Big Data Learning Note 4 • Big data in Social computing (2)

This article continues to discuss the understanding of the rules of user movement: combining geographic modeling and matrix decomposition to make point-of-interest recommendations.

Location recommendations are a very popular application. In location recommendations, we need to understand the potential interest of the user and be familiar with the environment in which the user is located. We can then discover places where the user might be interested, based on the attributes of the user's interests and location. Geographical location recommendation is an important factor to improve the recommended performance compared with the general recommendation task.

In the previous article, we discussed how to recover user behavior data for the understanding of moving laws. We found that user mobility typically focuses on important sites such as homes, workplaces, and favorite restaurants. Moreover, the distances between the two locations are usually very short. So, we want to use this information to make a better location recommendation algorithm.

In order to provide a good location recommendation to the user, we use the user's location record as a kind of implicit feedback data.

1. We think of places where users have been to a particular location. The number of times a user goes to a location indicates the confidence level of preference. If you go to some places more often, then we are more convinced that you like these places. But that doesn't mean you like these places better than the other places you go. We lack information about places we haven't been to, so they may be positive or negative.
2. You can see this table or the numbers in this matrix. If these locations are close to the user's active area, then we assume they are more likely to be negative. This is because the user may be very familiar with the area, but deliberately do not go to those places. However, we do not know whether the user is unfamiliar with the area or deliberately not to go where the user is away from the active area and the user has not been there. So, the mixture of positive preferences and negative preferences.
3. In fact, the whole work is based on these important assumptions.

Matrix decomposition Model

Traditionally, in recommended tasks, researchers always use matrix decomposition models.

1. We have a matrix that contains the two dimensions of users and points of interest. The values in the matrix indicate whether the user has been to this place or point of interest. The values in the matrix may be 0 or 1.
2. A matrix can be decomposed into two latent factors. One is the user latent factor, the other is the location latent factor, two latent factors all have k this low dimension.
3. We want to distinguish between places we have not been, that is, these 0 values. Therefore, we increase the active area vector in the user latent factor, and increase the influence area vector in the location latent factor.
   The active area here, where both vectors have dimension l representing the number of regions. The active area vector refers to whether the user has been to these areas. The influence area vector refers to whether this position or point of interest is influential in these areas.
4. Therefore, we multiply the user latent factor, the position latent factor, the active region and the influence area, and finally get the original user interest point matrix.

Geomf

We used a structure of weighted matrix decomposition, called GEOMF:

Suppose Cu,i represents the number of times that user U accesses the point of interest I, and we use a monotonically increasing function that uses cu,i as the argument to calculate weights. The more times you go, the greater the weight. Here, the greater the weight means that we need to have a more accurate approximation of the value of this position. From this function, you can see that r is decomposed into p multiplied by Q and x multiplied by Y. We have added W, which is the weight matrix. We also have some regular items for P, Q, and X. Here, in order to simplify the calculation, we assume that Y is given in the optimization. We use a two-dimensional kernel density estimate to estimate y,y as the area of interest. We assume that the position of the point of interest is affected by the Gaussian distribution of each grid. This means that the grid that is closer to the location is more susceptible to the point of interest.

Here we use an iterative approach to optimize:

First, we fix X, which is the user's active area, and update p and Q. This shows us how to update p and Q and the time complexity of these steps.

Then I fixed p and Q and updated x. This slide illustrates the way we update x and the time complexity of these steps.

Here we can see how our approach distinguishes between sites that have not been visited. Suppose X does not change. Since Y is given, we can estimate (r-x*y). For a given user, (R-x*y) can be represented by this equation. For one location, we have an active area delineated for user U. Therefore, the value of Ru,i is likely to be negative. In fact, this value depends on how many times you go to this area. If the user often goes to this area, then this value is likely to be negative. This means that the places that have not been visited are around the places where they often go. Therefore, they are more likely to be negative in optimization. This indicates that the user is not interested in these places. However, this value may still be 0 for a distance away from the area that the user has been to, which means that we cannot distinguish between the user's dislike of the place or the place that has not been visited.

Performance comparison

We have data from five cities in Shanghai, Beijing, Guangzhou, Tianjin and Hangzhou. Shanghai has 400,000 users, and Beijing has 160,000 users. We have 25 million entries for Shanghai users. We divide the data into training sets and test sets. About 70% of the data belongs to the training set, and 30% of the data belongs to the test set. In the experiment, we conducted five independent tests. Use recall rate and accuracy as a measurement item. We compare weighted matrix decomposition with five other benchmark algorithms.

The baseline algorithm includes user-based collaborative filtering (UCF) and Bayesian matrix decomposition (B-NMF).
We also compare the decomposition of weighted matrices with the singular value decomposition of specifications and matrix decomposition based on access frequency matrices. The difference between the two methods is whether the user accesses are represented in the matrix using the number of accesses or 0 or 1 values. We also compare weighted matrix decomposition and biased weighted matrix decomposition. Here are two graphs that show the recall rate (left) and the accuracy rate (right), respectively.

The performance of these algorithms is similar, so we can only look at the graph representing the accuracy rate. We can find that the performance of weighted matrix decomposition and biased weighted matrix decomposition is the best, but their performance is very close. The performance of matrix decomposition based on the number of access matrices is worst. This means that the number of accesses cannot be used directly in the matrix. We'd better use the weighted matrix decomposition method, which means the number of uses as the confidence level, but still use 0 and 1 in the matrix. The performance of weighted matrix decomposition is better than UCF and B-NMF.
Finally, we use the weighted matrix decomposition as the framework.

We want to study the phenomenon of spatial clustering, there are many studies on this phenomenon in the literature.
In order to study these phenomena, the user latent factor and the item latent factor are neglected first. This means that p and q are removed, and only X and Y are retained, that is, the user activity area and the location-affected area. We compare the weighted version with the non-weighted version. We call the weighted and non-weighted versions geowls and Geols, respectively. We also compare different parameters and the baseline method for two-dimensional kernel density estimation. The following two graphs show that the recall rate is very similar to the accuracy rate. We can see that our method is better than the two-dimensional kernel density estimation method. In this case, the two-dimensional kernel density estimation method has the worst performance. In addition, the performance of the weighted version is better than the performance of the non-weighted version.

Finally, we compare the weighted MF, geowls, and GEOMF that combine the two methods.

As you can see, Geowls has the worst performance. This means that the user latent factor and the location latent factor, which is P and Q, are also needed. GEOMF with geo-constrained performance is better than WMF. This means that geographic modeling can improve the performance of matrix decomposition, which has been verified in experiments.

Summarize

• Geo-modeling using two-dimensional kernel density estimation.
• Use weighted matrix decomposition to make recommendations based on location-access data, where location access data is a good feedback.
• A GEOMF model is proposed, which combines geographic modeling and matrix decomposition, and we also propose a learning algorithm to optimize GEOMF and analyze its time complexity. The experiments show that the performance of GEOMF is better than other datum algorithms.

Big Data Learning Note 4 • Big data in Social computing (2)