Machine learning--Neighbor Component Analysis (NCA) algorithm and Metric learning

1. Nearest Neighbor Component analysis (NCA) algorithm

Above content reproduced from: http://blog.csdn.net/chlele0105/article/details/13006443

2. Metric Learning

In machine learning, the main purpose of dimensionality reduction of high dimensional data is to find a suitable low-dimensional space, in which the learning can be better than the original space performance. Each space corresponds to a distance metric defined on the sample properties, and finding the right space is essentially looking for a suitable distance metric. The basic motivation of metric learning (metric learning) is to learn a suitable distance metric.

The core of dimensionality is to find the right space, and the definition of suitable space is the distance measure, so learning the appropriate distance measurement is the goal of measuring learning. To learn about distance measurement, there is an easy-to-learn distance measurement expression.

where m is called the metric matrix, the metric learning is learning M. To maintain a non-negative and symmetrical distance, m must be a semi-positive symmetric matrix, i.e. an orthogonal base p is required to allow m to be written as m=ppt.

At this point, the object that has been built to learn is M, the metric matrix, and the next step is to set a goal for learning M. Assuming that you want to improve the performance of the nearest neighbor classifier, you can embed m directly into the evaluation index of the nearest neighbor classifier, and by optimizing the performance Index to obtain m accordingly, the nearest neighbor component analysis (neighbourhood Component Analysis,nca) is discussed.

The nearest neighbor classifier usually uses the majority voting method, each sample in the field casts 1 votes, the sample of the field throws 0 votes. It is replaced by a probabilistic voting method, and the probability of its effect on the XI classification results on the arbitrary sample XJ is:

Machine learning--Neighbor Component Analysis (NCA) algorithm and Metric learning