Applied Computational Intelligence and Soft Computing 3
Table 2: User-item rating matrix.
User/item Item 1 Item 2 Item 3 Item 4
User 1 1 3 4 3
User 2 3 2 3 3
User 3 3 5 2 3
One
Two 1 Two n
Three 1 Three p Three 1 Three q
Item 1 Item r
· · ·
· · ·· · ·
· · ·
Figure 1: Commodity hierarchy in E-commerce.
E-commerce websites, each commodity owns its category,
which has a parent category. Namely, commodities in E-
commerce own the concept of level and different commodi-
ties own different hierarchies, shown as in Figure 1. The
level of one commodity is considered in the construction
of rating matrix. For commodities at different levels, this
paper supposes its subordinate commodities to fill different
prediction rating through calculation. This paper combines
traditional classification methods with user rating data and
through calculation a preliminary rating is made on the
nonrated data of recommendation users. This method is used
to construct a new user-item rating matrix.
For rated data, ratings are extracted to the belonging
category. In the construction of rating matrix by collaborative
filtering technology, for one category, its Rated Frequency
(RF) is calculated and the calculation method is shown as
follows:
RF = the number of rated items
the total number to be rated items . (1)
Item Rated Frequency (IRF) represents the weight of
rated items and the calculation method is shown as follows:
IRF = log ( SUMallrate
SUMdefaultrate
) , (2)
where SUMallrate represents the total amount of rated data and
automatically filled prediction rating. SUMdefaultrate represents
the total number of automatically filled prediction ratings.
This paper proposes a user-item rating matrix construc-
tion algorithm, which automatically fills ratings of nonrated
data in RF ∗ IRF greater than the threshold. The design flow
of hierarchical filling method is shown as follows:
Input: initial user-item rating matrix 𝑃.
Output: user rating matrix 𝑄 after the prediction
rating is filled.
Step 1. Calculate RF ∗ IRF of each category in matrix 𝑃.
Step 2. Fill in the average item rating of RF ∗ IRF greater than
threshold of the rating matrix.
Step 3. For new items in rating matrix, 3 is automatically filled
and finally constructs the user-item rating matrix 𝑄.
Through calculating RF∗IRF of specific category of items,
this paper fills scores of the top-𝑁 category items of RF ∗ IRF
instead of simply filling dataset 0, which can reduce the data
sparsity. Finally, the algorithm automatically fills new items
with 3, aiming at solving cold start of new items.
3.2. Improvement of Recommendation Timeliness. CF algo-
rithm does not take the influences of time on rating data
into consideration and it treats item ratings of different users
visited at different moments equally. Interests and preferences
of different users dynamically change with time, so the
time when different users have interests in the same item
differs. However, if the rating is the same, they are likely to
be regarded as similar neighbor users, further influencing
the recommendation quality. This paper introduces time
function, shown as follows:
𝑓 (𝑡𝑎,𝑖) = 𝑒−𝑡𝑎,𝑖 , (3)
where 𝑡𝑎,𝑖 represents the time that user a has interests in
item 𝑖. Time function 𝑓(𝑡) is a monotone decreasing function
and decreases with the increase of time 𝑡 and time weight
maintains (0, 1). Namely, the newer the data is, the greater the
weight is and the time function is. In this way, the influence
of time on recommendation quality is solved.
3.3. Time Weighted Based Prediction Function. CF algorithm
predicts the rating of item 𝑖 by current user 𝑢 according to the
rating similarity of users or items, shown as follows:
𝑅𝑢,𝑖 = 𝑅𝑢 + ∑𝑁
𝑎=1 (𝑅𝑎,𝑖 − 𝑅𝑎) ⋅ sim (𝑢, 𝑎)
∑𝑁
𝑎=1 |sim (𝑢, 𝑎)| , (4)
where sim(𝑢, 𝑎) represents the rating similarity between users
𝑢 and 𝑎 and (5) calculates the similarity between users 𝑢 and
𝑎 by Pearson’s correlation coefficient:
sim (𝑢, 𝑎)
= ∑𝑖∈𝐼𝑢,𝑎 (𝑅𝑢,𝑖 − 𝑅𝑢) (𝑅𝑎,𝑖 − 𝑅𝑎)
√∑𝑖∈𝐼𝑢,𝑎 (𝑅𝑢,𝑖 − 𝑅𝑢)2√∑𝑖∈𝐼𝑢,𝑎 (𝑅𝑎,𝑖 − 𝑅𝑎)2
, (5)
where 𝐼𝑢,𝑎 represents the item set rated by users 𝑢 and 𝑎. 𝑅𝑢,𝑖
and 𝑅𝑎,𝑖, respectively, represent the score of item 𝑖 by users 𝑢
and 𝑎, and 𝑅𝑢 and 𝑅𝑎, respectively, represent the mean score
of all items by users 𝑢 and 𝑎.
Time function 𝑓(𝑡) is added in (4) and the weighted
prediction rating of item 𝑖 by target user 𝑢 is improved:
𝑃𝑢,𝑖 = 𝑅𝑢 + ∑𝑛
𝑎=1 (𝑅𝑎,𝑖 − 𝑅𝑎) ⋅ sim (𝑢, 𝑎) ⋅ 𝑓 (𝑡𝑎,𝑖)
∑𝑛
𝑎=1 |sim (𝑢, 𝑎)| ⋅ 𝑓 (𝑡𝑎,𝑖) . (6)

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