TY - JOUR
T1 - Properties of embedding methods for similarity searching in metric spaces
JF - Pattern Analysis and Machine Intelligence, IEEE Transactions on
Y1 - 2003
A1 - Hjaltason,G. R
A1 - Samet, Hanan
KW - complex
KW - contractiveness;
KW - data
KW - databases;
KW - decomposition;
KW - dimension
KW - distance
KW - distortion;
KW - DNA
KW - documents;
KW - EMBEDDING
KW - embeddings;
KW - Euclidean
KW - evaluations;
KW - FastMap;
KW - images;
KW - Lipschitz
KW - methods;
KW - metric
KW - MetricMap;
KW - multimedia
KW - processing;
KW - query
KW - reduction
KW - search;
KW - searching;
KW - sequences;
KW - similarity
KW - singular
KW - spaces;
KW - SparseMap;
KW - types;
KW - value
AB - Complex data types-such as images, documents, DNA sequences, etc.-are becoming increasingly important in modern database applications. A typical query in many of these applications seeks to find objects that are similar to some target object, where (dis)similarity is defined by some distance function. Often, the cost of evaluating the distance between two objects is very high. Thus, the number of distance evaluations should be kept at a minimum, while (ideally) maintaining the quality of the result. One way to approach this goal is to embed the data objects in a vector space so that the distances of the embedded objects approximates the actual distances. Thus, queries can be performed (for the most part) on the embedded objects. We are especially interested in examining the issue of whether or not the embedding methods will ensure that no relevant objects are left out. Particular attention is paid to the SparseMap, FastMap, and MetricMap embedding methods. SparseMap is a variant of Lipschitz embeddings, while FastMap and MetricMap are inspired by dimension reduction methods for Euclidean spaces. We show that, in general, none of these embedding methods guarantee that queries on the embedded objects have no false dismissals, while also demonstrating the limited cases in which the guarantee does hold. Moreover, we describe a variant of SparseMap that allows queries with no false dismissals. In addition, we show that with FastMap and MetricMap, the distances of the embedded objects can be much greater than the actual distances. This makes it impossible (or at least impractical) to modify FastMap and MetricMap to guarantee no false dismissals.
VL - 25
SN - 0162-8828
CP - 5
M3 - 10.1109/TPAMI.2003.1195989
ER -