagation of Trust and Distrust" by Kumar, Raghavan, Guha, and Tomkins

	This paper describes systems for modeling the propagation of trust and distrust through a network of users.  Four atomic propagation operations are defined in terms of both matrix arithmetic and semantic meaning.  Results of several techniques on a data set collected from Epinions are presented and summarized.

	This paper is generally well-written.  I particularly liked the way the atomic operations were both defined in simple mathematics and described with respect to their semantic meaning.  The explanations of propagation methods and potential semantic issues were done well also.  There are a few points about which I am unclear.  Among these are the ordering implied by Majority Rounding and why a user may have both a trust and distrust rating for the same user.  Also, the authors speak in their introduction that "trust relationships that have been built and maintained over time" are more useful than simple opinions.  It was not clear to me how the algorithms involved consider the length of time over which trust scores are generated.  The caption on table 4 appears to be incorrect, as gamma values are only used to describe the Weighted Linear Combinations method of propagation, not the Eigenvalue Propagation method.

	The experimental results do indeed validate the authors' hypothesis that distrust is highly important for correctly predicting the trust and distrust levels between users that are not explicitly known.  It is interesting that propagating distrust is generally more useful through a single iteration than many.  I suspect this is related to the semantic issue of multiplicative versus additive propagation as described in section 3.3, but the authors should make this more explicit.

	One important issue that has not been discussed in this paper is the representation of a user's trust for himself.  The most intuitive approach would be to assume each user trusts themselves completely.  However, this causes computational problems.  Consider a web of trust containing 3 users a, b, and c where each user trust themselves and additionally a trusts c and c trusts b.  Applying the direct propagation operator is shown in Figure 1.  Note that the matrix now contains 3 possible values - 0, 1, and 2.  This is not immediately problematic, but consider how the entries with a 2 were derived.  The rule a trusts c is a ground truth, but we have also chosen to extend the rules a trusts c and c trusts c to form a new rule a trusts c, which already exists.  Thus, this obvious trust is having a substantial impact on the system, and now we predict that a trusts c more than he trusts himself!  A second possibility is to assume users have no opinions about themselves.  The second figure shows applying the direct propagation operator for this altered matrix.  In this case, the result contains only those relationships that were directly inferred, without those that are known as ground truth.  The proper way to acquire a matrix that contains both types of values appears to be C = ( B x (1 - I) ) x ( B x (1 - I) ) + B.  I am not sure if the authors have failed to discuss this because they did not realize it or because they thought it was obvious, but in either case I disagree with them.

	I would recommend this paper for publication, although it could benefit from a few minor corrections and a moderate addition.

Figure 1
-------------------------------------
|                                   |
| | 1 0 1 |   | 1 0 1 |   | 1 1 2 | |
| | 0 1 0 | x | 0 1 0 | = | 0 1 0 | |
| | 0 1 1 |   | 0 1 1 |   | 0 2 1 | |
|                                   |
|  a -> a      a -> a      a -> a   |
|  a -> c      a -> c      a -> b   |
|  b -> b      b -> b      a -> c   |
|  c -> b      c -> b      a -> c   |
|  c -> c      c -> c      b -> b   |
|                          c -> b   |
|                          c -> b   |
|                          c -> c   |
|                                   |
-------------------------------------

Figure 2
-------------------------------------
|                                   |
| | 0 0 1 |   | 0 0 1 |   | 0 1 0 | |
| | 0 0 0 | x | 0 0 0 | = | 0 0 0 | |
| | 0 1 0 |   | 0 1 0 |   | 0 0 0 | |
|                                   |
|  a -> c      a -> c      a -> b   |
|  c -> b      c -> b               |
|                                   |
-------------------------------------